Role of standard incidence in an eco-epidemiological system: A mathematical study |
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Authors: | S. Pal Kusumika Kundu J. Chattopadhyay |
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Affiliation: | 1. Department of Mathematics, Ramakrishna Mission Vivekananda Centenary College, Rahara, Kolkata 700118, India;2. Agricultural and Ecological Research Unit, Indian Statistical Institute, 203, B.T. Road, Kolkata 700108, India |
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Abstract: | Ecology and epidemiology are two major fields of study in their own right, but they have some common features. [Chattopadhyay, J., Pal, S., El Abdllaoui, A., 2003. Classical predator–prey system with infection of prey population—a mathematical model. Math. Meth. Appl. Sci. 26, 1211–1222] considered a predator–prey model with disease in the prey population. They analyzed the system based on the assumption that horizontal incidence follows simple mass action incidence. Mass action incidence is appropriate for a constant population, but for a large population, standard incidence is more appropriate. The complicated dynamics around (0, 0, 0) arise because of standard incidence. The conditions under which the population reaches the origin either by following the axis or in a spiral pattern were determined. Numerical experiments were performed to observe the dynamics of the system with mass action incidence and standard incidence. This investigation showed that the infection rate plays a crucial role for predicting the behavior of the dynamics in the long run. |
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Keywords: | Susceptible and infected prey Predator Horizontal incidence Standard incidence Simple mass action incidence |
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