Stability Analysis of a Mathematical Model SI$_{u}$I$_{a}$QR for COVID-19 with the Effect of Contamination Control (Filiation) Strategy

Abstract

In this study, using a system of delay nonlinear ordinary differential equations, we introduce a new compartmental epidemic model considered the effect of filiation (contamination) control strategy to the spread of Covid-19. Firstly, the formulation of this new $SI_{u}I_{a}QR$ epidemic model with delay process and the parameters arised from isolation and filiation is formed. Then the disease-free and endemic equilibrium points of the model is obtained. Also, the basic reproduction number $\mathcal{R}_{0}$ is found by using the next-generation matrix method, and the results on stabilities of the disease-free and endemic equilibrium points are investigated. Finally some examples are presented to show the effect of filiation control strategy.

Keywords

• Basic reproduction number
• COVID-19
• Filiation control strategy
• Lyapunov Function
• Mathematical epidemiology
• Quarantine
• Stability Analysis

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