Mathematical modeling of COVID-19 transmission: the roles of intervention strategies and lockdown

Sarita Bugalia; Vijay Pal Bajiya; Jai Prakash Tripathi; Ming-Tao Li; Gui-Quan Sun; Sarita Bugalia; Vijay Pal Bajiya; Jai Prakash Tripathi; Ming-Tao Li; Gui-Quan Sun

doi:10.3934/mbe.2020318

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 5: 5961-5986. doi: 10.3934/mbe.2020318

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Mathematical modeling of COVID-19 transmission: the roles of intervention strategies and lockdown

1.
Department of Mathematics, Central University of Rajasthan, Bandar Sindri, Kishangarh-305817, Ajmer, Rajasthan, India
2.
School of Mathematics, Taiyuan University of Technology, Taiyuan, 030024, China
3.
Department of Mathematics, North University of China, Taiyuan, 030051, China
4.
Complex Systems Research Center, Shanxi University, Taiyuan, 030006, China

Received: 27 July 2020 Accepted: 07 September 2020 Published: 10 September 2020

An outbreak of rapidly spreading coronavirus established human to human transmission and now became a pandemic across the world. The new confirmed cases of infected individuals of COVID-19 are increasing day by day. Therefore, the prediction of infected individuals has become of utmost important for health care arrangements and to control the spread of COVID-19. In this study, we propose a compartmental epidemic model with intervention strategies such as lockdown, quarantine, and hospitalization. We compute the basic reproduction number (R₀), which plays a vital role in mathematical epidemiology. Based on R₀, it is revealed that the system has two equilibrium, namely disease-free and endemic. We also demonstrate the non-negativity and boundedness of the solutions, local and global stability of equilibria, transcritical bifurcation to analyze its epidemiological relevance. Furthermore, to validate our system, we fit the cumulative and new daily cases in India. We estimate the model parameters and predict the near future scenario of the disease. The global sensitivity analysis has also been performed to observe the impact of different parameters on R₀. We also investigate the dynamics of disease in respect of different situations of lockdown, e.g., complete lockdown, partial lockdown, and no lockdown. Our analysis concludes that if there is partial or no lockdown case, then endemic level would be high. Along with this, the high transmission rate ensures higher level of endemicity. From the short time prediction, we predict that India may face a crucial phase (approx 6000000 infected individuals within 140 days) in near future due to COVID-19. Finally, numerical results show that COVID-19 may be controllable by reducing the contacts and increasing the efficacy of lockdown.
- COVID-19,
- stability,
- lockdown,
- quarantine,
- transcritical bifurcation,
- transmission rate
Citation: Sarita Bugalia, Vijay Pal Bajiya, Jai Prakash Tripathi, Ming-Tao Li, Gui-Quan Sun. Mathematical modeling of COVID-19 transmission: the roles of intervention strategies and lockdown[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 5961-5986. doi: 10.3934/mbe.2020318

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Abstract

An outbreak of rapidly spreading coronavirus established human to human transmission and now became a pandemic across the world. The new confirmed cases of infected individuals of COVID-19 are increasing day by day. Therefore, the prediction of infected individuals has become of utmost important for health care arrangements and to control the spread of COVID-19. In this study, we propose a compartmental epidemic model with intervention strategies such as lockdown, quarantine, and hospitalization. We compute the basic reproduction number (R₀), which plays a vital role in mathematical epidemiology. Based on R₀, it is revealed that the system has two equilibrium, namely disease-free and endemic. We also demonstrate the non-negativity and boundedness of the solutions, local and global stability of equilibria, transcritical bifurcation to analyze its epidemiological relevance. Furthermore, to validate our system, we fit the cumulative and new daily cases in India. We estimate the model parameters and predict the near future scenario of the disease. The global sensitivity analysis has also been performed to observe the impact of different parameters on R₀. We also investigate the dynamics of disease in respect of different situations of lockdown, e.g., complete lockdown, partial lockdown, and no lockdown. Our analysis concludes that if there is partial or no lockdown case, then endemic level would be high. Along with this, the high transmission rate ensures higher level of endemicity. From the short time prediction, we predict that India may face a crucial phase (approx 6000000 infected individuals within 140 days) in near future due to COVID-19. Finally, numerical results show that COVID-19 may be controllable by reducing the contacts and increasing the efficacy of lockdown.

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