Mathematical Analysis of Optimal Cost-effective Control of COVID-19: A Case Study

Currently, coronavirus disease 2019 (COVID-19) pandemic is a worldwide health issue. In this paper, a nonlinear optimal control problem for COVID-19 is formulated by extending an existing mathematical deterministic model involving 8-dimensional autonomous system of differential equations analysed for the disease spread in Malaysia. The new model includes three time-dependent variables measuring the levels of preventive, treatment and management controls. Pontryagin's maximum principle is used to determine the necessary conditions required for the existence of optimal control triplet. The effect of different control strategies on the dynamics of the disease spread is measured through the numerical implementation of the derived optimality system. Cost-effectiveness analysis is conducted to ascertain the most cost-effective strategy required to curtail the spread of COVID-19 in the population.