Modelling and Stability Analysis of Typhoid Fever Transmission Dynamics with control Strategies

Stephen Edward

Abstract


Typhoid, an acute gastro-intestinal infection and a waterborne disease continues to emerge in developing countries and remains an important global health challenge. In this paper, we develop a deterministic compartmental mathematical model for assessing the effects of education campaigns, vaccination and treatment on controlling the transmission dynamics of typhoid fever in the community. We have shown that the disease free equilibrium state of the model is locally asymptotically stable if the basic reproduction number is less than unity otherwise if the basic reproduction number is greater than unity then the disease persists and the unique endemic equilibrium is globally asymptotically stable in the interior of the feasible region under some conditions. Numerical simulation reveals that when each of the controls increased it tends to decrease the disease outbreak, this is in support with analytical results which yielded the same results. We performed sensitivity analysis on the key parameters that drive the disease dynamics in order to determine their relative importance to disease transmission and prevalence.


Keywords


typhoid; reproductive number; treatment; vaccination; stability; gastro-intestinal infection.

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