Insights into dengue transmission modeling: Index of memory, carriers, and vaccination dynamics explored via non-integer derivative

Rashid Jan; Imtiaz Ahmad; Hijaz Ahmad; Narcisa Vrinceanu; Adrian Gheorghe Hasegan; Rashid Jan; Imtiaz Ahmad; Hijaz Ahmad; Narcisa Vrinceanu; Adrian Gheorghe Hasegan

doi:10.3934/bioeng.2024004

AIMS Bioengineering

2024, Volume 11, Issue 1: 44-65. doi: 10.3934/bioeng.2024004

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Research article

Insights into dengue transmission modeling: Index of memory, carriers, and vaccination dynamics explored via non-integer derivative

1.
Institute of Energy Infrastructure (IEI), Department of Civil Engineering, College of Engineering, Universiti Tenaga Nasional (UNITEN), Putrajaya Campus, Jalan IKRAM-UNITEN, 43000 Kajang, Selangor, Malaysia
2.
Institute of Informatics and Computing in Energy (IICE), Universiti Tenaga Nasional, Kajang, Selangor, Malaysia
3.
Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, Saudi Arabia
4.
Near East University, Operational Research Center in Healthcare, TRNC Mersin 10, Nicosia, 99138, Turkey
5.
Department of Mathematics and Informatics, Azerbaijan University, Jeyhun Hajibeyli street, 71, AZ1007, Baku, Azerbaijan
6.
Faculty of Engineering, Department of Industrial Machines and Equipments, “Lucian Blaga” University of Sibiu, Romania, 10 Victoriei Boulevard
7.
Lucian Blaga University of Sibiu, Faculty of Medicine, 2A Lucian Blaga Str., 550169, Sibiu, Romania

Received: 20 September 2023 Revised: 02 November 2023 Accepted: 13 November 2023 Published: 20 March 2024

It is acknowledged that dengue infection has a significant economic impact due to healthcare costs and lost productivity. Research can provide insights into the economic burden of the disease, guiding policymakers in their allocation of resources for prevention and control interventions. In this work, we structured a novel mathematical model that describes the spread of dengue with the effects of carriers, an index of memory and vaccination. To show the effect of treatment on the dynamics of dengue, we have incorporated medication-related treatment into the system. The proposed dynamics are represented by using fractional derivatives to capture the role of memory in the control of the infection. We introduced the fundamental principles and notions of non-integer derivatives for the analysis of the model; moreover, the existence and uniqueness results for the solution of the system have been established with the help of mathematical skills. The theory of fixed points has been utilized for the analysis and examination of the system. We have established Ulam-Hyers stability for the recommended system of dengue infection. Regarding the numerical findings, a numerical method is presented to highlight the solution pathways for the system of dengue infection. Several simulations have been performed to visualize the contribution of the input parameters of the system to the prevention and control of the infection. The index of memory, vaccination, and treatment are suggested to be attractive parameters which can reduce the level of infection while the biting rate, asymptomatic carriers and transmission rate are critical as they can increase the risk of the infection in society. Our findings not only provide information for the effective management of the infection they also possess valuable insights that can improve public health.
- dengue infection,
- epidemic models,
- fractional calculus,
- asymptomatic carriers,
- numerical solution,
- dynamical behavior
Citation: Rashid Jan, Imtiaz Ahmad, Hijaz Ahmad, Narcisa Vrinceanu, Adrian Gheorghe Hasegan. Insights into dengue transmission modeling: Index of memory, carriers, and vaccination dynamics explored via non-integer derivative[J]. AIMS Bioengineering, 2024, 11(1): 44-65. doi: 10.3934/bioeng.2024004

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Abstract

It is acknowledged that dengue infection has a significant economic impact due to healthcare costs and lost productivity. Research can provide insights into the economic burden of the disease, guiding policymakers in their allocation of resources for prevention and control interventions. In this work, we structured a novel mathematical model that describes the spread of dengue with the effects of carriers, an index of memory and vaccination. To show the effect of treatment on the dynamics of dengue, we have incorporated medication-related treatment into the system. The proposed dynamics are represented by using fractional derivatives to capture the role of memory in the control of the infection. We introduced the fundamental principles and notions of non-integer derivatives for the analysis of the model; moreover, the existence and uniqueness results for the solution of the system have been established with the help of mathematical skills. The theory of fixed points has been utilized for the analysis and examination of the system. We have established Ulam-Hyers stability for the recommended system of dengue infection. Regarding the numerical findings, a numerical method is presented to highlight the solution pathways for the system of dengue infection. Several simulations have been performed to visualize the contribution of the input parameters of the system to the prevention and control of the infection. The index of memory, vaccination, and treatment are suggested to be attractive parameters which can reduce the level of infection while the biting rate, asymptomatic carriers and transmission rate are critical as they can increase the risk of the infection in society. Our findings not only provide information for the effective management of the infection they also possess valuable insights that can improve public health.

Acknowledgments

Project financed by Lucian Blaga University of Sibiu through research grant LBUS-IRG-2023-09.

Conflict of interest

Hijaz Ahmad is on a special issue editorial board for AIMS Bioengineering and was not involved in the editorial review or the decision to publish this article. All authors declare that there are no competing interests. The authors declare that there is no conflict of interests regarding the publication of this paper.

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