An optimal control model with sensitivity analysis for COVID-19 transmission using logistic recruitment rate

Abstract

This study proposes an optimal control model for COVID-19 spread, incorporating a logistic recruitment rate. The observations show the disease-free equilibrium exists when the population-existing threshold exceeds 1. The stability of equilibrium is determined by the basic reproduction number $R_0$. This implies that equilibrium is stable when $R_0$ is less than or equal to 1, but it is unstable when the value is greater than 1. Furthermore, an endemic equilibrium and stability is recorded when $R_0$ exceeds 1. To identify influential factors in COVID-19 spread, sensitivity index and sensitivity analyses of $R_0$ are conducted. The model perfectly integrates both prevention and therapy controls. As a result, numerical simulations show that the prevention control is more effective than the treatment control in reducing COVID-19 spread. Moreover, the simultaneous implementation of prevention and treatment controls outperforms individual control methods in mitigating COVID-19 spread. Finally, sensitivity analysis conducted with constant controls shows the contributions of the controls to disease dynamics.