Mathematical Analysis of a Tuberculosis-Schistosomiasis Co-infection Model with Vaccination and Treatment
Abstract
We present a mathematical model, that is deterministic, for investigating the impact of schistosomiasis infection on the immunogenicity of the BCG vaccine affects the use of vaccination as a measure of control against TB infection at population level in Nigeria. The presence of the backward bifurcation phenomenon was established from the analysis of the model, and it was discovered that the following parameters were responsible the adjustment parameter for comparative contagiousness of individuals re-contaminated with TB ($\Theta_{RT}$), the rate of therapy for schistosomiasis-only infected persons ($\zeta_S$), the impact of schistosomiasis on the BCG protection against TB ($\zeta_{TS}$), BCG vaccine waning ($\theta_V$), the BCG vaccine efficacy ($\epsilon_1$), the treatment rate for TB ($\zeta_T$), the comparative rates by which individuals having dormant schistosomiasis ($\eta_1$) cum virulent schistosomiasis ($\eta_2$) are tainted with TB, correspondingly, the depreciated rate of contamination with schistosomiasis ($\psi$), the regulation parameter for comparative infectiousness of persons possessing virulent TB cum dormant schistosomiasis ($\Pi_1$), the treatment rate for TB for co-infected persons ($\zeta_{T1}$), the progression rate from contagious TB/unprotected from schistosomiasis to contagious TB/contagious schistosomiasis ($\sigma$), and the rate of advancement from unprotected against the two infirmities TB/schistosomiasis to unprotected against TB/infectious schistosomiasis ($\alpha_2$). The disease-free equilibrium was found to be globally asymptotically stable when the parameters responsible for the backward bifurcation phenomenon were negligible, the the effective reproduction number is less than unity.
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