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 R0. This implies that equilibrium is stable when R0 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 R0 exceeds 1. To identify influential factors in COVID-19 spread, sensitivity index and sensitivity analyses of R0 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.