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Modelling Typhoid Fever with Education, Vaccination and Treatment
International Journal of Theoretical and Applied Mathematics
Volume 2, Issue 2, December 2016, Pages: 156-164
Received: Dec. 9, 2016; Accepted: Dec. 27, 2016; Published: Jan. 21, 2017
Authors
Stephen Edward, Department of Mathematics, College of Natural and Mathematical Sciences, University of Dodoma (UDOM), Dodoma, Tanzania
Nkuba Nyerere, Departments of Biometry and Mathematics, Sokoine University of Agriculture, Morogoro, Tanzania
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Abstract
Typhoid is among the most endemic diseases, and thus, of major public health concerns in tropical developing countries. In this study, 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. Careful analysis of the effective reproduction number has shown that, each of the intervention; education campaigns, vaccination or treatment has an effect in decreasing the transmission of typhoid fever in the community. Sensitivity analysis shows that, the most sensitive parameters are recovery rate for symptomatic infectious individuals, recruitment rate, vaccination rate, education campaign and transmission rate for carrier individuals. Both numerical and analytical results suggest that multiple control strategies are more effective than a single control strategy.
Keywords
Typhoid, Reproductive Number, Treatment, Vaccination
Stephen Edward, Nkuba Nyerere, Modelling Typhoid Fever with Education, Vaccination and Treatment, International Journal of Theoretical and Applied Mathematics. Vol. 2, No. 2, 2016, pp. 156-164. doi: 10.11648/j.ijtam.20160202.30
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