On the effect of vaccination, screening and treatment in controlling typhoid fever spread dynamics: Deterministic and stochastic applications

Abstract

This work concerns a deterministic and stochastic model describing the transmission of typhoid fever infection in human host community, where the vaccination of susceptible births and immigrants as well as screening and treatment of carriers and infected individuals are considered in the model build-up. The well-posedness and computation of the basic reproduction number Rtyp of the deterministic model are obtained and analysed. The deterministic model is further transformed into a stochastic model, where the drift and diffusion parts of the model are obtained, and the existence and uniqueness of the stochastic model are discussed. Numerical simulations involving the model parameters of Rtyp showed that vaccination of susceptible births and influx of immigrants as well as screening and treatment of carriers and infected humans are effective in bringing the threshold Rtyp (Rtyp ≈ 0.7944) below 1, and the results of other simulations suggest more health policies are to be implemented, as low Rtyp may not be guaranteed because vaccination wanes over time. In addition, the numerical simulations of the stochastic model equations describing the sub-population of human individuals in the total human host community are carried out using the computational software MATLAB.