Mathematical Model for the Effects of Intervention Measures on the Transmission Dynamics of Tungiasis

Tungiasis is a zoonosis affecting human beings and a broad range of domestic and syvatic animals caused by the penetration of an ectoparasite known as “Tunga penetrans” into the skin of its host. In this paper we derive and analyze a mathematical model of control measures and then examine the effect of the control strategies on the transmission dynamics of Tungiasis. The model effective reproduction number is determined using the next generation operator method and the analysis is performed using the stability theory of the differential equations. The analytical results show that the disease free equilibrium is locally asymptotically stable when and unstable when . Using Meltzer matrix stability theorem we found that the disease free equilibrium is globally asymptotically stable and by Lyapunov method, the endemic equilibrium is globally asymptotically stable when . From the numerical simulation it was observed that the control strategies have positive impact on the reduction of transmission of Tungiasis disease and that they work better in combination than when applied as singly. The results from simulations will help the decision makers from national health care to advise people at risk with Tungiasis to apply the control strategies based on: educational campaign, personal protection, personal treatment, environmental hygiene and insecticides application to control the flea.

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Keywords: Tungiasis , Control strategies , Steady states , Effective reproduction number , Stability , numerical simulation