Comparing functional responses in predator-infected eco-epidemics models |
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| Authors: | Mainul Haque Md Sabiar Rahman Ezio Venturino |
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| Institution: | 1. Division of Anaesthesia & Intensive Care, School of Clinical Sciences, Queen''s Medical Centre, University of Nottingham, UK;2. Department of Mathematics, SSHS, WB, India;3. Dipartimento di Matematica, Giuseppe Peano, Università di Torino, Torino, Italy |
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| Abstract: | The current paper deals with the mathematical models of predator–prey system where a transmissible disease spreads among the predator species only. Four mathematical models are proposed and analysed with several popular predator functional responses in order to show the influence of functional response on eco-epidemic models. The existence, boundedness, uniqueness of solutions of all the models are established. Mathematical analysis including stability and bifurcation are observed. Comparison among the results of these models allows the general conclusion that relevant behaviour of the eco-epidemic predator–prey system, including switching of stability, extinction, persistence and oscillations for any species depends on four important parameters viz. the rate of infection, predator interspecies competition and the attack rate on susceptible predator. The paper ends with a discussion of the biological implications of the analytical and numerical results. |
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| Keywords: | Predator&ndash prey models Transmissible disease in predator Intra-specific competition among the predator Limit cycles Biological implications |
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