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.
