In this paper, a mathematical model based on a system of nonlinear parabolic partial differential equations is developed to investigate the effect of human mobility on the dynamics of coronavirus 2019 (COVID-19) disease. Positivity and boundedness of the model solutions are shown. The existence of the disease-free, the endemic equilibria, and the travelling wave solutions of the model are shown. From the numerical analysis, it is shown that human mobility plays a crucial role in the disease transmission. Therefore, interventions that affect diffusion (human mobility), such as lock-down, travel restrictions, and cessation of movement, may play a significant role in controlling and preventing the spread of COVID-19.

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In this paper, a mathematical model based on a system of ordinary differential equations is developed with vaccination as an intervention for the transmission dynamics of coronavirus 2019 (COVID-19). The model solutions are shown to be well posed. The vaccine reproduction number is computed by using the next-generation matrix approach. The sensitivity analysis carried out on this model showed that the vaccination rate and vaccine efficacy are among the most sensitive parameters of the vaccine reproduction number, R V . The optimal control problem is solved with the rate of vaccination and the transition rate from the vaccinated class to the infected class as control variables. Finally, the numerical simulations showed that the control intervention should aim to increase the vaccination rate with a high-efficacy vaccine.