Mathematical Model and Analysis on the Impact of Awareness Campaign and Asymptomatic Human Immigrants in the Transmission of COVID-19

Abstract

In this study, an autonomous type deterministic nonlinear mathematical model that explains the transmission dynamics of COVID-19 is proposed and analyzed by considering awareness campaign between humans and infectives of COVID-19 asymptomatic human immigrants. Unlike some of other previous model studies about this disease, we have taken into account the impact of awareness c between humans and infectives of COVID-19 asymptomatic human immigrants on COVID-19 transmission. The existence and uniqueness of model solutions are proved using the fundamental existence and uniqueness theorem. We also showed positivity and the invariant region of the model system with initial conditions in a certain meaningful set. The model exhibits two equilibria: disease (COVID-19) free and COVID-19 persistent equilibrium points and also the basic reproduction number, $R_0$ which is derived via the help of next generation approach. Our analytical analysis showed that disease-free equilibrium point is obtained only in the absence of asymptomatic COVID-19 human immigrants and disease (COVID-19) in the population. Moreover, local stability of disease-free equilibrium point is verified via the help of Jacobian and Hurwitz criteria, and the global stability is verified using Castillo-Chavez and Song approach. The disease-free equilibrium point is both locally and globally asymptotically stable whenever $R_0<1$ , so that disease dies out in the population. If $R_0>1$ , then disease-free equilibrium point is unstable while the endemic equilibrium point exists and stable, which implies the disease persist and reinvasion will occur within a population. Furthermore, sensitivity analysis of the basic reproduction number, $R_0$ with respect to model parameters, is computed to identify the most influential parameters in transmission as well as in the control of COVID-19. Finally, some numerical simulations are illustrated to verify the theoretical results of the model.