## Jñānābha‎, Vol. 52 (2) (2022), (182-190)

AN SIQR MATHEMATICAL MODEL TO CONTROL CORONA - VIRUS DISEASE (COVID-19) WITH SATURATED INCIDENCE RATE

By

Shuchita Vaidya1, V. K. Gupta2 and S. K. Tiwari1

Email: shuchitavaidya@gmail.com, dr_vkg61@yahoo.com, skt_tiwari75@yahoo.co.in

(Received: February 16, 2022; In format: March 05, 2022; Revised: May 30, 2022; Accepted : November 15, 2022) DOI:

https://doi.org/10.58250/jnanabha.2022.52221

Abstract

In this paper, we have established SIQR epidemic model with saturated incidence rate for Corona - virus Disease (COVID-19). For more specified study the Quarantine Compartment is subdivided into two quarantine compartments QS , quarantine from susceptible individual class and QI, quarantine from infected individuals. At any given time the size of susceptible compartment will be bigger than the size of other compartments so, considering the criticality of the disease it is necessary to have the hold on this compartment for this the whole model is incorporated with saturated incidence rate. The local and global stability at equilibrium points are discussed which depends on the basic reproduction number (R0) of the model. It has been observed if R0 < 1, then the disease free equilibrium is globally asymptotically stable and if R0 > 1, then the endemic equilibria will be globally stable. At R0 = 1, behaviour of disease-free equilibrium is examined using Center manifold theory. The major finding shows that the measure of inhibition taken by the susceptible reduces the severity of disease.

2020 Mathematical Sciences Classification: 93A30, 92D30, 93D20, 93D05.

Keywords and Phrases: Mathematical Model SIQR, Second additive compound matrix, Lyapunov function, Stability Geometric approaches.