Modelling transmission dynamics of typhoid fever with vaccination, isolation and treatment of infected individuals

In this study, a deterministic mathematical model for typhoid disease transmission with vaccination, isolation, and treatment is developed and analysed. The basic reproduction number R0 is computed and stability analysis is done for both the disease-free and endemic equilibria. The disease-free equilibrium has been found to be locally asymptotically stable whenever R0 < 1, and the endemic equilibrium is locally asymptotically stable whenever R0 > 1. The sensitivity analysis computed revealed the parameters that have a great impact on the R0. Numerical simulations indicate that a combination of vaccination, isolation, and treatment of infected individuals considerably decreases the number of exposed individuals, infected individuals and the bacteria population, whereas the number of individuals isolated for treatment and the recovered individuals first increase and drastically decrease with time. We concluded that implementing all the three control measures is significantly more effective in typhoid fever control and management.