Dynamics of a prey-generalized predator system with disease in prey and gestation delay for predator

Abstract

In the present study, a prey-generalized predator model is proposed with disease in the prey and gestation delay for predator. The asymptotic behavior of the model is studied for all the feasible equilibrium states. The criterion for local stability of the system are established around steady states and thresholds for Hopf bifurcation are determined at the endemic as well as disease-free state. The respective sensitive indices of the variables are identified at the endemic state by performing the sensitivity analysis. Further numerical simulations have been carried out to justify our analytic findings.

Eco-epidemic Dynamics with Infected Communicable Infection from Prey to Predator: Effect of Recovery Delay for Predator

“…Considering the parameter values specified in [7,28,[46][47][48], we set the following parameters value are: α = 2.5, β = 0.5, r = 4, d 1 = 0.07, d = 0.02, K = 100, α 1 = 0.6, b = 50, b 1 = 20. These values fall within the observed range, except where model solutions were not obtained.…”

“…Among the ratio-dependent functional response is oft regarded as very emphatic in modeling prey-predator interactions [23][24][25][26]. Other studies [27,28] have considered scenarios in which healthy prey exhibit greater activity than infected ones, making them less susceptible to predation by predators. Certain mathematicians [29,30] have developed models incorporating diseases in predator populations, positing that infected predators are unable to effectively hunt healthy prey.…”

Infection dynamics of rabbit and red fox with alternative prey

“…We will first simulate the temporal system (2.1), and then the spatiotemporal system (2.2). We studied the parameter values of [8,21,[28][29][30][31]36] and set range for each parameter. The default parameter values for the model are midway through the given range except where the model solution did not occur.…”

“…Recently many researchers also discussed the dynamical properties of the system where both prey-predator are suffering from an infection [7,13,14,20,27]. It is discussed in [8,31] that healthy prey is active than the infected one. Some articles [6,16] discussed models with the disease in the predator population, where the diseased predator is not capable to predate on healthy prey [6].…”

An epidemic model of childhood disease dynamics with maturation delay and latent period of infection

“…Epidemics is defined as a rapid spread of a infectious disease that infects a large portion of the population in a particular region and this study of disease dynamics is a dominating theme for many biologists and mathematicians (Singh et al 2016;Samanta 2010;Zhang et al 2013;Xu and Ma 2010;Zhou and Cui 2011;Kang and Fu 2015;Upadhyay and Roy 2014;Bansal and Meyers 2012;Liu et al 2013;Gao et al 2013;Tharakaraman et al 2013;Chao et al 2012;Safi and Gumel 2013;Hu et al 2012Hu et al , 2014Alexander and Moghadas 2005;Kaddar et al 2010;Zhang et al 2009;Samsuzzoha et al 2013;Sahu and Dhar 2012;He et al 2013;Sun et al 2011;Liu et al 2007;Tchuenche et al 2011;Liu and Cui 2008;Cui et al 2008a, b;Funk et al 2009). Further, there are a number of diseases, which affects mostly the children, for example, Rubella, Measles, Chickenpox, Polio, Mumps, etc., because premature (child) population is more prone to the diseases than the mature (adult) population Reef et al (2002).…”