A novel multi-scale immuno-epidemiological model of visceral leishmaniasis in dogs

Jonathan Shane Welker, Maia Martcheva

Abstract


Leishmaniasis is a neglected and emerging disease prevalent in Mediterranean and tropical climates. As such, the study and development of new models are of increasing importance. We introduce a new immuno-epidemiological model of visceral leishmaniasis in dogs. The within-host system is based on previously  collected  and published data, showing the movement and proliferation of the parasite in the skin and the bone-marrow, as well as the IgG response. The between-host system structures the infected individuals in  time-since-infection and is of vector-host type. The within-host system has a parasite-free equilibrium and at least one endemic equilibrium, consistent with the fact that infected dogs do not recover without treatment. We compute the basic reproduction number R0 of the immuno-epidemiological model  and provide the existence and stability results of the population-level  disease-free equilibrium. Additionally, we prove existence of an unique  endemic equilibrium when R0 > 1, and evidence of backward bifurcation and existence of multiple endemic equilibria when R0 < 1.

Keywords


leishmaniasis in dogs; backward bifurcation; immuno-epidemiological model; stability; parameter estimation; immune dynamics

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DOI: http://dx.doi.org/10.11145/j.biomath.2019.01.026

BIOMATH is indexed in Mathematical Reviews (MathSciNet), Zentralblatt fuer Mathemathik (zbMATH), Scopus (from 2019), EBSCO databasis Academic (Complete, Elite, Premier, Ultimate), Directory of Open Access Journals (DOAJ).

 ISSN: 1314-684X (print), 1314-7218 (online)