A Mathematical Model on the Dynamics of In-Host Infection Cholera Disease with Vaccination

Abstract

In this paper, a within-host cholera mathematical model has been developed using a system of ordinary differential equations incorporating vaccine efficacy. The formulated model considers cells in an already vaccinated individual with a vaccine whose efficacy is γ . The solutions of the model have been shown to be both positive and bounded hence well-posed. The vaccine basic reproduction number has been carried out using the next generation matrix approach and is given by R 0 V = γ / d + μ 2 and R 0 V < 1 if γ < d + μ 2 . Analysis of the model shows that i n f e c t i o n f r e e e q u i l i b r i u m I F E point is both locally and globally asymptotically stable when R 0 V < 1 and i n f e c t i o n e q u i l i b r i u m I E point is locally asymptotically stable when R 0 V > 1 . Furthermore, analysis of the model shows that R 0 V < 1 is not sufficient enough to eradicate in-host cholera disease, hence the existence of backward bifurcation which is an indication as to why cholera disease is persistent. To highlight the relevance of vaccine efficacy, a numerical simulation of the model with respect to vaccination is carried out and shows that when the vaccine efficacy γ is high, there will be a lower infection rate of cells, hence the need to improve cholera vaccine efficacy.