A mathematical model to study the spread of COVID-19 and its control in India
Author:
Naresh Ram1, Sundar Shyam2, Verma Sandhya Rani1, Shukla Jang Bahadur3
Affiliation:
1. Department of Mathematics, School of Basic and Applied Sciences, Harcourt Butler Technical University , Kanpur-208002 , India 2. Department of Mathematics, Pranveer Singh Institute of Technology , Kanpur-208020 , India 3. Innovative Internet University for Research (A Think Tank) , Kanpur-208017 , U.P. , India
Abstract
Abstract
In this article, a nonlinear mathematical model is proposed and analyzed to study the spread of coronavirus disease (COVID-19) and its control. Due to sudden emergence of a peculiar kind of infection, no vaccines were available, and therefore, the nonpharmaceutical interventions such as lockdown, isolation, and hospitalization were imposed to stop spreading of the infectious disease. The proposed model consists of six dependent variables, namely, susceptible population, infective population, isolated susceptible population who are aware of the undesirable consequences of the COVID-19, quarantined population of known infectives (symptomatic), recovered class, and the coronavirus population. The model exhibits two equilibria namely, the COVID-19-free equilibrium and the COVID-19-endemic equilibrium. It is observed that if basic reproduction number
R
0
<
1
{R}_{0}\lt 1
, then the COVID-19-free equilibrium is locally asymptotically stable. However, the endemic equilibrium is locally as well as nonlinearly asymptotically stable under certain conditions if
R
0
>
1
{R}_{0}\gt 1
. Model analysis shows that if safety measures are adopted by way of isolation of susceptibles and quarantine of infectives, the spread of COVID-19 disease can be kept under control.
Publisher
Walter de Gruyter GmbH
Subject
Applied Mathematics,Computational Mathematics,Mathematical Physics,Molecular Biology,Biophysics
Reference25 articles.
1. Aldila, D., Khoshnaw, S. H. A., Safitri, E., Anwar, Y. R., Bakry, A. R., Samiadji, B. M., …, Salim, S. N. (2020). A mathematical study on the spread of covid-19 considering social distancing and rapid assessment: The case of Jakarta, Indonesia. Chaos, Solitons and Fractals, 139, 110042. doi: 10.1016/j.chaos.2020.110042. 2. Annas, S., Pratama, M. I., Rifandi, M., Sanusi, W., & Side, S. (2020). Stability analysis and numerical simulation of SEIR model for pandemic covid-19 spread in Indonesia. Chaos, Solitons and Fractals, 139, 110072. doi: 10.1016/j.chaos.2020.110072. 3. Aronson, J. (2020). Coronaviruses-a general introduction. www.cebm.net/covid-19/coronaviruses-a-general-introduction/. 4. Batista, M. (2020). Estimation of the final size of the corona virus epidemic by SIR model. doi: 10.1101/2020.02.16.20023606. 5. Bugalia, S., Bajiya, V. P., Tripathi, J. P., Li, M., & Sun, G. (2020). Mathematical modeling of covid-19 transmission: The roles of intervention strategies and lockdown. Mathematical Biosciences and Engineering, 17(5), 5961–5986.
|
|