On the deterministic and stochastic model applications to typhoid fever disease dynamics

Abstract A deterministic and stochastic model depicting typhoid fever spread in human host community is considered. The deterministic model is analyzed and found to be positively invariant, well – posed and meaningful in the sense of typhoid infection spread. Using the typhoid fever – absent equilibrium points, the control basic reproduction threshold (Rtyp ) of the model is obtained and the estimation yields Rtyp ≈ 0.744. This value implies that controls of vaccination, screening and treatment is effective enough to drive Rtyp below unity, that is, the level of infection is not effective to cause a typhoid epidemic. Also, the deterministic model is changed into a stochastic model system and the mean and variance of the stochastic model are obtained. The existence and uniqueness of the stochastic model is discussed and the corresponding graphical description of the impact of some parameters against is Rtyp plotted, while the stochastic simulations are done using the Euler - Maruyama numerical scheme coded in matlab to describe the behavior of each sub - population of human individuals of the model system.