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

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.