Narrow Results

A deterministic model for the transmission of two-strain typhoid fever is developed. The aim is to predict the influence of the typhoid conjugate vaccine on the prevalence of antimicrobial-resistant typhoid infection. Two mechanisms of antimicrobial resistance are incorporated in the model, namely treatment-induced/acquired resistance and transmission of resistant S. Typhi strain. The mathematical analysis is performed using both analytical and numerical approaches. The results show that the disease-free state is locally asymptotically stable if the effective reproduction number ${{ℛ}}_e$ is less than unity. Further analysis reveals that the model exhibits vaccine-induced backward bifurcation, suggesting that ${{ℛ}}_e<1$ is not sufficient for disease elimination. Furthermore, numerical simulations have shown that the existence of endemic equilibrium depends on the sign of ${{ℛ}}_e^r-{{ℛ}}_e^s$. Here, ${{ℛ}}_e^r$ and ${{ℛ}}_e^s$ denote the effective reproduction numbers for the resistant and sensitive strains, respectively. When $\varphi >0$, where $\varphi$ is the rate of treatment-induced/acquired resistance, the resistant strain will cause the extinction of the sensitive strain if ${{ℛ}}_e^r>{{ℛ}}_e^s$. However, the two strains co-exist if ${{ℛ}}_e^r\le {{ℛ}}_e^s$. When $\varphi =0$, the co-existence equilibrium exists if ${{ℛ}}_e^s={{ℛ}}_e^r$; otherwise, the strain with a higher reproduction number would cause the other strain to become extinct, showing the competitive exclusion of the two competing strains. Moreover, the sensitivities of various parameters on the fraction of AMR infections are demonstrated. Also, the prevalence of typhoid decreases with the increase in the number of vaccinated individuals, but vaccination alone is unlikely to control the AMR typhoid infection. The study suggests that more preventive interventions need to be implemented to effectively control antimicrobial-resistant typhoid infections.