The biological system relies heavily on the interaction between prey and predator. Infections may spread from prey to predators or vice versa. This study proposes a virus-controlled prey-predator system with a Crowley–Martin functional response in the prey and an SI-type in the prey. A prey-predator model in which the predator uses both susceptible and sick prey is used to investigate the influence of harvesting parameters on the formation of dynamical fluctuations and stability at the interior equilibrium point. In the analytical section, we outlined the current circumstances for all possible equilibria. The stability of the system has also been explored, and the required conditions for the model’s stability at the equilibrium point have been found. In addition, we give numerical verification for our analytical findings with the help of graphical illustrations.

In an ecological point of view, fears from predator cause physiological changes of prey population and these physiological changes may reduce the reproduction of prey. This paper deals with studying the effect of fear that is incorporated in the growth rate of prey on the dynamics of a delay ecological model consisting of two logistically growing prey species, namely, prey X and prey Y , and a predator species. The predators take energy and biomass on predating on prey X as well as prey Y with extended Holling Type II functional response. We conduct a thorough analytical examination of the system, demonstrating the positivity and boundedness of the solutions. Criteria for the persistence of the model are founded. Seven biologically possible steady states are determined, and the local dynamics around the steady states based on the parameters are also investigated. Next, we investigated the occurrence of Hopf bifurcation around the prey X – and Y –free steady state, by taking the value of the time delay as a bifurcation parameter. Finally, we perform extensive numerical simulations to support the evidence of our analytical results and reveal the occurrence of Hopf bifurcation within the proposed model.

In this paper, the effect of contaminated object on an SIRS Model with vaccination and hospitalization compartments is modeled. Positivity and boundedness properties of the solutions of model are proved, basic reproduction number of the model is founded through criteria which make the eigen values of the Jacobean matrix at the disease free equilibrium point, negative. Globally stability analysis of the disease free equilibrium point is proved when the basic reproduction number is less than unity and the vaccination efficacy approaches unity. The existence, uniqueness of the endemic equilibrium point are investigated when the basic reproduction number greater than unity. Parameter values regarding to spreading covid-19 in Kurdistan region are estimated. Finally, sensitivity analysis of the reproduction number is carried out.

This paper deals with dynamical analysis of a food-web including three logistically growing interaction species, prey, intermediate predators and apex predators. The intermediate predator species predate the prey species according to the Holling type-II functional response, while the apex predator species predate both prey species and intermediate predator species according to extended Holling type II functional response for two prey species. Firstly, the criteria that make the model permanent are determined and then all biologically possible steady states are explored, and their local stability as well as global stability is analyzed based on the sample parameters. The occurrence of Hopf-bifurcation of thee model near all steady states, are discussed. Finally, with the help of MATLAB program, it is performed numerical simulations to support the evidence of our analytical results.

In ecological point of view, fears from predator may reduce the reproduction of prey and harvesting and intraspecific competition among predators, may changes the behavior of dynamical interaction between predator and their prey. In this paper, a Holling Type II prey–predator model with SI ‐type of disease in prey has been modified and analyzed. Firstly, some properties like positivity and boundedness of the solutions of the model are proved and then the criterion that makes the model equilibrium points persist is determined. The criterion for locally as well as globally asymptotically stable of the each model is investigated. The application of the hypothesis of the Sotomayor theorem for local bifurcation near the equilibrium points is adopted. Finally, further investigations for the global dynamics and confirmation the analytical results of the system are carried out with the help of numerical simulations. It is observed that both fear and harvesting rate may cause extinction in the predator.

The aim of this paper is to consider and analyze the dynamic behavior of a modified Leslie-Gower prey-predator model with SIS-disease in predator incorporating prey protection and harvesting factor. The disease is spread from one predator to another through two ways. Physical contact; or external source. Firstly, the details of the assumptions in the proposed model and the significant of the parameters used in are discussed. Then the boundedness of the model is proved, certain conditions for persistence of the model are given and the existence as well as stability analysis of all possible non-negative equilibrium points is studied. Finally, to confirm our analytical finding we discussed numerical simulation of the model.