Abstract

MATHEMATICAL ANALYSIS OF A TYPHOID TRANSMISSION MODEL WITH VACCINATION

Ocheme, Ameh Christian; *Eguda, Felix Yakubu; Shuaibu, Ali Maianguwa & Sule, Mustapha Mohammed

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In this paper, a six compartmental model for typhoid transmission dynamics incorporating vaccination as a controlling measure in human population was formulated. Mathematical analysis was carried out to determine the transmission pattern of typhoid infection in the population. The model was formulated using system of differential equations and we determined the control reproduction number which is a vital threshold parameter for measuring the control and propagation of infectious diseases. The stability analysis was carried out and it was found that typhoid infection undergoes both local and global asymptotic stability. Disease free equilibrium exist, and is locally and globally asymptotically stable if the control reproduction number is less than one and unstable if greater than one. The study shows that typhoid infection is endemic, and locally and globally asymptotically stable if the control reproduction number is greater than one. The model exhibits backward bifurcation which is caused by loss of temporary immunity of recovered human population. Keywords: Typhoid, Salmonellae, Model, Bifurcation, Local and Global Stabilities.

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