Modeling the impact of screening and treatment on typhoid fever dynamics in unprotected population

Abstract

Typhoid fever is a potentially fatal human infection that is caused by the Salmonella Typhi bacterium. The disease is usually spread through contaminated water or food. In this work, we formulate and analyze a mathematical model for transmission dynamics of typhoid fever that incorporates screening and treatment of disease carriers in unprotected population. We obtain the basic model in the absence of screening and treatment. The analysis shows that both the typhoid free and endemic equilibria exist. The basic and effective reproduction numbers R0 and Re respectively are computed using the next generation method. The results show that the typhoid free equilibria are asymptotically stable when the basic and effective reproduction numbers R0<1 and Re<1 whereas endemic equilibria are asymptotically stable when R0>1 and Re>1. The normalized forward sensitivity index method is adopted to study the influence of model parameters on the spread of typhoid fever. The results show that the effective contact rate, the shedding rate of Salmonella Typhi bacteria on the environment and the recruitment rate of susceptible humans drive the disease, suggesting that screening of disease carriers and treatment of infected individuals are effective in controlling typhoid fever. Simulation results indicate that screening of disease careers and treatment of infected individuals play a significant role in controlling the transmission of typhoid fever in unprotected population. Thus, to control typhoid fever in unprotected population, more efforts should be directed to screening of disease carriers and treatment of infected individuals.