Browsing by Author "Ntagalinda, Elimercy"

Now showing 1 - 1 of 1
  • Thumbnail Image
    Item
    Mathematical modelling of the effects of vaccination and treatment on the transmission dynamics of typhoid.
    (University of Dar es Salaam, 2018) Ntagalinda, Elimercy
    Typhoid is the disease causing deaths to people in the world. In this study, we developed a basic deterministic model without interventions, the model with interventions by incorporating vaccination and treatment. These models were qualitatively analysed to determine their respective thresholds necessary for the control of the disease. Equilibrium points of the typhoid models were determined. The disease-free equilibrium points for the basic and extended model were found to be locally and globally asymptotically stable when the thresholds are less than one. The results also showed that the endemic equilibrium point exists for the extended model and is locally asymptotically stable when the threshold is greater than unity. Under this condition the extended model reveal the trend of forward bifurcation. Sensitivity analysis and numerical simulations were carried out to show the investigative results and also to test the impacts of some parameters. The outcome from sensitivity analysis show that vaccination rate, concentration of pathogen in the water supply, death rate due to disease, natural recovery rate, waning rate and treatment rate are the main factors in facilitating the spread and control of the disease. Numerical results show that typhoid epidemic can be reduced when both vaccination and treatment interventions are implemented.