Mathematical Modeling and Optimal Control of Intervention Strategies for Covid-19 Disease

Abstract

This research work used mathematical modeling in understanding the dynamics of covid-19 disease. We modified the work of Chen et al. (2020) by incorporating vaccination and pets (spread agents) compartments, making the model a ten (10) compartmental model, and also augmenting four controls to it namely: vaccination, use of face mask and physical distancing, sanitation, and treatment. We developed from the model, a system of non-linear Ordinary Differential Equations from which the positivity of solution was proven. We established the equilibrium states, determined the reproduction number which was utilized to predict the disease's transmission dynamics, hence establishing the conditions for local and global stability of the disease free- equilibrium using Routh- Hurwitz criterion and the Castillo-Chavez technique, respectively. The outcome of the investigation of the stability of the disease-free equilibrium state that covid-19 disease transmission can be significantly degraded and eliminated if the secondary infection’s rate is maintained at a value less than unity. We also used Pontryagin's Maximum Principle to establish the optimality system. The optimality system was numerically solved in Matlab to establish the best strategy in controlling the transmission of covid-19 disease in the population. The graphical solutions revealed that the most effective strategy is the combination of vaccination, use of face mask and physical distancing, sanitation, and treatment of infected individuals in the population.