Fractional dynamical model to assess the efficacy of facemask to the community transmission of COVID-19.

The emergence of highly contagious Alpha, Beta, Gamma and Delta variants and strains of COVID-19 put healthy people on high risk of contracting the infection. In addition to the vaccination strategies, the nonpharmaceutical intervention use of face mask gives protection against the contraction of the virus. To understand the efficacy of such, we present a Caputo type fractional dynamical model to assess the efficacy of facemask to the community transmission of COVID-19. The existence and uniqueness of the solution was established, and subsequently, with the use of the generalized mean value theorem, the positivity and boundedness of the solutions were established. The disease free equilibrium (DFE) was found to be asymptotically stable when the basic reproduction number R0<1. By constructing quadratic Lyapunov function, the equilibria (DFE and Endemic) were found to be globally asymptotically stable.

Fractional Order Model for the Role of Mild Cases in the Transmission of COVID-19.

Most of the nations with deplorable health conditions lack rapid COVID-19diagnostic test due to limited testing kits and laboratories. The un-diagnosticmild cases (who show no critical sign and symptoms) play the role as a route that spread the infection unknowingly to healthy individuals. In this paper, we present a fractional order SIR model incorporating individual with mild cases as a compartment to become SMIR model. The existence of the solutions of the model is investigated by solving the fractional Gronwall's inequality using the Laplace transform approach. The equilibrium solutions (DFE & Endemic) are found to be locally asymptotically stable, and subsequently the basic reproduction number is obtained. Also the global stability analysis is carried out by constructing Lyapunov function. Lastly, numerical simulations that support analytic solution follow. It was also shown that when the rate of infection of the mild cases increases, there is equivalent increase in the overall population of infected individuals. Hence to curtail the spread of the disease there is need to take care of the Mild cases as well.