An Epidemic Model of Zoonotic Visceral Leishmaniasis with Time Delay

  • L. Adamu Department of Mathematical Sciences, Bayero University, Kano, Nigeria.
  • N. Hussaini Department of Mathematical Sciences, Bayero University, Kano, Nigeria
Keywords: ZVL, Stability, Hopf bifurcation, Time delay

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.

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Published
2019-10-23
How to Cite
Adamu, L., & Hussaini, N. (2019). An Epidemic Model of Zoonotic Visceral Leishmaniasis with Time Delay. Journal of the Nigerian Society of Physical Sciences, 1(1), 20-29. Retrieved from https://journal.nsps.org.ng/index.php/jnsps/article/view/5
Section
Original Research