Abstract
This paper presents a mathematical model with time delay for the transmission dynamics of zoonotic visceral leishmaniasis (ZVL which is caused by protozoan parasite leishmania infantum and transmitted by female sandflies). Qualitative analysis of the ODE version of the model reveals that the disease-free equilibrium of the model is globally asymptotically stable when the basic reproduction number, R0, is less than unity. Using time delay as a bifurcation parameter in the delay-differential version of the model, it has been shown that the incubation period has a significant effect on the stability of the equilibria and we derived the condition for Hopf bifurcation to occur.
Highlights
Leishmaniasis is a disease caused by a group of protozoan parasite called leishmania
Visceral leishmaniasis (VL) known as kala azar has two major forms which differ in their characteristics transmission, namely (i) zoonotic visceral leishmaniasis (ZVL) and (ii) Anthroponotic visceral leishmaniasis (AVL)
This paper presents a new deterministic delay-deferential model for assessing the effect of time delay on the dynamics of ZVL by looking at the stability of the equilibria
Summary
Leishmaniasis is a disease caused by a group of protozoan parasite called leishmania. The incubation periods for humans, sandflies and reservoir range from 2 to 6 months, 8 to 6 days, and 3 to 7 years, respectively [6, 17, 18]. PH = (1 − f1)ζH IH − (β + γ + μH)PH, RH = f1ζH IH + (γ + β)PH − μHRH, S V = ΠV − λV S V IR − μV S V , IV = λV S V IR − μV IV , dynamics of ZVL it is important to incorporate delay caused by the incubation period in the ZVL model. Since the incubation period in the reservoir is the longest in comparison to the time the parasite takes to develop in humans or sandflies. It is instructive to study the effect of ZVL latency period in the reservoir population on the transmission dynamics of the disease.
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