Activity and efficiency of the building sector in Morocco: A review of status and measures in Ifrane

Hamza El Hafdaoui; Ahmed Khallaayoun; Kamar Ouazzani; Hamza El Hafdaoui; Ahmed Khallaayoun; Kamar Ouazzani

doi:10.3934/energy.2023024

AIMS Energy

2023, Volume 11, Issue 3: 454-485. doi: 10.3934/energy.2023024

Previous Article Next Article

Review Special Issues

Activity and efficiency of the building sector in Morocco: A review of status and measures in Ifrane

1.
School of Science & Engineering, Al Akhawayn University in Ifrane, Morocco
2.
National School of Applied Sciences, Sidi Mohamed Ben Abdellah University, Morocco
3.
Higher School of Technology, Sidi Mohamed Ben Abdellah University, Morocco

Received: 12 January 2023 Revised: 22 April 2023 Accepted: 25 April 2023 Published: 11 May 2023

One-third of all greenhouse gas emissions come from the world's building stock while accounting for 40% of global energy use. There is no way to combat global warming or attain energy independence without addressing the inefficiency of the building sector. This sector is the second consumer of electricity after the industrial sector in Morocco and is ranked third emitter after the energy sector and transportation sector. Using Ifrane as a case study, this paper examines and reviews the city's energy use and the initiatives taken to improve building efficiency. The findings showed that, during the analyzed period, i.e., from 2014 to 2022, Ifrane's annual electricity consumption climbed steadily from 35 to 43 GWh. The government of Morocco has implemented effective laws, guidelines and regulations, as well as publicized ways to reduce energy consumption and increase energy efficiency. However, gathered data and survey results revealed opportunities and challenges for enhancing Ifrane's efficient energy use.

The study also evaluates government programs, codes/standards and related actions for the improvement of household energy efficiency. As part of the review, the available literature was analyzed to assess the effectiveness of energy behavior and awareness, the impact of an economical and sustainable building envelope, the impact of building retrofitting programs, the importance of energy-performing devices and appliances, the adoption of smart home energy management systems, the integration of renewable energies for on-site clean energy generation and the role of policies and governance in the building sector in Ifrane. A benchmark evaluation and potential ideas are offered to guide energy policies and improve energy efficiency in Ifrane and other cities within the same climate zone.

Keywords:

Citation: Hamza El Hafdaoui, Ahmed Khallaayoun, Kamar Ouazzani. Activity and efficiency of the building sector in Morocco: A review of status and measures in Ifrane[J]. AIMS Energy, 2023, 11(3): 454-485. doi: 10.3934/energy.2023024

Related Papers:

[1]	Ali Moussaoui, El Hadi Zerga . Transmission dynamics of COVID-19 in Algeria: The impact of physical distancing and face masks. AIMS Public Health, 2020, 7(4): 816-827. doi: 10.3934/publichealth.2020063
[2]	Saina Abolmaali, Samira Shirzaei . A comparative study of SIR Model, Linear Regression, Logistic Function and ARIMA Model for forecasting COVID-19 cases. AIMS Public Health, 2021, 8(4): 598-613. doi: 10.3934/publichealth.2021048
[3]	Musyoka Kinyili, Justin B Munyakazi, Abdulaziz YA Mukhtar . Mathematical modeling and impact analysis of the use of COVID Alert SA app. AIMS Public Health, 2022, 9(1): 106-128. doi: 10.3934/publichealth.2022009
[4]	Pooja Yadav, Shah Jahan, Kottakkaran Sooppy Nisar . Analysis of fractal-fractional Alzheimer's disease mathematical model in sense of Caputo derivative. AIMS Public Health, 2024, 11(2): 399-419. doi: 10.3934/publichealth.2024020
[5]	Ahmed A Mohsen, Hassan Fadhil AL-Husseiny, Xueyong Zhou, Khalid Hattaf . Global stability of COVID-19 model involving the quarantine strategy and media coverage effects. AIMS Public Health, 2020, 7(3): 587-605. doi: 10.3934/publichealth.2020047
[6]	Mehreen Tariq, Margaret Haworth-Brockman, Seyed M Moghadas . Ten years of Pan-InfORM: modelling research for public health in Canada. AIMS Public Health, 2021, 8(2): 265-274. doi: 10.3934/publichealth.2021020
[7]	Kottakkaran Sooppy Nisar, Muhammad Wajahat Anjum, Muhammad Asif Zahoor Raja, Muhammad Shoaib . Recurrent neural network for the dynamics of Zika virus spreading. AIMS Public Health, 2024, 11(2): 432-458. doi: 10.3934/publichealth.2024022
[8]	Shahid Ahmed, Shah Jahan, Kamal Shah, Thabet Abdeljawad . On mathematical modelling of measles disease via collocation approach. AIMS Public Health, 2024, 11(2): 628-653. doi: 10.3934/publichealth.2024032
[9]	Rafat Zreiq, Souad Kamel, Sahbi Boubaker, Asma A Al-Shammary, Fahad D Algahtani, Fares Alshammari . Generalized Richards model for predicting COVID-19 dynamics in Saudi Arabia based on particle swarm optimization Algorithm. AIMS Public Health, 2020, 7(4): 828-843. doi: 10.3934/publichealth.2020064
[10]	Mario Coccia . Sources, diffusion and prediction in COVID-19 pandemic: lessons learned to face next health emergency. AIMS Public Health, 2023, 10(1): 145-168. doi: 10.3934/publichealth.2023012

Abstract

1. Introduction

A mathematical model is a helpful tool to recognize the conduct of an infection when it starts to affect the community and it is useful to analyze under what conditions it can be screened out or to be continued [1]. A virus is known as infectious when any disease is transferred from one person to another via different ways of transmission like droplets generated when an infected person coughs, sneezes, or exhales, or direct contact with another human, water, or any physical product. To analyze this type of transmission we need some authentic mathematical tools in which few of them are difference equations, initial conditions, working parameters, and statistical estimation. In this new era, new mathematical techniques give us more updated and reliable tools to understand many diseases or infections in epidemiology and even give us updated strategies to control disease or infection in different and suitable conditions [2].

From all of the viruses, the COVID-19 is gradually becoming a watershed pandemic in the antiquity of the planet. COVID-19 is an abbreviation of Coronavirus disease which started in 2019. In December of 2019, the first case of COVID-19 was observed in Wuhan, the city of China [3]. The common symptoms of COVID-19 are loss of smell and taste, fever, dry cough, shortening of breath, fatigue, muscle, and joint pain, phlegm production, sore throat, headache, and chills, these symptoms vary from person to person. The most common incubation period ranges from 1 to 12 days. COVID-19 spreads by physical interaction between individuals. Use of masks, sanitizer, and having a distance of 2 m between individuals results in minimizing the spread of the virus up to much extent [4]. These vaccines played a bold role in minimizing the spread of COVID-19. The main focused area of this spread is the working area, schools, offices, markets, and other open circles [5],[6].

Fractional derivative was originated in 1695. If we describe the list of fractional derivatives then it is divided into two types. Caputo, Riemann-Liouville, and Katugampola [7] are fractional derivatives with the singular kernel. Caputo-Fabrizio(exponential) [8] and ABC(Mittag-Leffler) [9] are fractional derivatives without singular kernels. Fractional calculus has very vast application properties in our daily life. It is being used in chemical, biological, physical, finance, pharmaceutical, engineering [10],[11], and many other fields [12]–[14]. FFD is mostly used because it gives a realistic way of representation of our model and hence we have used this same for representing our COVID-19 epidemics [15]–[18]. A time-fractional compartmental model for the COVID-19 pandemic [21] and classical SIR model for COVID-19 in United States is study in [22]. The COVID-19 pandemic (caused by SARS-CoV-2) has introduced significant challenges for accurate prediction of population morbidity and mortality by traditional variable-based methods of estimation. Challenges to modeling include inadequate viral physiology comprehension and fluctuating definitions of positivity between national-to-international data. This paper proposes that accurate forecasting of COVID-19 caseload may be best preformed non-perimetrically, by vector autoregressive (VAR) of verifiable data regionally [23]. Fundamental properties of the new generalized fractional derivatives in the sense of Caputo and RiemannLiouville are rigorously studied and its related work [24]–[26]. COVID-19 Decision-Making System (CDMS) was developed to study disease transmission in [27]. The change in atmospheric pollution from a public lockdown in Greece introduced to curb the spread of the COVID-19 is examined based on ground-based and satellite observations and some related issues in [28]–[30].

2. Basic concepts

The fractional-order derivative of AB in Reimann Liouville-Caputo sense (ABC) [19] is given by

$_{γ}^{A B C} D_{t}^{γ} {f (t)} = \frac{A B (γ)}{m - γ} \int_{γ}^{t} \frac{d^{m}}{d w^{m}} f (w) E_{γ} [- γ \frac{{(t - w)}^{γ}}{m - γ}] d w, m - 1 < γ < m$ (1)

where E_γ is the Mittag-Leffler function and AB(γ) is a normalization function and AB(0) = AB(1) = 1. The Laplace transform of above is given by

$[_{γ}^{A B C} D_{t}^{γ} f (t)] (s) = \frac{A B (γ)}{1 - γ} \frac{s^{γ} L [f (t)] (s) - s^{γ - 1} f (0)}{s^{γ} + \frac{γ}{1 - γ}}$ (2)

with the aid of sumudu transformation, we get

$S T [_{γ}^{A B C} D_{t}^{γ} f (t)] (s) = \frac{B (γ)}{1 - γ} (γ Γ (γ + 1) E_{γ} (- \frac{1}{1 - γ} ν^{γ})) \times [S T (f (t)) - f (0)]$ (3)

The ABC fractional integral of order γ of a function f(t) is given by

$_{γ}^{A B C} I_{t}^{γ} {f (t)} = \frac{1 - (γ)}{B - γ} f (t) + \frac{(γ)}{B (γ) Γ (γ)} \int_{γ}^{t} f (s) (t - s)^{γ - 1} d s$ (4)

3. Materials and methods

In this section, consider the improved SEIR model given in [20] having compartments SEIQRPD, where S represents the number of uninfected individuals, E represents infected individuals at the time t but still in incubation period (without clinical symptoms and low infectivity), I represents the number of infected individuals at the time t (with obvious clinical symptoms), Q represents the number of individuals who have been diagnosed and isolated at the time t, R represents the number of recovered individuals at the time t, P represents the number of susceptible individuals who are not exposed to the external environment at the time t and D represents the number of death cases at time t.

$\begin{matrix} _{0}^{A B C} D_{t}^{γ} S (t) = - β_{1} (t) a_{1} (S (t)) b_{1} (I (t)) - β_{2} a_{2} (S (t)) b_{2} (E (t)) - ρ S (t), \\ _{0}^{A B C} D_{t}^{γ} E (t) = β_{1} (t) a_{1} (S (t)) b_{1} (I (t)) + β_{2} a_{2} (S (t)) b_{2} (E (t)) - ϵ E (t), \\ _{0}^{A B C} D_{t}^{γ} I (t) = ϵ E (t) - δ I (t), \\ _{0}^{A B C} D_{t}^{γ} Q (t) = δ I (t) - (λ (t) + κ (t)) Q (t), \\ _{0}^{A B C} D_{t}^{γ} R (t) = λ (t) Q (t), \\ _{0}^{A B C} D_{t}^{γ} P (t) = ρ S (t) \\ _{0}^{A B C} D_{t}^{γ} D (t) = κ (t) Q (t) \end{matrix}$ (5)

here $β_{1} (t) = σ_{1} e x p (- σ_{2} t), λ (t) = λ_{1} (1 - e x p (λ_{2} t))$ and $κ (t) = κ_{1} e x p (- κ_{2} t)$ $σ_{1}, σ_{2}, λ_{1}, λ_{2}, κ_{1}$ and κ₂ are the parameters which are all positive, here simulation is used by the σ affect of government control. It should be emphasized that the protection rate ρ for susceptible individuals also reflects the intensity of government control [18]. $_{0}^{A B C} D_{t}^{γ}$ , is the ABC sense fractional derivative with $0 < γ \leq 1$ . The initial conditions of the system Eq 5 are:

$\begin{matrix} S_{0} (t) = S (0), E_{0} (t) = E (0), I_{0} (t) = I (0), Q_{0} (t) = Q (0) \\ R_{0} (t) = R (0), P_{0} (t) = P (0), D_{0} (t) = D (0) \end{matrix}$ (6)

applying ST operator on both sides, we get

$\begin{matrix} O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ}) [S T (S (t)) - S (0)] \\ = S T [- β_{1} (t) a_{1} (S (t)) b_{1} (I (t)) - β_{2} a_{2} (S (t)) b_{2} (E (t)) - ρ S (t)], \\ O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ}) [S T (E (t)) - E (0)] \\ = S T [β_{1} (t) a_{1} (S (t)) b_{1} (I (t)) + β_{2} a_{2} (S (t)) b_{2} (E (t)) - ϵ E (t)], \\ O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ}) [S T (I (t)) - I (0)] \\ = S T [ϵ E (t) - δ I (t)], \\ O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ}) [S T (Q (t)) - Q (0)] \\ = S T [δ I (t) - (λ (t) + κ (t)) Q (t)], \\ O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ}) [S T (R (t)) - R (0)] \\ = S T [λ (t) Q (t)], \\ O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ}) [S T (P (t)) - P (0)] \\ = S T [ρ S (t)], \\ O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ}) [S T (D (t)) - D (0)] \\ = S T [κ (t) Q (t)] \end{matrix}$ (7)

where $O_{γ} = \frac{B (γ) γ Γ (γ + 1)}{1 - γ}$ system Eq 7 becomes

$\begin{matrix} S T [S (t)] = S (0) + \frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [- β_{1} (t) a_{1} (S (t)) b_{1} (I (t)) - β_{2} a_{2} (S (t)) b_{2} (E (t)) - ρ S (t)], \\ S T [E (t)] = E (0) + \frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [β_{1} (t) a_{1} (S (t)) b_{1} (I (t)) + β_{2} a_{2} (S (t)) b_{2} (E (t)) - ϵ E (t)], \\ S T [I (t)] = I (0) + \frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [ϵ E (t) - δ I (t)], \\ S T [Q (t)] = Q (0) + \frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [δ I (t) - (λ (t) + κ (t)) Q (t)], \\ S T [R (t)] = R (0) + \frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [λ (t) Q (t)], \\ S T [P (t)] = P (0) + \frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [ρ S (t)], \\ S T [D (t)] = D (0) + \frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [κ (t) Q (t)] \end{matrix}$ (8)

taking inverse Sumudu Transform on both sides, we get

$\begin{matrix} S (t) = S (0) + S T^{- 1} {\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [- β_{1} (t) a_{1} (S (t)) b_{1} (I (t)) - β_{2} a_{2} (S (t)) b_{2} (E (t)) - ρ S (t)]}, \\ E (t) = E (0) + S T^{- 1} {\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [β_{1} (t) a_{1} (S (t)) b_{1} (I (t)) + β_{2} a_{2} (S (t)) b_{2} (E (t)) - ϵ E (t)]}, \\ I (t) = I (0) + S T^{- 1} {\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [ϵ E (t) - δ I (t)]}, \\ Q (t) = Q (0) + S T^{- 1} {\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [δ I (t) - (λ (t) + κ (t)) Q (t)]}, \\ R (t) = R (0) + S T^{- 1} {\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [λ (t) Q (t)]}, \\ P (t) = P (0) + S T^{- 1} {\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [ρ S (t)]}, \\ D (t) = D (0) + S T^{- 1} {\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [κ (t) Q (t)]} \end{matrix}$ (9)

Therefore, the following is obtained

$\begin{matrix} S_{(m + 1)} (t) = S_{m} (0) + S T^{- 1} {\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [- β_{1} a_{1} (S_{m} (t)) b_{1} (I_{m} (t)) - β_{2} a_{2} (S_{m} (t)) b_{2} (E_{m} (t)) - ρ S_{m} (t)]}, \\ E_{(m + 1)} (t) = E_{m} (0) + S T^{- 1} {\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [β_{1} a_{1} (S_{m} (t)) b_{1} (I_{m} (t)) + β_{2} a_{2} (S_{m} (t)) b_{2} (E_{m} (t)) - ϵ E_{m} (t)]}, \\ I_{(m + 1)} (t) = I_{m} (0) + S T^{- 1} {\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [ϵ E_{m} (t) - δ I_{m} (t)]}, \\ Q_{(m + 1)} (t) = Q_{m} (0) + S T^{- 1} {\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [δ I_{m} (t) - (λ + κ) Q_{m} (t)]}, \\ R_{(m + 1)} (t) = R_{m} (0) + S T^{- 1} {\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [λ Q_{m} (t)]}, \\ P_{(m + 1)} (t) = P_{m} (0) + S T^{- 1} {\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [ρ S_{m} (t)]}, \\ D_{(m + 1)} (t) = D_{m} (0) + S T^{- 1} {\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [κ Q_{m} (t)]} \end{matrix}$ (10)

Let's consider Eq 10, and then we get

$\begin{array}{l} S (t) = \underset{m \to \infty}{l i m} S_{m} (t); E (t) = \underset{m \to \infty}{l i m} E_{m} (t); I (t) = \underset{m \to \infty}{l i m} I_{m} (t); \\ Q (t) = \underset{m \to \infty}{l i m} Q_{m} (t); R (t) = \underset{m \to \infty}{l i m} R_{m} (t); P (t) = \underset{m \to \infty}{l i m} P_{m} (t)); D (t) = \underset{m \to \infty}{l i m} D_{m} (t) \end{array}$ (11)

Theorem 3.1: Let $(X, | . |)$ be a Banach space and H a self-map of X satisfying

$∥ H_{r} - H_{x} ∥ \leq θ ∥ X - H_{r} ∥ + θ ∥ r - x ∥$ (12)

for all $r, x \in X$ , where $0 \leq θ < 1$ . Assume that H is Pichard H-stable

Let us consider Eq 10, and we obtain

$\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})}$ (13)

the above equation is associated with the fractional Lagrange multiplier.

Proof

Define K be a self-map is given by

$\begin{matrix} K [S_{(m + 1)} (t)] = S_{(m + 1)} (t) = S_{m} (0) + S T^{- 1} [\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [- β_{1} a_{1} (S_{m} (t)) b_{1} (I_{m} (t)) - β_{2} a_{2} (S_{m} (t)) b_{2} (E_{m} (t)) - ρ S_{m} (t)] \\ K [E_{(m + 1)} (t)] = E_{(m + 1)} (t) = E_{m} (0) + S T^{- 1} [\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [β_{1} a_{1} (S_{m} (t)) b_{1} (I_{m} (t)) + β_{2} a_{2} (S_{m} (t)) b_{2} (E_{m} (t)) - ϵ E_{m} (t)] \\ K [I_{(m + 1)} (t)] = I_{(m + 1)} (t) = I_{m} (0) + S T^{- 1} [\frac{1 -}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [ϵ E_{m} (t) - δ I_{m} (t)] \\ K [Q_{(m + 1)} (t)] = Q_{(m + 1)} (t) = Q_{m} (0) + S T^{- 1} [\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [δ I_{m} (t) - (λ + κ) Q_{m} (t)] \\ K [R_{(m + 1)} (t)] = R_{(m + 1)} (t) = R_{m} (0) + S T^{- 1} [\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [λ Q_{m} (t)] \\ K [P_{(m + 1)} (t)] = P_{(m + 1)} (t) = P_{m} (0) + S T^{- 1} [\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [ρ S_{m} (t)] \\ K [D_{(m + 1)} (t)] = D_{(m + 1)} (t) = D_{m} (0) + S T^{- 1} [\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [κ Q_{m} (t)] \end{matrix}$ (14)

Applying the properties of the norm and triangular inequality, we get

$\begin{matrix} ∥ K [S_{m} (t)] - K [S_{n} (t)] ∥ \leq ∥ S_{m} (t) - S_{n} (t) ∥ + ∥ S T^{- 1} {\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [- β_{1} a_{1} S_{m} (t) b_{1} (I_{m} (t)) - β_{2} a_{2} (S_{m} (t)) b_{2} (E_{m} (t)) - ρ S_{m} (t)]} \\ - S T^{- 1} {\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [- β_{1} a_{1} (S_{n} (t)) b_{1} (I_{n} (t)) - β_{2} a_{2} (S_{n} (t)) b_{2} (E_{n} (t)) - ρ S_{n} (t)]} ∥, \\ ∥ K [E_{m} (t)] - K [E_{n} (t)] ∥ \leq ∥ E_{m} (t) - E_{n} (t) ∥ + ∥ S T^{- 1} [\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [β_{1} a_{1} (S_{m} (t)) b_{1} (I_{m} (t)) + β_{2} a_{2} (S_{m} (t)) b_{2} (E_{m} (t)) - ϵ E_{m} (t)]} \\ - S T^{- 1} [\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [β_{1} a_{1} (S_{n} (t)) b_{1} (I_{n} (t)) + β_{2} a_{2} (S_{n} (t)) b_{2} (E_{n} (t)) - ϵ E_{n} (t)]} ∥, \\ ∥ K [I_{m} (t)] - K [I_{n} (t)] ∥ \leq ∥ I_{m} (t) - I_{n} (t) ∥ + ∥ S T^{- 1} [\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [ϵ (E_{m} (t)) - δ (I_{m} (t)))]} - S T^{- 1} [\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [ϵ E_{n} (t) - δ I_{n} (t)]} ∥, \\ ∥ K [Q_{m} (t)] - K [Q_{n} (t)] ∥ \leq ∥ Q_{m} (t) - Q_{n} (t) ∥ + ∥ S T^{- 1} [\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [δ I_{m} (t) - (λ + κ) Q_{m} (t))]} - S T^{- 1} [\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [δ I_{n} (t) - (λ + κ) Q_{n} (t)]} ∥ \\ ∥ K [R_{m} (t)] - K [R_{n} (t)] ∥ \leq ∥ R_{m} (t) - R_{n} (t) ∥ + ∥ S T^{- 1} [\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [λ (Q_{m} (t))]} - S T^{- 1} [\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [λ Q_{n} (t)]} ∥, \\ ∥ K [P_{m} (t)] - K [P_{n} (t)] ∥ \leq ∥ P_{m} (t) - P_{n} (t) ∥ + ∥ S T^{- 1} [\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [ρ S_{m} (t)]} - S T^{- 1} [\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [ρ S_{n} (t)]} ∥, \\ ∥ K [D_{m} (t)] - K [D_{n} (t)] ∥ \leq ∥ D_{m} (t) - D_{n} (t) ∥ + ∥ S T^{- 1} [\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [κ Q_{m} (t)]} - S T^{- 1} [\frac{1}{O_{γ} E_{γ} (- \frac{1}{1 - γ} ω^{γ})} \\ \times S T [κ Q_{n} (t)]} ∥ \end{matrix}$ (15)

K fulfills the conditions associated with theorem 3.1 when

$θ = (0,0,0,0,0,0,0), θ = (\begin{array}{l} ∥ S_{m} (t) - S_{n} (t) ∥ \times ∥ - S_{m} (t) + S_{n} (t) ∥ \\ - ∥ β_{1} a_{1} (S_{m} (t) - S_{n} (t)) b_{1} (I_{m} (t) - I_{n} (t)) ∥ \\ - ∥ β_{2} a_{2} (S_{m} (t) - S_{n} (t)) b_{2} (E_{m} (t) - E_{n} (t)) ∥ \\ - ∥ ρ (S_{m} (t) - S_{n} (t)) ∥ \\ \times ∥ E_{m} (t) - E_{n} (t) ∥ \times ∥ - E_{m} (t) + E_{n} (t) ∥ \\ + ∥ β_{1} a_{1} (S_{m} (t) - S_{n} (t)) b_{2} (E_{m} (t) - E_{n} (t)) ∥ \\ - ∥ ϵ (E_{m} (t) - E_{n} (t)) ∥ \\ \times ∥ I_{m} (t) - I_{n} (t) ∥ \times ∥ - I_{m} (t) + I_{n} (t) ∥ \\ + ∥ ϵ (E_{m} (t) - E_{n} (t)) ∥ - δ ∥ I_{m} (t) - I_{n} (t) ∥ \\ \times ∥ Q_{m} (t) - Q_{n} (t) ∥ \times ∥ - Q_{m} (t) + Q_{n} (t) ∥ \\ + ∥ δ (I_{m} (t) - I_{n} (t)) ∥ - (λ (t) + κ (t)) ∥ Q_{m} (t) - Q_{n} (t) ∥ \\ \times ∥ R_{m} (t) - R_{n} (t) ∥ \times ∥ - R_{m} (t) + R_{n} (t) ∥ \\ + ∥ λ (Q_{m} (t) - Q_{n} (t)) ∥ \\ \times ∥ P_{m} (t) - P_{n} (t) ∥ - ∥ - P_{m} (t) + P_{n} (t) ∥ \\ + ∥ ρ (S_{m} (t) - S_{n} (t)) ∥ \\ \times ∥ D_{m} (t) - D_{n} (t) ∥ - ∥ - D_{m} (t) + D_{n} (t) ∥ \\ + ∥ κ (Q_{m} (t) - Q_{n} (t)) ∥ \end{array}$ (16)

and we add that K is Picard K-stable.

4. Numerical results and discussion

In this section, consider the numerical simulations of the proposed scheme using the ABC technique for the fractional-order COVID-19 model. Figure 1 shows the simulation S(t) represents the number of uninfected individuals. Shows a deep decreasing curve till point (20, 0.25) and then becomes constant and reduced to zero at (100, 0). Figure 2 shows the simulation E(t) of infected individuals but still is in the incubation period (without clinical symptoms and low infectivity). Figure 3 I(t) which represents the number of infected individuals. Here the graph shows a rapid increase (10, 9) and then decrease rapidly with the same rate and then it becomes constant at (100, 0). Figure 4 represents the number of individuals who have been diagnosed and isolated. Figures 5 and 6 shows the simulation of recovered individuals and those not exposed to the external environment respectively. Figure 7 shows the simulation D(t), which represents the death due to increasing or decreasing the infection rate of COVID-19 in society. It can be easily observed from all figures the solution will converge to steady-state and lie in the bounded domain by decreasing the fractional value. Moreover, it has been demonstrated that physical processes are better well described using the derivatives of fractional order which are more accurate and reliable in comparison with the classical-order derivatives. Moreover, it can be seen from all figures that tell that all infected individual comes zero after a few days due to the quarantine effect. The behavior of the dynamics obtained for different instances of fractional-order was shown in the form of numerical results has been reported.

Figure 1. Simulation of S(t) at the time t with parametric value of γ with ABC.

DownLoad: Full-Size Img PowerPoint

Figure 2. Simulation of E(t) at the time t with parametric value of γ with ABC.

DownLoad: Full-Size Img PowerPoint

Figure 3. Simulation of I(t) at the time t with parametric value of γ with ABC.

DownLoad: Full-Size Img PowerPoint

Figure 4. Simulation of Q(t) at the time t with parametric value of γ with ABC.

DownLoad: Full-Size Img PowerPoint

Figure 5. Simulation of R(t) at the time t with parametric value of γ with ABC.

DownLoad: Full-Size Img PowerPoint

Figure 6. Simulation of P(t) at the time t with parametric value of γ with ABC.

DownLoad: Full-Size Img PowerPoint

Figure 7. Simulation of D(t) at the time t with parametric value of γ with ABC.

DownLoad: Full-Size Img PowerPoint

5. Conclusions

We consider the COVID-19 model with fractional operator for this work to check the dynamical behavior of infection of disease in society. In this regard, ABC derivative gave a realistic approach to analyze the effect of disseise during Quarantine which will be helpful for such type of epidemic. The existence and unique solution of the fractional-order model was made with the help of fixed point theory and iterative method. Numerical simulation has been made to check the actual behavior of the COVID-19 effect during quarantine which shows that infected individuals start decreasing after a few days. Such kind of results are very helpful for planning, decision-making, and developing control strategies to overcome the effect of COVID-19 in society.

References

[1]	UN-Habitat, The Value of Sustainable Urbanization. World Cities Report, Nairobi, 2020. Available from: https://unhabitat.org/sites/default/files/2020/10/wcr_2020_report.pdf.
[2]	Agence Française de Développement, Sustainable Cities. Focus, Paris, 2019. Available from: https://upfi-med.eib.org/wp-content/uploads/2020/04/AFD_CIS_FOCUS-VILLES_DURABLES_ENG_WEB-VF-BAT-1.pdf.
[3]	Dixon T, Connaughton J, Green S (2018) Sustainable Futures in the Built Environment to 2050: A Foresight Approach to Construction and Development, John Wiley & Sons. https://doi.org/10.1002/9781119063834
[4]	IEA (International Energy Agency), Energy technology perspectives pathways to a clean energy system, 2012. Available from: https://iea.blob.core.windows.net/assets/7136f3eb-4394-47fd-9106-c478283fcf7f/ETP2012_free.pdf.
[5]	UNEP (United Nation for Environment Programme), Transport. Investing in energy and resource efficiency, UNEP, 2011. Available from: https://wedocs.unep.org/bitstream/handle/20.500.11822/22013/10.0_transport.pdf?sequence=1&%3BisAllowed.
[6]	Bulkeley H, Broto VC, Maassen A (2013) Low-carbon transitions and the reconfiguration of urban infrastructure. Urban Studies 51: 1471–1486. https://doi.org/10.1177/0042098013500089 doi: 10.1177/0042098013500089
[7]	Dowling R, McGuirk P, Bulkeley H (2014) Retrofitting cities: Local governance in Sydney, Australia. Cities 38: 18–24. https://doi.org/10.1016/j.cities.2013.12.004 doi: 10.1016/j.cities.2013.12.004
[8]	Rutherford J, Jaglin S (2015) Introduction to the special issue—Urban energy governance: Local actions, capacities and politics. Energy Policy 78: 173–178. https://doi.org/10.1016/j.enpol.2014.11.033 doi: 10.1016/j.enpol.2014.11.033
[9]	UN-Habitat, Sustainable Urban Energy Planning—A handbook for cities and towns in developing countries. UNEP, Nairobi, 2009. Available from: https://seors.unfccc.int/applications/seors/attachments/get_attachment?code=LUZ4E1JJHTISK0JLBY55WLV36ICQR6WT.
[10]	Webb J, Hawkey D, Tingey M (2016) Governing cities for sustainable energy: The UK case. Cities 54: 28–35. https://doi.org/10.1016/j.cities.2015.10.014 doi: 10.1016/j.cities.2015.10.014
[11]	Ji C, Choi M, Hong T, et al. (2021) Evaluation of the effect of a building energy efficiency certificate in reducing energy consumption in Korean apartments. Energy Build 248: 111168. https://doi.org/10.1016/j.enbuild.2021.111168 doi: 10.1016/j.enbuild.2021.111168
[12]	El Hafdaoui H, Jelti F, Khallaayoun A, et al. (2023) Energy and environmental national assessment of alternative fuel buses in Morocco. World Electr Veh J 14: 105. https://doi.org/10.3390/wevj14040105 doi: 10.3390/wevj14040105
[13]	Prafitasiwi AG, Rohman MA, Ongkowijoyo CS (2022) The occupant's awareness to achieve energy efficiency in campus building. Results Eng 14: 10039. https://doi.org/10.1016/j.rineng.2022.100397 doi: 10.1016/j.rineng.2022.100397
[14]	Cô té-Roy L, Moser S (2022) A kingdom of new cities: Morocco's national Villes Nouvelles strategy. Geoforum 131: 27–38. https://doi.org/10.1016/j.geoforum.2022.02.005 doi: 10.1016/j.geoforum.2022.02.005
[15]	Delmastro, Chiara; De Bienassis, Tanguy; Goodson, Timothy; Lane, Kevin; Le Marois, Jean-Baptiste; Martinez-Gordon, Rafael; Husek, Martin, "Buildings, " IEA, 2021. Available from: https://www.iea.org/reports/buildings.
[16]	Ministère de la Transition Energétique et du Développement Durable, Stratégie Bas Carbone à Long Terme—Maroc 2050, Rabat, 2021. Available from: https://unfccc.int/sites/default/files/resource/MAR_LTS_Dec2021.pdf.
[17]	IEA (International Energy Agency), Transport—Improving the sustainability of passenger and freight transport, 2021. Available from: https://www.iea.org/topics/transport.
[18]	Ministère de la Transition Energétique et du Développement Durable (MTEDD), Consommation Energetique par l'Administration—Fès et Meknès, SIREDD, Rabat, Morocco, 2012. Available from: https://siredd.environnement.gov.ma/fes-meknes/indicateur/DetailIndicateurPartial?idIndicateur=2988.
[19]	Chegari B, Tabaa M, Moutaouakkil F, et al. (2020) Local energy self-sufficiency for passive buildings: Case study of a typical Moroccan building. J Build Eng 29: 101164. https://doi.org/10.1016/j.jobe.2019.101164 doi: 10.1016/j.jobe.2019.101164
[20]	Oubourhim A, El-Hami K (2020) Efficiency energy standards and labelling for residential appliances in Morocco. In Advanced Intelligent Systems for Sustainable Development, Marrakesh, Morocco, Springer, 97–109. https://doi.org/10.1007/978-3-030-36475-5_10
[21]	El Majaty S, Touzani A, Kasseh Y (2023) Results and perspectives of the application of an energy management system based on ISO 50001 in administrative buildings—case of Morocco. Mater Today: Proc 72: 3233–323. https://doi.org/10.1016/j.matpr.2022.07.094 doi: 10.1016/j.matpr.2022.07.094
[22]	Merini I, Molina-García A, García-Cascales MS, et al. (2020) Analysis and comparison of energy efficiency code requirements for buildings: A Morocco—Spain case study. Energies 13: 5979. https://doi.org/10.3390/en13225979 doi: 10.3390/en13225979
[23]	Sghiouri H, Mezrhab A, Karkri M, et al. (2018) Shading devices optimization to enhance thermal comfort and energy performance of a residential building in Morocco. J Build Eng 18: 292–302. https://doi.org/10.1016/j.jobe.2018.03.018 doi: 10.1016/j.jobe.2018.03.018
[24]	Jihad AS, Tahiri M (2018) Forecasting the heating and cooling load of residential buildings by using a learning algorithm "gradient descent", Morocco. Case Studies Therm Eng 12: 85–93. https://doi.org/10.1016/j.csite.2018.03.006 doi: 10.1016/j.csite.2018.03.006
[25]	Romani Z, Draoui A, Allard F (2015) Metamodeling the heating and cooling energy needs and simultaneous building envelope optimization for low energy building design in Morocco. Energy Build 102: 139–148. https://doi.org/10.1016/j.enbuild.2015.04.014 doi: 10.1016/j.enbuild.2015.04.014
[26]	Sghiouri H, Charai M, Mezrhab A, et al. (2020) Comparison of passive cooling techniques in reducing overheating of clay-straw building in semi-arid climate. Build Simul 13: 65–88. https://doi.org/10.1007/s12273-019-0562-0 doi: 10.1007/s12273-019-0562-0
[27]	Bendara S, Bekkouche MA, Benouaz T, et al. (2019) Energy efficiency and insulation thickness according to the compactness index case of a studio apartment under saharan weather conditions. J Sol Energy Eng 141: 04101. https://doi.org/10.1115/1.4042455 doi: 10.1115/1.4042455
[28]	Rochd A, Benazzouz A, Ait Abdelmoula I, et al. (2021) Design and implementation of an AI-based & IoT-enabled home energy management system: A case study in Benguerir—Morocco. Energy Rep 7: 699–719. https://doi.org/10.1016/j.egyr.2021.07.084 doi: 10.1016/j.egyr.2021.07.084
[29]	Lebied M, Sick F, Choulli Z, et al. (2018) Improving the passive building energy efficiency through numerical simulation—A case study for Tetouan climate in northern of Morocco. Case Studies Therm Eng 11: 125–134. https://doi.org/10.1016/j.csite.2018.01.007 doi: 10.1016/j.csite.2018.01.007
[30]	Bouhal T, Fertahi S e.-D, Agrouaz Y, et al. (2018) Technical assessment, economic viability and investment risk analysis of solar heating/cooling systems in residential buildings in Morocco. Sol Energy 170: 1043–1062. https://doi.org/10.1016/j.solener.2018.06.032 doi: 10.1016/j.solener.2018.06.032
[31]	Swan LG, Ugursal VI (2009) Modeling of end-use energy consumption in the residential sector: A review of modeling techniques. Renewable Sustainable Energy Rev 13: 1819–1835. https://doi.org/10.1016/j.rser.2008.09.033 doi: 10.1016/j.rser.2008.09.033
[32]	Martos A, Pacheco-Torres R, Ordóñ ez J, et al. (2016) Towards successful environmental performance of sustainable cities: Intervening sectors—A review. Renewable Sustainable Energy Rev 57: 479–495. https://doi.org/10.1016/j.rser.2015.12.095 doi: 10.1016/j.rser.2015.12.095
[33]	Howard B, Parshall L, Thompson J, et al. (2012) Spatial distribution of urban building energy consumption by end use. Energy Build 45: 141–151. https://doi.org/10.1016/j.enbuild.2011.10.061 doi: 10.1016/j.enbuild.2011.10.061
[34]	Pereira IM, Sad de Assis E (2013) Urban energy consumption mapping for energy management. Energy Policy 59: 257–269. https://doi.org/10.1016/j.enpol.2013.03.024 doi: 10.1016/j.enpol.2013.03.024
[35]	Mutani G, Todeschi V (2021) GIS-based urban energy modelling and energy efficiency scenarios using the energy performance certificate database. Energy Efficiency 14: 1–28. https://doi.org/10.1007/s12053-021-09962-z doi: 10.1007/s12053-021-09962-z
[36]	Todeschi V, Boghetti R, Kämpf JH, et al. (2021) Evaluation of urban-scale building energy-use models and tools—Application for the city of Fribourg, Switzerland. Sustainability 13: 1595. https://doi.org/10.3390/su13041595 doi: 10.3390/su13041595
[37]	Population of Ifrane 2023, AZNations, 2023. Available from: https://www.aznations.com/population/ma/cities/ifrane-1.[Accessed 27 March 2023].
[38]	Ministère de l'Intérieur, Monographie Générale. La Région de Fès-Meknès, 2015. Available from: https://knowledge-uclga.org/IMG/pdf/regiondefesmeknes-2.pdf.
[39]	Sick F, Schade S, Mourtada A, et al. (2014) Dynamic building simulations for the establishment of a Moroccan thermal regulation for buildings. J Green Build 9: 145–165. https://doi.org/10.3992/1943-4618-9.1.145 doi: 10.3992/1943-4618-9.1.145
[40]	Boujnah M, Jraida K, Farchi A, et al. (2016) Comparison of the calculation methods of heating and cooling. Int J Current Trends Eng Technol 2. Available from: http://ijctet.org/assets/upload/7371IJCTET2016120301.pdf.
[41]	Kharbouch Y, Ameur M (2021) Prediction of the impact of climate change on the thermal performance of walls and roof in Morocco. Int Rev Appl Sci Eng 13: 174–184. https://doi.org/10.1556/1848.2021.00330 doi: 10.1556/1848.2021.00330
[42]	Morocco sets regulations for energy efficiency. Oxford Business Group, 2015.[Online]. Available: https://oxfordbusinessgroup.com/analysis/morocco-sets-regulations-energy-efficiency.[Accessed 11 November 2022].
[43]	AMEE (Agence Marocaine pour l'Efficacité Energétique), Règlement Thermique de Construction au Maroc. Rabat, 2018. Available from: https://www.amee.ma/sites/default/files/inline-files/Lereglementthermique.pdf.
[44]	Bouroubat K, La construction durable: étude juridique comparative. HAL Open Science, Paris, 2017. Available from: https://theses.hal.science/tel-01617586/document.
[45]	M'Gbra N, Touzani A (2013) Energy efficiency codes in residential buildings and energy efficiency improvement in commercial and hospital buildings in Morocco. Mid-Term Evaluation Report on the UNDP/GEP Project, 5–34. Available from: https://procurement-notices.undp.org/view_file.cfm?doc_id=35481.
[46]	El Wardi FZ, Khabbazi A, Bencheikh C, et al. (2017) Insulation material for a model house in Zaouiat Sidi Abdessalam. In International Renewable and Sustainable Energy Conference (IRSEC), Tangier. https://doi.org/10.1109/IRSEC.2017.8477582
[47]	Gounni A, Ouhaibi S, Belouaggadia N, et al. (2022) Impact of COVID-19 restrictions on building energy consumption using Phase Change Materials (PCM) and insulation: A case study in six climatic zones of Morocco. J Energy Storage 55: 105374. https://doi.org/10.1016/j.est.2022.105374 doi: 10.1016/j.est.2022.105374
[48]	MHPV (Ministère de l'Habitat et de la Politique de la Ville), Guide des Bonnes Pratiques pour la Maitrise de l'Energie à l'Echelle de la Ville et de l'Habitat. Rabat, 2014. Available from: www.mhpv.gov.ma/wp-content/uploads/2021/11/Guide-de-bonnes-pratiques-pour-la-maitrise-de-l-energie.pdf.
[49]	PEEB (Programme for Energy Efficiency in Buildings), Building Sector Brief: Morocco. Agence Française de Développement, Paris, 2019. Available from: https://www.peeb.build/imglib/downloads/PEEB_Morocco_Country Brief_Mar 2019.pdf.
[50]	HCP (Haut-Commissariat au Plan), Les Indicateurs Sociaux du Maroc. Rabat, 2022. Available from: https://www.hcp.ma/Les-Indicateurs-sociaux-du-Maroc-Edition-2022_a3192.html#: ~: text=L'objectif%20de%20cette%20publication, une%20%C3%A9valuation%20des%20politiques%20publiques.
[51]	Lahlimi Alami A, Prospective Maroc—Energie 2030. HCP (Haut-Commissariat au Plan), Rabat, 2022. Available from: https://www.hcp.ma/downloads/?tag=Prospective+Maroc+2030.
[52]	Energy Efficiency in Buildings. AMEE, 2016. Available from: https://www.amee.ma/en/node/118.[Accessed 8 September 2022].
[53]	MTEDD (Ministère de la Transition Energétique et du Développement Durable), Campagne de Sensibilisation sur l'Economie d'Energie. 29 June 2022. Available from: https://www.mem.gov.ma/Pages/actualite.aspx?act=333.[Accessed 11 November 2022].
[54]	Ferreira D, Dey AK, Kostakos V (2011) Understanding human-smartphone concerns: A study of battery life. In International Conference of Pervasive Computing. https://doi.org/10.1007/978-3-642-21726-5_2
[55]	Karunarathna WKS, Jayaratne W, Dasanayaka S, et al. (2023) Factors affecting household's use of energy-saving appliances in Sri Lanka: An empirical study using a conceptualized technology acceptance model. Energy Effic, 16. https://doi.org/10.1007/s12053-023-10096-7
[56]	Waris I, Hameed I (2020) Promoting environmentally sustainable consumption behavior: an empirical evaluation of purchase intention of energy-efficient appliances. Energy Effic 13: 1653–1664. https://doi.org/10.1007/s12053-020-09901-4 doi: 10.1007/s12053-020-09901-4
[57]	HCP (Haut-Commissariat au Plan), Le secteur de l'emploi au Maroc. World Bank, Washington DC, 2021. Available from: https://www.hcp.ma/region-oriental/docs/Paysage%20de%20l%27%27emploi%20au%20Maroc%20_%20Recenser%20les%20obstacles%20a%20un%20marche%20du%20travail%20inclusif.pdf.
[58]	Gustafson S, Hartman W, Sellers B, et al. (2015) Energy sustainability in Morocco. Worcester Polytechnic Institute, Worcester. Available from: https://web.wpi.edu/Pubs/E-project/Available/E-project-101615-143625/unrestricted/energy-iqp_report-final2.pdf.
[59]	Hu Q, Qian X, Shen X, et al. (2022) Investigations on vapor cloud explosion hazards and critical safe reserves of LPG tanks. J Loss Prev Process Ind 80: 104904. https://doi.org/10.1016/j.jlp.2022.104904 doi: 10.1016/j.jlp.2022.104904
[60]	Zinecker A, Gagnon-Lebrun F, Touchette Y, et al. (2018) Swap: Reforming support for butane gas to invest in solar in Morocco. Int Inst Sustainable Dev. Available from: https://www.iisd.org/system/files/publications/swap-morocco-fr.pdf.
[61]	MEME (Ministère de l'Energie, des Mines et de l'Environnement), Feuille de Route Nationale pour la Valorisation Energétique de la Biomasse. Rabat, 2021. Available from: https://www.mem.gov.ma/Lists/Lst_rapports/Attachments/32/Feuille de Route Nationale pour la Valorisation Energétique de la Biomasse à l'horizon 2030.pdf.
[62]	Loutia M (2016) The applicability of geothermal energy for heating purposes in the region of Ifrane. Al Akhawayn University, Ifrane, 2016. Available from: www.aui.ma/sse-capstone-repository/pdf/spring2016/The Applicability Of Geothermal Energy For Heating Purposes In The Region of Ifrane.pdf.
[63]	Krarouch M, Lamghari S, Hamdi H, et al. (2020) Simulation and experimental investigation of a combined solar thermal and biomass heating system in Morocco. Energy Rep 6: 188–194. https://doi.org/10.1016/j.egyr.2020.11.270 doi: 10.1016/j.egyr.2020.11.270
[64]	HCP (Haut-Commissariat au Plan), Caractéristiques Démographiques et Socio-Economiques—Province Ifrane. Rabat, 2022. Available from: https://www.hcp.ma/region-meknes/attachment/1605477/.
[65]	HCP (Haut-Commissariat au Plan), Recensement Général de la Population et de l'Habitat 2014. HCP, Rabat, 2015. Available from: www.mhpv.gov.ma/wp-content/uploads/2019/12/RGPH-HABITAT.pdf.
[66]	Driouchi A, Zouag N (2006) Eléments pour le Renforcement de l'Insertion du Maroc dans l'Economie de Croissance. Haut-Commissariat au Plan, Ifrane, 2006. Available from: https://www.hcp.ma/downloads/?tag=Prospective+Maroc+2030.
[67]	MTEDD (Ministère de la Transition Energétique et du Développement Durable), Consommation énergétique par l'administration, 2019. Available from: https://siredd.environnement.gov.ma/fes-meknes/indicateur/DetailIndicateurPartial?idIndicateur=2988.[Accessed 3 September 2022].
[68]	Bami R (2022) Ifrane: L'énergie solaire remplace le bois. Yabiladi, 2022. Available from: https://www.yabiladi.com/article-societe-1636.html.[Accessed 18 November 2022].
[69]	MEMEE (Ministère de l'Energie, des Mines, de l'Eau et de l'Environnement), Stratégie Energétique Nationale—Horizon 2030. Rabat, 2021. Available from: https://www.mem.gov.ma/Lists/Lst_rapports/Attachments/33/Strat%C3%A9gue%20Nationale%20de%20l'Efficacit%C3%A9%20%C3%A9nerg%C3%A9tique%20%C3%A0%20l'horizon%202030.pdf.
[70]	Laroussi I (2017) Cost Study and Analysis of PV Installation per Watt Capacity in Ifrane. Al Akhawayn University, Ifrane, 2017. Available from: http://www.aui.ma/sse-capstone-repository/pdf/fall2017/PV%20INSTALLATION%20COST%20IN%20MOROCCO.%20ILIAS%20LAROUSSI.pdf.
[71]	Arechkik A, Sekkat A, Loudiyi K, et al. (2019) Performance evaluation of different photovoltaic technologies in the region of Ifrane, Morocco. Energy Sustainable Dev 52: 96–103. https://doi.org/10.1016/j.esd.2019.07.007 doi: 10.1016/j.esd.2019.07.007
[72]	Biodiesel Produced at AUI. Al Akhawayn University, Ifrane, 28 April 2016. Available from: http://www.aui.ma/en/media-room/news/al-akhawayn-news/3201-biodiesel-produced-at-aui.html.[Accessed 9 November 2022].
[73]	Derj A, Clean Energies Based Refurbishment of the Heating System of Al Akhawayn University Swimming Pool. Al Akhawayn University, Ifrane, 2015. Available from: www.aui.ma/sse-capstone-repository/pdf/Clean Energies Based Refurbishment of the Heating System of Al Akhawayn University Swimming Pool.pdf.
[74]	Farissi A, Driouach L, Zarbane K, et al. (2021) Covid-19 impact on moroccan small and medium-sized enterprises: Can lean practices be an effective solution for getting out of crisis? Manage Syst Prod Eng 29: 83–90. https://doi.org/10.2478/mspe-2021-0011
[75]	Yoo S-H (2005) Electricity consumption and economic growth: evidence from Korea. Energy Policy 33: 1627–1632. https://doi.org/10.2478/mspe-2021-0011 doi: 10.2478/mspe-2021-0011
[76]	Fatmi A (2022) Student Handbook & Planner. Al Akhawayn University, Ifrane. Available from: www.aui.ma/Student-handbook_2021-2022.pdf.
[77]	World Bank, The Social and Economic Impact of the Covid-19 Crisis in Morocco. Haut-Commissariat au Plan, Rabat, 2021. Available from: https://thedocs.worldbank.org/en/doc/852971598449488981-0280022020/original/ENGTheSocialandEconomicImpactoftheCovid19CrisisinMorocco.pdf.
[78]	Kharbouch Y, Mimet A, El Ganaoui M, et al. (2018) Thermal energy and economic analysis of a PCM-enhanced household envelope considering different climate zones in Morocco. Int J Sustainable Energy 37: 515–532. https://doi.org/10.1080/14786451.2017.1365076 doi: 10.1080/14786451.2017.1365076
[79]	Lachheb A, Allouhi A, Saadani R, et al. (2021) Thermal and economic analyses of different glazing systems for a commercial building in various Moroccan climates. Int J Energy Clean Environ 22: 15–41. https://doi.org/10.1615/InterJEnerCleanEnv.2020034790 doi: 10.1615/InterJEnerCleanEnv.2020034790
[80]	Nacer H, Radoine H, Mastouri H, et al. (2021) Sustainability assessment of an existing school building in Ifrane Morocco using LEED and WELL certification and environmental approach. In 9th International Renewable and Sustainable Energy Conference (IRSEC). https://doi.org/10.1109/IRSEC53969.2021.9741142
[81]	Houzir M, Plan Sectoriel—Eco Construction et Bâ timent Durable. UNEP, Rabat, 2016. Available from: https://switchmed.eu/wp-content/uploads/2020/04/02.-Sectoral-plan-construction-Morocco-in-french.pdf.
[82]	Beccali M, Finocchiaro P, Gentile V et al. (2017) Monitoring and energy performance assessment of an advanced DEC HVAC system in Morocco. In ISES Solar World Conference. https://doi.org/10.18086/swc.2017.28.01
[83]	Taimouri O, Souissi A (2019) Validation of a cooling loads calculation of an office building in Rabat Morocco based on manuel heat balance (Carrier Method). Int J Sci Technol Res 8: 2478–2484. Available from: https://www.ijstr.org/final-print/dec2019/Validation-Of-A-Cooling-Loads-Calculation-Of-An-Office-Building-In-Rabat-Morocco-Based-On-Manuel-Heat-Balance-carrier-Method.pdf.
[84]	IEA (International Energy Agency), Decree n. 2-17-746 on Mandatory energy audits and energy audit organizations, 2019. Available from: https://www.iea.org/policies/8571-decree-n-2-17-746-on-mandatory-energy-audits-and-energy-audit-organisations.[Accessed 26 October 2022].
[85]	Chramate I, Assadiki R, Zerrouq F, et al. (2018) Energy audit in Moroccan industries. Asial Life Sciences. Available from: https://www.researchgate.net/publication/330553987_Energy_audit_in_Moroccan_industries.
[86]	Lillemo SC (2014) Measuring the effect of procrastination and environmental awareness on households' energy-saving behaviours: An empirical approach. Energy Policy 66: 249–256. https://doi.org/10.1016/j.enpol.2013.10.077 doi: 10.1016/j.enpol.2013.10.077
[87]	Kang NN, Cho SH, Kim JT (2012) The energy-saving effects of apartment residents' awareness and behavior. Energy Build 46: 112–122. https://doi.org/10.1016/j.enbuild.2011.10.039 doi: 10.1016/j.enbuild.2011.10.039
[88]	Biresselioglu ME, Nilsen M, Demir MH, et al. (2018) Examining the barriers and motivators affecting European decision-makers in the development of smart and green energy technologies. J Cleaner Prod 198: 417–429. https://doi.org/10.1016/j.jclepro.2018.06.308 doi: 10.1016/j.jclepro.2018.06.308
[89]	Hartwig J, Kockat J (2016) Macroeconomic effects of energetic building retrofit: input-output sensitivity analyses. Constr Manage Econ 34: 79–97. https://doi.org/10.1080/01446193.2016.1144928 doi: 10.1080/01446193.2016.1144928
[90]	Pikas E, Kurnitski J, Liias R, et al. (2015) Quantification of economic benefits of renovation of apartment buildings as a basis for cost optimal 2030 energy efficiency strategies. Energy Build 86: 151–160. https://doi.org/10.1016/j.enbuild.2014.10.004 doi: 10.1016/j.enbuild.2014.10.004
[91]	Ferreira M, Almeida M (2015) Benefits from energy related building renovation beyond costs, energy and emissions. Energy Procedia 78: 2397–2402. https://doi.org/10.1016/j.egypro.2015.11.199 doi: 10.1016/j.egypro.2015.11.199
[92]	Song X, Ye C, Li H, et al. (2016) Field study on energy economic assessment of office buildings envelope retrofitting in southern China. Sustainable Cities Soc 28: 154–161. https://doi.org/10.1016/j.scs.2016.08.029 doi: 10.1016/j.scs.2016.08.029
[93]	Kaynakli O (2012) A review of the economical and optimum thermal insulation thickness for building applications. Renewable Sustainable Energy Rev 16,415–425. https://doi.org/10.1016/j.rser.2011.08.006
[94]	Bambara J, Athienitis AK (2018) Energy and economic analysis for greenhouse envelope design. Trans ASABE 61: 1795–1810. https://doi.org/10.13031/trans.13025 doi: 10.13031/trans.13025
[95]	Struhala K, Ostrý M (2022) Life-Cycle Assessment of phase-change materials in buildings: A review. J Cleaner Prod 336: 130359. https://doi.org/10.1016/j.jclepro.2022.130359 doi: 10.1016/j.jclepro.2022.130359
[96]	Arumugam P, Ramalingam V, Vellaichamy P (2022) Effective PCM, insulation, natural and/or night ventilation techniques to enhance the thermal performance of buildings located in various climates—A review. Energy Build 258: 111840. https://doi.org/10.1016/j.enbuild.2022.111840 doi: 10.1016/j.enbuild.2022.111840
[97]	Jaffe AB, Stavins RN (1994) The energy-efficiency gap—What does it mean? Energy Policy 22: 804–810. https://doi.org/10.1016/0301-4215(94)90138-4 doi: 10.1016/0301-4215(94)90138-4
[98]	Backlund S, Thollander P, Palm J, et al. (2012) Extending the energy efficiency gap. Energy Policy 51: 392–396. https://doi.org/10.1016/j.enpol.2012.08.042 doi: 10.1016/j.enpol.2012.08.042
[99]	Gerarden TD, Newell RG, Stavins RN (2017) Assessing the energy-efficiency gap. J Econ Lit 55: 1486–1525. https://doi.org/10.1257/jel.20161360 doi: 10.1257/jel.20161360
[100]	Chai K-H, Yeo C (2012) Overcoming energy efficiency barriers through systems approach—A conceptual framework. Energy Policy 46: 460–472. https://doi.org/10.1016/j.enpol.2012.04.012 doi: 10.1016/j.enpol.2012.04.012
[101]	Allcott H (2011) Consumers' perceptions and misperceptions of energy costs. Am Econ Rev 101: 98–104. https://doi.org/10.1257/aer.101.3.98 doi: 10.1257/aer.101.3.98
[102]	Davis LW, Metcalf GE (2016) Does better information lead to better choices? Evidence from energy-efficiency labels. J Assoc Environ Resour Econ 3: 589–625. https://doi.org/10.1086/686252 doi: 10.1086/686252
[103]	Shen J (2012) Understanding the Determinants of Consumers' Willingness to Pay for Eco-Labeled Products: An Empirical Analysis of the China Environmental Label. J Serv Sci Manage 5: 87–94. https://doi.org/10.4236/jssm.2012.51011 doi: 10.4236/jssm.2012.51011
[104]	Poortinga W, Steg L, Vlek C, et al. (2003) Household preferences for energy-saving measures: A conjoint analysis. J Econ Psychol 24: 49–64. https://doi.org/10.1016/S0167-4870(02)00154-X doi: 10.1016/S0167-4870(02)00154-X
[105]	Banerjee A, Solomon BD (2003) Eco-labeling for energy efficiency and sustainability: a meta-evaluation of US programs. Energy Policy 31: 109–123. https://doi.org/10.1016/S0301-4215(02)00012-5 doi: 10.1016/S0301-4215(02)00012-5
[106]	Sammer K, Wüstenhagen R (2006) The influence of eco-labelling on consumer behaviour—results of a discrete choice analysis for washing machines. Bus Strategy Environ 15: 185–199. https://doi.org/10.1002/bse.522 doi: 10.1002/bse.522
[107]	Shen L, Sun Y (2016) Performance comparisons of two system sizing approaches for net zero energy building clusters under uncertainties. Energy Build 127: 10–21. https://doi.org/10.1016/j.enbuild.2016.05.072 doi: 10.1016/j.enbuild.2016.05.072
[108]	Good C, Andresen I, Hestnes AG (2015) Solar energy for net zero energy buildings—A comparison between solar thermal, PV and photovoltaic–thermal (PV/T) systems. Sol Energy 123: 986–996. https://doi.org/10.1016/j.solener.2015.10.013 doi: 10.1016/j.solener.2015.10.013
[109]	Harkouss F, Fardoun F, Biwole PH (2018) Passive design optimization of low energy buildings in different climates. Energy 165: 591–613, 2018. https://doi.org/10.1016/j.energy.2018.09.019 doi: 10.1016/j.energy.2018.09.019
[110]	Penna P, Prada A, Cappelletti F, et al. (2015) Multi-objectives optimization of energy efficiency measures in existing buildings. Energy Build 95: 57–69. https://doi.org/10.1016/j.enbuild.2014.11.003 doi: 10.1016/j.enbuild.2014.11.003
[111]	Serbouti A, Rattal M, Boulal A, et al. (2018) Multi-Objective optimization of a family house performance and forecast of its energy needs by 2100. Int J Eng Technol 7: 7–10. Available from: https://www.sciencepubco.com/index.php/ijet/article/view/23235.
[112]	ONEEP (Office National de l'Electricité et de l'Eau Potable), Tarif Général (MT). ONEE, 1 January 2017. Available from: http://www.one.org.ma/FR/pages/interne.asp?esp=1&id1=2&id2=35&id3=10&t2=1&t3=1.[Accessed 24 November 2022].
[113]	ONEEP (Office National de l'Electricité et de l'Eau Potable), Nos tarifs. ONEEP, 1 January 2017. Available from: http://www.one.org.ma/FR/pages/interne.asp?esp=1&id1=3&id2=113&t2=1.[Accessed 24 November 2022].
[114]	Abdou N, EL Mghouchi Y, Hamdaoui S, et al. (2021) Multi-objective optimization of passive energy efficiency measures for net-zero energy building in Morocco. Build Environ 204: 108141. https://doi.org/10.1016/j.buildenv.2021.108141 doi: 10.1016/j.buildenv.2021.108141
[115]	Srinivas M (2011) Domestic solar hot water systems: Developments, evaluations and essentials for viability with a special reference to India. Renewable Sustainable Energy Rev 15: 3850–3861. https://doi.org/10.1016/j.rser.2011.07.006 doi: 10.1016/j.rser.2011.07.006
[116]	Hudon K (2014) Chapter 20—Solar Energy—Water Heating. In Future Energy: Improved, Sustainable and Clean Options for our Planet. Elsevier Science, 433–451. https://doi.org/10.1016/B978-0-08-099424-6.00020-X
[117]	Bertoldi P (2022) Policies for energy conservation and sufficiency: Review of existing. Energy Build 26: 112075. https://doi.org/10.1016/j.enbuild.2022.112075 doi: 10.1016/j.enbuild.2022.112075
[118]	Bertoldi P (2020) Chapter 4.3—Overview of the European Union policies to promote more sustainable behaviours in energy end-users, Energy and Behaviour: Towards a Low Carbon Future. Academic Press: 451–477. https://doi.org/10.1016/B978-0-12-818567-4.00018-1
[119]	Herring H (2006) Energy efficiency—A critical view. Energy 31: 10–20. https://doi.org/10.1016/j.energy.2004.04.055 doi: 10.1016/j.energy.2004.04.055
[120]	Sorrell S, Gatersleben B, Druckman A (2020) The limits of energy sufficiency: A review of the evidence for rebound effects and negative spillovers from behavioural change. Energy Res Soc Sci 64: 101439. https://doi.org/10.1016/j.erss.2020.101439 doi: 10.1016/j.erss.2020.101439
[121]	Sachs W (1999) The Power of Limits: An Inquiry into New Models of Wealth, in Planet Dialectics. Explorations in Environment and Development, London, ZED-BOOKS. Available from: https://www.researchgate.net/publication/310580761_The_power_of_limits.
[122]	Brischke LA, Lehmann F, Leuser L, et al. (2015) Energy sufficiency in private households enabled by adequate appliances. In ECEEE Summer Study proceedings. Available from: https://epub.wupperinst.org/frontdoor/deliver/index/docId/5932/file/5932_Brischke.pdf.
[123]	Spangenberg JH, Lorek S (2019) Sufficiency and consumer behaviour: From theory to policy. Energy Policy 129: 1070–1079. https://doi.org/10.1016/j.enpol.2019.03.013 doi: 10.1016/j.enpol.2019.03.013
[124]	Heindl P, Kanschik P (2016) Ecological sufficiency, individual liberties, and distributive justice: Implications for policy making. Ecol Econ 126: 42–50. https://doi.org/10.1016/j.ecolecon.2016.03.019 doi: 10.1016/j.ecolecon.2016.03.019
[125]	IEA (International Energy Agency), Energy Policies beyond IEA Countries: Morocco 2019. IEA, 2019. Available from: https://www.iea.org/reports/energy-policies-beyond-iea-countries-morocco-2019.
[126]	Palermo V, Bertoldi P, Apostolou M, et al. (2020) Assessment of climate change mitigation policies in 315 cities in the Covenant of Mayors initiative. Sustainable Cities Soc 60: 102258. https://doi.org/10.1016/j.scs.2020.102258 doi: 10.1016/j.scs.2020.102258
[127]	Kona A, Bertoldi P, Kilkis S (2019) Covenant of mayors: Local energy generation, methodology, policies and good practice examples. Energies 12: 985. https://doi.org/10.3390/en12060985 doi: 10.3390/en12060985
[128]	Tsemekidi Tzeiranaki S, Bertoldi P, Diluiso F, et al. (2019) Analysis of the EU residential energy consumption: Trends and determinants. Energies 12: 1065. https://doi.org/10.3390/en12061065 doi: 10.3390/en12061065
[129]	Köppen W (1900) Klassification der Klimate nach Temperatur, Niederschlag and Jahreslauf. Petermanns Geographische Mitteilungen 6: 593–611. Available from: koeppen-geiger.vu-wien.ac.at/pdf/Koppen_1918.pdf.
[130]	Chen D, Chen HW (2013) Using the Köppen classification to quantify climate variation and change: An example for 1901–2010. Environ Dev 6: 69–79. https://doi.org/10.1016/j.envdev.2013.03.007 doi: 10.1016/j.envdev.2013.03.007
[131]	Perez-Garcia A, Guardiola AP, Gómez-Martínez F, et al. (2018) Energy-saving potential of large housing stocks of listed buildings, case study: l'Eixample of Valencia. Sustainable Cities Soc 42: 59–81. https://doi.org/10.1016/j.scs.2018.06.018 doi: 10.1016/j.scs.2018.06.018
[132]	Wang X, Ding C, Zhou M, et al. (2023) Assessment of space heating consumption efficiency based on a household survey in the hot summer and cold winter climate zone in China. Energy 274: 127381. https://doi.org/10.1016/j.energy.2023.127381 doi: 10.1016/j.energy.2023.127381
[133]	Cao X, Yao R, Ding C, et al. (2021) Energy-quota-based integrated solutions for heating and cooling of residential buildings in the Hot Summer and Cold Winter zone in China. Energy Build 236: 110767. https://doi.org/10.1016/j.enbuild.2021.110767 doi: 10.1016/j.enbuild.2021.110767
[134]	Deng Y, Gou Z, Gui X, et al. (2021) Energy consumption characteristics and influential use behaviors in university dormitory buildings in China's hot summer-cold winter climate region. J Build Eng 33: 101870. https://doi.org/10.1016/j.jobe.2020.101870 doi: 10.1016/j.jobe.2020.101870
[135]	Liu H, Kojima S (2017) Evaluation on the energy consumption and thermal performance in different residential building types during mid-season in hot-summer and cold-winter zone in China. Proc Eng 180: 282–291. https://doi.org/10.1016/j.proeng.2017.04.187 doi: 10.1016/j.proeng.2017.04.187
[136]	Geraldi MS, Melo AP, Lamberts R, et al. (2022) Assessment of the energy consumption in non-residential building sector in Brazil. Energy Build 273: 112371. https://doi.org/10.1016/j.enbuild.2022.112371 doi: 10.1016/j.enbuild.2022.112371
[137]	El Hafdaoui H, El Alaoui H, Mahidat S, et al. (2023) Impact of hot arid climate on optimal placement of electric vehicle charging stations. Energies 16: 753. https://doi.org/10.3390/en16020753 doi: 10.3390/en16020753

This article has been cited by:

Changjin Xu, Muhammad Farman, Ali Hasan, Ali Akgül, Mohammed Zakarya, Wedad Albalawi, Choonkil Park, Lyapunov stability and wave analysis of Covid-19 omicron variant of real data with fractional operator, 2022, 61, 11100168, 11787, 10.1016/j.aej.2022.05.025

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)