Math. Model. Nat. Phenom.
Volume 15, 2020
Mathematical Models and Methods in Epidemiology
|Number of page(s)||39|
|Published online||04 December 2020|
Analysis and simulations with a multi-scale model of canine visceral leishmaniasis
Department of Mathematics, University of Florida,
FL 32611, USA.
* Corresponding author: firstname.lastname@example.org
Accepted: 29 June 2020
Visceral leishmaniasis in dogs is believed to have an impact on the prevalence of the disease in human populations. Here, we continue the analysis of the nested immuno-epidemiological model of visceral leishmaniasis in dogs, including a proof of well-posedness using functional analytical methods. Once well-posedness is established, we continue stability analysis of the endemic equilibria and provide necessary and sufficient conditions for the presence of backward bifurcation, and prove the instability of the lower endemic equilibrium in the presence of backward bifurcation. Lastly, we provide a number of simulations of the model using a number of control strategies. Control measures currently in use attempt to reduce the parasite load in the host, reduce the vector population, reduce the vector biting rate, and remove infected hosts. We examine various combinations of these strategies and conclude that a strategy combining culling infected dogs and removing vectors from the population by means such as insecticide will be the most effective.
Mathematics Subject Classification: 92D30
Key words: Leishmaniasis in dogs / backward bifurcation / immuno-epidemiological model / stability / fixed-point methods / controls / simulations
© The authors. Published by EDP Sciences, 2020
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