Abstract
A nonlinear mathematical model to study the effect of transmission dynamics of COVID-19 virus in a population with variable size structure is proposed and analyzed. The model divides the total human population into five subclasses: susceptibles, self-protected susceptibles, infectives, quarantined infectives, and recovered population including a class representing cumulative density of coronavirus in the environmental reservoir. The model exhibits two equilibria, namely, the diseasefree and the endemic equilibrium. Model analysis reveals the global dynamics of the spread of COVID-19 is completely determined by the basic reproduction number. If basic reproduction number is greater than one, the endemic equilibrium is locally asymptotically stable and is globally asymptotically stable under certain conditions showing that the disease becomes endemic. It is found that the infective population can be decreased if the individuals from susceptible population self protect themselves and do not come in direct contact with viral density deposited on surfaces or airborne droplets accumulated in the environmental reservoir. However, if higher number of individuals from infective class are quarantined at home or hospital, the spread of the disease can further be slowed down. Numerical analysis of the model is also performed to investigate the influence of certain key parameters on the spread of the disease and to support the analytical results.
Recommended Citation
Sharma, Dileep; Tripathi, Agraj; and Tripathi, Ram Naresh
(2023).
(R2059) Modeling the Spread of Coronavirus with Self-protection and Quarantine Effect,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 19,
Iss.
1, Article 8.
Available at:
https://digitalcommons.pvamu.edu/aam/vol19/iss1/8