University of Khartoum

# Assessing Control Strategies Against Visceral Leishmaniasis Under Different Assumptions Using Mathematical Modeling

 Title: Assessing Control Strategies Against Visceral Leishmaniasis Under Different Assumptions Using Mathematical Modeling Author: Mohammed ELmojtaba Ibrahim, Ibrahim Abstract: In this study, several mathematical models have been formulated and analyzed to understand the dynamics of visceral leishmaniasis in a population with reservoir host, and to assess some control measurements against the disease. These models were constructed based on data and knowledge come from medical research carried out on leishmaniasis. First, a mathematical model to study the dynamics of visceral leishmaniasis (VL) in the population was developed. Results show that the disease can be eliminated if R0, the basic reproduction number, is less than unity, and when R0 > 1 the endemic equilibrium is locally asymptotically stable. It is also concluded that human treatment helps in disease control, but it is not sufficient to eliminate the disease and it should be followed by vector control in order to eradicate the disease from the human population. In order to investigate the role of cross-immunity between two different strains of leishmania in the disease dynamics, a mathematical model was developed and analyzed. Results show that R0 decreases as the cross-immunity increases, moreover, if the crossimmunity between the two different strains is perfect, then the disease-free equilibrium is globally asymptotically stable. Results also show that in the case of partial crossimmunity the model undergoes backward bifurcation, where R0 < 1 is not enough for eradication of the disease. A mathematical model to understand the dynamics of malaria-visceral leishmaniasis xv co-infection is proposed and analyzed. Results show that both diseases can be eliminated if R0 is less than unity, and the system undergoes a backward bifurcation where an endemic equilibrium co-exists with the disease-free equilibrium when one of Rm or Rl, the basic reproduction numbers of malaria-only and visceral leishmaniasis-only, respectively, is precisely less than unity. A mathematical model to describe the dynamics of visceral leishmaniasis in a population with immigration of infective humans under mass vaccination strategy, was presented and analyzed. Result shows that in order for the vaccine to play a role on the disease control it must be very effective. Results also show that vaccination coverage does not have any impact on the disease control when the immigration rate is small, and it does not affect the long term behavior when the immigration rate is high. xvi URI: http://khartoumspace.uofk.edu/handle/123456789/9130 Date: 2015-04-20
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