Typhoid fever spreads through consumption of food or water contaminated with human feces due to poor hygiene and sanitation. In this paper, a nonlinear mathematical model is developed to study the transmission dynamics of typhoid fever in individuals with access to clean water and adequate hygiene and sanitation (protected individuals) and individuals who do not have such access (at‐risk individuals). A model with treatment is formulated and then decoupled to obtain a basic model which is analyzed by deriving equilibrium states, computation of the basic reproduction number R 0 , and qualitative assessment of equilibria via Metzler matrix and Lyapunov functions. Monte Carlo Markov chain (MCMC) method is used to estimate some parameters. The basic model exhibits either backward or forward bifurcation at R 0 = 1 depending on the choice of relative susceptibility parameter ϵ . Backward bifurcation occurs when ϵ ∈ 0.02, 0.06, and forward bifurcation occurs when ϵ < 0.02. The backward bifurcation indicates the coexistence of typhoid‐free and typhoid equilibria when R 0 < 1. Thus, R 0 < 1 is not a sufficient condition to eliminate typhoid fever. Forward bifurcation implies that R 0 < 1 is a sufficient condition to eliminate typhoid fever. An analysis shows that, the probability of typhoid fever transmission, human recruitment rate, the rate of shedding Salmonella typhi bacteria by at‐risk infectious individuals, the rate of switching to protected individuals, natural mortality rate of S. typhi bacteria and typhoid‐induced death for at‐risk infectious individuals are the drivers of average secondary infections R 0 . The impact of shedding S. typhi bacteria by at‐risk infectious individuals and their typhoid‐induced death highlight the role played by at‐risk individuals in the transmission of typhoid fever. The findings demonstrate that clinical intervention reduces secondary infections and lowers disease transmission. The study highlights the importance of improving access to clean water, hygiene and sanitation in rural areas, and effective treatment for control and potential elimination of typhoid fever.
Irunde et al. (Thu,) studied this question.