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# Modelling the Effect of Self-Immunity and the Impacts of Asymptomatic and Symptomatic Individuals on COVID-19 Outbreak

M. H. A. Biswas1,*, M. A. Islam1, S. Akter2, S. Mandal2, M. S. Khatun1, S. A. Samad1, A. K. Paul1, M. R. Khatun1

1 Mathematics Discipline, Science Engineering and Technology School, Khulna University, Khulna, 9208, Bangladesh
2 Department of Mathematics, Bangabandhu Sheikh Mujibur Rahman Science and Technology University, Gopalganj, 8100, Bangladesh

* Corresponding Author: M. H. A. Biswas. Email:

(This article belongs to this Special Issue: Computer Modelling of Transmission, Spread, Control and Diagnosis of COVID-19)

Computer Modeling in Engineering & Sciences 2020, 125(3), 1033-1060. https://doi.org/10.32604/cmes.2020.012792

## Abstract

COVID-19 is one of the most highly infectious diseases ever emerged and caused by newly discovered severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). It has already led the entire world to health and economic crisis. It has invaded the whole universe all most every way. The present study demonstrates with a nine mutually exclusive compartmental model on transmission dynamics of this pandemic disease (COVID-19), with special focus on the transmissibility of symptomatic and asymptomatic infection from susceptible individuals. Herein, the compartmental model has been investigated with mathematical analysis and computer simulations in order to understand the dynamics of COVID-19 transmission. Initially, mathematical analysis of the model has been carried out in broadly by illustrating some well-known methods including exactness, equilibrium and stability analysis in terms of basic reproduction number. We investigate the sensitivity of the model with respect to the variation of the parameters’ values. Furthermore, computer simulations are performed to illustrate the results. Our analysis reveals that the death rate from coronavirus disease increases as the infection rate increases, whereas infection rate extensively decreases with the increase of quarantined individuals. The quarantined individuals also lead to increase the concentration of recovered individuals. However, the infection rate of COVID-19 increases more surprisingly as the rate of asymptomatic individuals increases than that of the symptomatic individuals.Moreover, the infection rate decreases significantly due to increase of self-immunity rate.

## Keywords

Biswas, M. H. A., Islam, M. A., Akter, S., Mandal, S., Khatun, M. S. et al. (2020). Modelling the Effect of Self-Immunity and the Impacts of Asymptomatic and Symptomatic Individuals on COVID-19 Outbreak. CMES-Computer Modeling in Engineering & Sciences, 125(3), 1033–1060.

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