Cost-effectiveness and backward bifurcation analysis on COVID-19 transmission model considering direct and indirect transmission

Abstract

Since it was first discovered in Wuhan, China, COVID-19 has continued to spread throughout the world. Since then, many research works have been conducted to understand the spread of COVID-19. In this article, we propose an epidemiological model to understand the spread of COVID-19, considering the saturated treatment rate, direct/indirect transmission, and optimal control problem to find the best strategy for the COVID-19 eradication program. The model constructed is based on a nonlinear system of ordinary differential equations. Analytical results regarding the basic reproduction number and all equilibrium points are obtained analytically. Our model shows a possibility of the existence of the COVID-19 endemic state such that even the basic reproduction number is less than unity. We also found that indirect transmission contributes to the increases in the basic reproduction number and also the occurrence of the multiple endemic states. An optimal control approach was applied to determine the best strategy for the COVID-19 eradication program. Three control parameters were considered in the model: medical mask, disinfectant, and medical treatment. A Pontryagin’s Maximum Principle was used to derive the optimal control characterization of the related model and was solved numerically using the forward-backward iterative method. Several simulations were conducted to determine the impact of interventions for short time experiments. From the cost-effectiveness analysis, we found that using a medical mask as a single intervention is the most effective strategy to reduce the spread of infection.