Eco-epidemiological model with fatal disease in the prey

Jana

2023

Preprint

This study explores the impact of fear of predators among prey populations in an eco-epidemiological model where an infectious disease infects prey. An incidence delay is introduced for the transition of the susceptible population into the infected population. Further, the dynamical behavior of the non-delay system is studied by modifying Holling type II functional response incorporating the fading memory. This is based on the concept that the predator’s growth rate not only depends on a single moment from the past but also over the whole past (chiefly, on recent history). The conditions for the existence of all the biologically feasible equilibrium points are established. The criterion for the local stability about equilibrium points of both (non-delay and delay) systems as well as for the global stability around the coexistence equilibria of the non-delay system are established here. Sufficient conditions for the existence of Hopf-bifurcation by taking the force of infection and delay as bifurcation parameters are derived. Numerical simulations are performed to verify the analytical results and illuminate the system’s dynamicity. The system’s complex dynamical behaviors are demonstrated using the bifurcation diagram, phase diagram, and spectrum. It is observed that fears reduce predator density and also convert an unstable (periodic or chaotic) system into a stable one. It is recommended that past influence over a short time interval and a higher value of the cost of fears are necessary to persist a sustainable and stable ecosystem. An effort is made to search for the correlation between the cost of fears and other biologically related parameters (viz., the growth rate of prey, the carrying capacity for prey, the force of infection, fading memory, and incidence delay) to understand the dynamicity of the system. The semi-relative as well as logarithmic sensitivities of the system are applied to the proposed model to observe how much change of a state variable occur due to perturbation of the parameters, like, the force of infection and cost of fears.

Section: Introductionmentioning

confidence: 99%

Impact of fear-effect on a delayed eco-epidemiological model with standard incidence rate, Holling type-II functional response and fading memory

Jana

2023

Preprint

“…Traditionally ecology and epidemiology are two different branches in mathematical biology until Anderson and May 1 intermixed them, creating a new field of research in 1986, which is now known as the eco-epidemiology. Since then many researchers [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] have made significant contributions to this area. For example, Hadeler and Freedman 11 constructed a deterministic eco-epidemiological model where both prey and predator populations suffer from parasitism, and pointed out that the endemic thresholds are different with the traditional equilibrium-based basic reproductive number.…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of a stochastic eco‐epidemiological model with disease in predators

2022

It is widely accepted that epidemics in biological populations and stochasticity in the environments are two important components significantly influencing the real ecosystems. To more accurately reveal developmental changes of the population dynamics and explore effective control methods for infectious disease, in this paper, we first construct a stochastic ecoepidemiological model with disease in predators, and mathematically analyze the fundamental properties of the model. Then, we establish sufficient criterion for the existence of a unique ergodic stationary distribution of the positive solution. Also, we derive sufficient conditions, respectively, for three different extinction scenarios of populations: (i) The predators go extinct, only the prey persists; (ii) both the predators and prey go extinct; and (iii) the disease is eradicated from the system, both the predators and prey persist. Finally, we perform some numerical simulations under different interferences of environment to illustrate the main theoretical results.Especially, we observe that once the disease is eradicated from the system, then the predators and prey will coexist in an oscillatory manner. Our research indicates that the environmental noises have significant impacts on the

“…Anderson and May [9] were the first to combine the two sciences and develop a predator-prey model with population illness. Many publications [10][11][12][13][14], Wang et al [15] examined numerous predator-prey models in the presence of infection in the system, and it was found that the illness is propagated by either prey or predator, or both prey and predator. The infectious illness divides prey-predator models into three categories.…”

Section: Introductionmentioning

confidence: 99%

An Eco-Epidemiological Model Incorporating Harvesting Factors

2021

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.