On the Spread of Rabies in Humans and Dogs

Authors

  • Michael Chapwanya* University of Pretoria
  • Yibeltal Terefe University of Pretoria
  • Jean Lubuma

DOI:

https://doi.org/10.11145/cb.v3i1.681

Abstract

Rabies is a fatal disease in dogs as well as in humans. In this work we present a simple model representing rabies transmission dynamics in human and dog populations. Mathematical analysis based on the basic reproduction number, $\mathcal{R}_0$, which is the average number of new infective individuals produced by one infective individual introduced into a completely susceptible population, is presented. It is observed that the disease-free equilibrium is globally asymptotically stable if $\mathcal{R}_0<1$, while it is unstable and there exists a locally asymptotically stable endemic equilibrium when when $\mathcal{R}_0>1$. A nonstandard finite difference scheme that replicates the dynamics of the continuous model is proposed. Numerical tests to support the theoretical analysis are provided.

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Published

2016-04-09

Issue

Vol. 3 No. 1 (2016)

Section

Conference Contributions

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