Stability and Parameter Sensitivity Analyses of SEI${}_{3}$R${}_{2}$D${}_{2}$V Model to Control COVID-19 Pandemic

Abstract

In this article, we have employed the SEI ${}_{3}$ R ${}_{2}$ D ${}_{2}$ V model for our analysis. We conducted stability analysis for infection-free equilibrium ( $X^{\prime}$ ) and endemic equilibrium ( $X^{*}$ ). The obtained equilibrium points are globally asymptotically stable. Our findings reveal that the contact dynamics of the infected and uninfected populations primarily influence the dynamics of COVID-19. In managing COVID-19, it is crucial to ensure that the number of secondary infections ( $R_{t}$ ) remains below the threshold $\left(\boldsymbol{\gamma}+(\boldsymbol{1-\gamma})/(\boldsymbol{\alpha_{t}})\right)$ which determines the growth or decline of the disease. Additionally, we conducted a sensitivity analysis of $R_{t}$ to identify the key factors that significantly affect its value. It is observed that the recovery rate, transmission probability of the virus, contact rate of unreported infections, testing inaccuracy and hesitancy, vaccination rate, and its efficacy have the most substantial impact on the value of $R_{t}$ . The influential parameters are categorized into two sets based on their effective controllability, allowing for the prioritization of intervention strategies that require fewer resources and are easier to manage, thereby optimizing efforts to control disease transmission.