A MATHEMATICAL MODEL ON REINFECTION AND VACCINATION ON THE DYNAMICS OF COVID-19

Abstract

In this study a mathematical model that investigates reinfection and vacci nation on the dynamics of COVID-19 was considered. The model particularly takes into account the waning rate of immunity after vaccination as well as ad ministration of booster vaccine. Positivity and boundedness of solutions of the model was proved as well as both the basic and effective reproduction numbers of the model determined by use of the next generation matrix. Further, using the effective reproduction number, the minimum critical value of individuals to be vaccinated for containment of the disease was determined. It was found that the value is less for a perfect vaccine compared to an imperfect vaccine. Sensitiv ity and elasticity of the effective reproduction number was also carried out and it was observed that the effective reproduction number is mostly affected by the recovery rate of individuals and least affected by natural death. Both disease free equilibrium and endemic equilibrium were determined as well as their stability an alyzed using Routh Hurwitz stability criteria and Lyapunov stability. Numerical simulation was performed and we established that re-infection and waning rate of immunity contribute a lot in the disease staying in the population. In addi tion, results from numerical simulations show that booster vaccination increases the period of protection against the disease. Administration of booster vaccines is thus recommended for management of Corona Virus disease. The results show that reinfection, the waning rate of immunity after vaccination and the waning of immunity after infection contributes much on the diseases staying in the popula tion.