Abstract
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.
Highlights
Refs. [1,2,3,4,5] are examples of works that used Lie symmetry approaches for epidemiological models
A mathematical model depicts an actual event employing mathematical terms in order to understand the characteristics of a biophysical phenomenon
We demonstrate the local stability of the model (1) around each of its equilibrium points
Summary
Consider that S(t) and I (t) represent the percentages of susceptible and infected prey populations at time t, and Z (t) denote the number of predators at time t. Consider the following system of differential equations. We first observe that the right-hand sides of the system (1) are continuously differentiable functions in the positive octant, by existence and uniqueness, the theorem systems (1) have a unique solution. X (t) is uniformly bounded for X0 in the positive octant, if the following condition holds μ>. The solution was found uniquely for certain interval (0, t f ) through the PicardLindelof theorem for t f < ∞ when W (t) ≤ x (t f ) < ∞. This would be in direct opposition to the assumption that t f < ∞.
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