This study investigates the influence of fear, refuge, and migration in a predator–prey model, where the interactions between the species follow an asymmetric function response. In contrast to some other findings, we propose that prey develop an anti-predator response in response to a concentration of predators, which in turn increases the fear factor of the predators. The conditions under which all ecologically meaningful equilibrium points exist are discussed in detail. The local and global dynamics of the model are determined at all equilibrium points. The model admits several interesting results by changing the rate of fear of predators and predator aggregate sensitivity. Numerical simulations have been performed to verify our theoret

In the present article, we implement the new iterative method proposed by Daftardar-Gejji and Jafari (NIM) [V. Daftardar-Gejji, H. Jafari, An iterative method for solving nonlinear functional equations, J. Math. Anal. Appl. 316 (2006) 753-763] to solve two problems; the first one is the problem of spread of a non-fatal disease in a population which is assumed to have constant size over the period of the epidemic, and the other one is the problem of the prey and predator. The results demonstrate that the method has many merits such as being derivative-free, overcome the difficulty arising in calculating Adomian polynomials to handle the nonlinear terms in Adomian Decomposition Method (ADM), does not require to calculate Lagrange multiplier a

In this paper, a mathematical model consisting of a prey-predator system incorporating infectious disease in the prey has been proposed and analyzed. It is assumed that the predator preys upon the nonrefugees prey only according to the modified Holling type-II functional response. There is a harvesting process from the predator. The existence and uniqueness of the solution in addition to their bounded are discussed. The stability analysis of the model around all possible equilibrium points is investigated. The persistence conditions of the system are established. Local bifurcation analysis in view of the Sotomayor theorem is carried out. Numerical simulation has been applied to investigate the global dynamics and specify the effect

Global warming has a serious impact on the survival of organisms. Very few studies have considered the effect of global warming as a mathematical model. The effect of global warming on the carrying capacity of prey and predators has not been studied before. In this article, an ecological model describing the relationship between prey and predator and the effect of global warming on the carrying capacity of prey was studied. Moreover, the wind speed was considered an influencing factor in the predation process after developing the function that describes it. From a biological perspective, the nonnegativity and uniform bounded of all solutions for the model are proven. The existence of equilibria for the model and its local stability is inves

A mathematical eco-epidemiological model consisting of harvested prey–predator system involving fear and disease in the prey population is formulated and studied. The prey population is supposed to be separated into two groups: susceptible and infected. The susceptible prey grows logistically, whereas the infected prey cannot reproduce and instead competes for the environment’s carrying capacity. Furthermore, the disease is transferred through contact from infected to susceptible individuals, and there is no inherited transmission. The existence, positivity, and boundedness of the model’s solution are discussed. The local stability analysis is carried out. The persistence requirements are established. The global behavior of th

The aim of this paper is to describe an epidemic model when two SI-Type of diseases are transmitted vertically as well as horizontally through one population. The population contains two subclasses: susceptible and infectious, while the infectious are divided into three subgroups: Those infected by AIDS disease, HCV disease, and by both diseases. A nonlinear mathematical model for AIDS and HCV diseases is Suggested and analyzed. Both local and global stability for each feasible equilibrium point are determined theoretically by using the stability theory of differential equations, Routh-Hurwitz and Gershgorin theorem. Moreover, the numerical simulation was carried out on the model parameters in order to determine their impact on the disease

In this paper, we study the incorporation of the commensalism interaction and harvesting on the Lotka–Volterra food chain model. The system provides one commensal prey, one harvested prey, and two predators. A set of preliminary results in local bifurcation analysis around each equilibrium point for the proposed model is discussed, such as saddle-node, transcritical and pitchfork. Some numerical analysis to confirm the accruing of local bifurcation is illustrated. To back up the conclusions of the mathematical study, a numerical simulation of the model is carried out with the help of the MATLAB program. It can be concluded that the system's coexistence can be achieved as long as the harvesting rate on the second prey population is