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Mathematical Medicine and Biology Advance Access published online on September 5, 2007
Mathematical Medicine and Biology, doi:10.1093/imammb/dqm005
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© The author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Role of horizontal incidence in the occurrence and control of chaos in an eco-epidemiological system

Samrat Chatterjee, Kusumika Kundu and J Chattopadhyay{dagger}

Agricultural and Ecological Research Unit, Indian Statistical Institute, 203, B. T. Road, Kolkata 700108, India

{dagger} Email: joydev{at}isical.ac.in

Received on 3 October 2005. Revised on 29 May 2006. Accepted on 25 October 2006.


  Abstract

A predator–prey model with disease in the prey population is proposed and analysed. The mode of disease transmission plays an important role in such dynamics. Keeping this factor in mind, we observe the dynamics of such a system for simple mass action incidence and standard incidence. Our observations indicate that the phenomenon of rarity or non-occurrence of chaos in our proposed model is well defined if the mode of disease transmission follows standard incidence. Moreover, using the method of Latin hypercube sampling, we show that the region of stability increases if the disease transmission follows the standard incidence law.

Keywords: eco-epidemiology; horizontal incidence; chaos; Lyapunov exponent; Latin hypercube sampling


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