Journal of
Ecology and The Natural Environment

  • Abbreviation: J. Ecol. Nat. Environ.
  • Language: English
  • ISSN: 2006-9847
  • DOI: 10.5897/JENE
  • Start Year: 2009
  • Published Articles: 389

Full Length Research Paper

An eco-epidemiological mathematical model with treatment and disease infection in both prey and predator population

Alfred Hugo1, Estomih S. Massawe1* and Oluwole Daniel Makinde2
1Mathematics Department, University of Dar es Salaam, P. O. Box 35062, Dar es Salaam, Tanzania. 2Institute for Advance Research in Mathematical Modelling and Computations, Cape-Peninsula University of technology, P. O. Box 1906, Bellville 7535, South  Africa.
Email: [email protected]

  •  Accepted: 20 May 2012
  •  Published: 31 July 2012

Abstract

This paper examines an eco-epidemiological mathematical model with treatment and disease infection in both prey and predator population. A system of differential equations for the problem is proposed and analyzed qualitatively using the stability theory of the differential equations. A local and global study of the model is performed around the disease-free equilibrium and the endemic equilibrium to estimate the effect of incorporated parameters that control disease eradication and species coexistence. Numerical simulations are carried out to justify analytical results. The model with and without infected predator together with treatment classes are finally compared.

 

Key words: Predator-prey system, eco-epidemiology.