Stability Analysis of the Dynamics of Tungiasis Transmission in Endemic Areas

Jairos Kahuru, Livingstone Luboobi, Yaw Nkansah-Gyekye

Abstract


Tungiasis refers to the infestation caused by the permanent penetration of the female sand flea “Tunga penetrans” into the skin of the human or animal hosts and causes cutaneous lesion. In this paper, we developed a deterministic model for the dynamics of tungiasis in communities of human beings, animal reservoirs and flea infested environment in order to understand the way tungiasis disease spreads in a poor resource community. We established the conditions for local and global stability of the disease-free and endemic equilibrium points. The computational results showed that the disease-free equilibrium point is locally and globally asymptotically stable when the model basic reproduction number  is less than unit, that is. Using the Lyapunov stability theory and LaSalle’s Invariant Principle we found that the endemic equilibrium point (EE) is globally asymptotically stable when. The numerical simulations have been presented to illustrate the way the model variables behave when there is no intervention and that the endemic equilibria exist and they are stable. On-host and off-host control measures which include focal spraying of insecticides to the premises, application of insecticidal dusts on animal bodies, environmental and personal hygiene, educational campaign, use of closed foot wear and application of plant based repellents should be implemented.

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