ASSESSING THE IMPACT OF BOOSTER VACCINE AND ISOLATION ON THE TRANSMISSION DYNAMICS OF PERTUSSIS: USING MATHEMATICAL MODELING APPROACH

Abstract

Pertussis is a highly contagious respiratory disease that is easily prevented by immunisation. The risk of whooping cough is particularly high for neonates. However, due to a lack of vaccinations against pertussis, the disease is still widespread in several nations, particularly in the wake of the COVID-19 pandemic. In this paper, a deterministic mathematical model that describes the transmission dynamics of pertussis  for assessing the impact of booster vaccines and isolation was proposed. The model comprises two equilibrium points, the DFE (disease free equilibrium point) and the EEP (endemic equilibrium point), as demonstrated by the determination of the solution's positivity and boundedness as well as the presence of disease equilibria in the mathematical analysis section. It was discovered that if {R}_c < 1, the DFE is both locally and globally asymptotically stable. The endemic equilibrium point, has been shown to be globally asymptotically stable if the basic reproduction number is greater than unity and $\omega=\psi=\phi_1=v=\delta=0$. This has been determined using a nonlinear Lyapunov function of the Go-Volterra type. Sensitivity analysis demonstrates that isolation and vaccine rates are highly sensitive in lowering the control reproduction number. Numerical simulation of model eq. (1) shows that the isolation rate of affected people and booster are crucial parameters for managing pertussis in a community