Received May 29, 2018. Published online October 11, 2018.
Abstract: The paper deals with two mathematical models of predator-prey type where a transmissible disease spreads among the predator species only. The proposed models are analyzed and compared in order to assess the influence of hidden and explicit alternative resource for predator. The analysis shows boundedness as well as local stability and transcritical bifurcations for equilibria of systems. Numerical simulations support our theoretical analysis.
Keywords: hidden prey; explicit prey; bifurcation; predator-prey model
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Affiliations: Luciana Assis, Faculdade de Ciências Exatas e Tecnológicas, Universidade do Estado de Mato Grosso, Av. dos Ingas, 3001 Jardim Imperial, Sinop, Brazil, e-mail: luciana.assis@unemat.br; Malay Banerjee, Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Uttar Pradesh 208016, India, e-mail: malayb@iitk.ac.in; Moiseis Cecconello, Departamento de Ciências Exatas e da Terra, Universidade Federal de Mato Grosso, Cuiabá-Mato Grosso, 78068-600, Brazil, e-mail: moiseis@gmail.com; Ezio Venturino, Dipartimento di Matematica "Giuseppe Peano", Università di Torino, via Carlo Alberto 10, 10123 Torino, Italy, Member of the INdAM research group GNCS, e-mail: ezio.venturino@unito.it
