Optimal control analysis on the impact of non-pharmaceutical interventions and vaccination on the dynamics of COVID-19

Abstract

COVID-19 is a serious issue, claiming millions of lives across the globe. Starting from the beginning of the pandemic, different controlling strategies, such as non-pharmaceutical interventions and vaccination, have been adapted to mitigate the virus. In this paper, we developed an epidemiological mathematical model to assess the transmission dynamics of COVID-19 with interventions. The impact of non-pharmaceutical interventions and vaccination of vulnerable individuals on its transmission has been discussed in the developed model. We have proved the mathematical well-posedness and epidemiological meaningfulness of the model. The disease free and endemic equilibrium points are calculated, and the stability analysis of the equilibria have been proved by obtaining the control as well as the basic reproduction numbers of the model. Furthermore, an optimal control analysis is implemented to assess the impacts of employing control interventions. The controls are employed as a time dependent self protective measures, vaccinating individuals, and treating the infected ones. Then we proved the existence and uniqueness of optimal controls, and analyzed the problem using Pontryagin’s Maximum Principle. We estimated the parameter values of the proposed model with collected epidemiological data. Different simulation cases were performed to compare the analytical results and identify the most appropriate control intervention strategies. After implementing the proposed control measures, and performing the efficiency analysis of the control strategies, we obtained a promising result for reducing the number of infected individuals by implementing the control measures properly.

Keywords

• COVID-19
• Vaccination
• Non-pharmaceutical interventions
• Optimal control
• Numerical simulation