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Mathematical analysis of the dynamics of visceral leishmaniasis in the Sudan. (English) Zbl 1200.92023

Summary: We develop a mathematical model to study the dynamics of visceral leishmaniasis in Sudan. To develop this model, we consider the dynamics of the disease between three different populations, human, reservoir and vector populations. The model is analyzed at equilibrium and the stability of the equilibria is investigated. The basic reproduction number is derived, and threshold conditions for disease elimination are established. The results show that the disease can be eliminated under certain conditions. Simulations of the model show that human treatment helps in disease control, and its synergy with vector control will more likely result in the elimination of the disease.

MSC:

92C50 Medical applications (general)
34D20 Stability of solutions to ordinary differential equations
93A30 Mathematical modelling of systems (MSC2010)
92C60 Medical epidemiology
65C20 Probabilistic models, generic numerical methods in probability and statistics
37N25 Dynamical systems in biology
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