Fear, harvesting, hunting cooperation, and antipredator behavior are all important subjects in ecology. As a result, a modified Leslie-Gower prey-predator model containing these biological aspects is mathematically constructed, when the predation processes are described using the Beddington-DeAngelis type of functional response. The solution's positivity and boundedness are studied. The qualitative characteristics of the model are explored, including stability, persistence, and bifurcation analysis. To verify the gained theoretical findings and comprehend the consequences of modifying the system's parameters on their dynamical behavior, a detailed numerical investigation is carried out using MATLAB and Mathematica. It is discovered that the

This article suggests and explores a three-species food chain model that includes fear effects, refuges depending on predators, and cannibalism at the second level. The Holling type II functional response determines food consumption between stages of the food chain. This study examined the long-term behavior and impacts of the suggested model's essential elements. The model's solution properties were studied. The existence and stability of every probable equilibrium point were examined. The persistence needs of the system have been determined. It was discovered what conditions could lead to local bifurcation at equilibrium points. Appropriate Lyapunov functions are utilized to investigate the overall dynamics of the system. To support the a

It is recognized that organisms live and interact in groups, exposing them to various elements like disease, fear, hunting cooperation, and others. As a result, in this paper, we adopted the construction of a mathematical model that describes the interaction of the prey with the predator when there is an infectious disease, as well as the predator community's characteristic of cooperation in hunting, which generates great fear in the prey community. Furthermore, the presence of an incubation period for the disease provides a delay in disease transmission from diseased predators to healthy predators. This research aims to examine the proposed mathematical model's solution behavior to better understand these elements' impact on an eco-epidemi

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

In the present paper, an eco-epidemiological model consisting of diseased prey consumed by a predator with fear cost, and hunting cooperation property is formulated and studied. It is assumed that the predator doesn’t distinguish between the healthy prey and sick prey and hence it consumed both. The solution’s properties such as existence, uniqueness, positivity, and bounded are discussed. The existence and stability conditions of all possible equilibrium points are studied. The persistence requirements of the proposed system are established. The bifurcation analysis near the non-hyperbolic equilibrium points is investigated. Numerically, some simulations are carried out to validate the main findings and obtain the critical values of th

Globally, the COVID-19 pandemic’s development has presented significant societal and economic challenges. The carriers of COVID-19 transmission have also been identified as asymptomatic infected people. Yet, most epidemic models do not consider their impact when accounting for the disease’s indirect transmission. This study suggested and investigated a mathematical model replicating the spread of coronavirus disease among asymptomatic infected people. A study was conducted on every aspect of the system’s solution. The equilibrium points and the basic reproduction number were computed. The endemic equilibrium point and the disease-free equilibrium point had both undergone local stability analyses. A geometric technique was used

This study has contributed to understanding a delayed prey-predator system involving cannibalism. The system is assumed to use the Holling type II functional response to describe the consuming process and incorporates the predator’s refuge against the cannibalism process. The characteristics of the solution are discussed. All potential equilibrium points have been identified. All equilibrium points’ local stability analyses for all time delay values are investigated. The system exhibits a Hopf bifurcation at the coexistence equilibrium, which is further demonstrated. The center manifold and normal form theorems for functional differential equations are then used to establish the direction of Hopf bifurcation and the stability of the per

The cheif aim of the present investigation is to develop Leslie Gower type three species food chain model with prey refuge. The intra-specific competition among the predators is considered in the proposed model. Besides the logistic growth rate for the prey species, Sokol Howell functional response for predation is chosen for our model formulation. The behaviour of the model system thoroughly analyses near the biologically significant equilibria. The linear stability analysis of the equilibria is carried out in order to examine the response of the system. The present model system experiences Hopf bifurcation depending on the choice of suitable model parameters. Extensive numerical simulation reveals the validity of the proposed model.

In this paper, the general framework for calculating the stability of equilibria, Hopf bifurcation of a delayed prey-predator system with an SI type of disease in the prey population, is investigated. The impact of the incubation period delay on disease transmission utilizing a nonlinear incidence rate was taken into account. For the purpose of explaining the predation process, a modified Holling type II functional response was used. First, the existence, uniform boundedness, and positivity of the solutions of the considered model system, along with the behavior of equilibria and the existence of Hopf bifurcation, are studied. The critical values of the delay parameter for which stability switches and the nature of the Hopf bifurcat

A modified Leslie-Gower predator-prey model with a Beddington-DeAngelis functional response is proposed and studied. The purpose is to examine the effects of fear and quadratic fixed effort harvesting on the system's dynamic behavior. The model's qualitative properties, such as local equilibria stability, permanence, and global stability, are examined. The analysis of local bifurcation has been studied. It is discovered that the system experiences a saddle-node bifurcation at the survival equilibrium point whereas a transcritical bifurcation occurs at the boundary equilibrium point. Additionally established are the prerequisites for Hopf bifurcation existence. Finally, using MATLAB, a numerical investigation is conducted to verify t

A prey-predator interaction model has been suggested in which the population of a predator consists of a two-stage structure. Modified Holling's disk equation is used to describe the consumption of the prey so that it involves the additional source of food for the predator. The fear function is imposed on prey. It is supposed that the prey exhibits anti-predator behavior and may kill the adult predator due to their struggle against predation. The proposed model is investigated for existence, uniqueness, and boundedness. After determining all feasible equilibrium points, the local stability analyses are performed. In addition, global stability analyses for this model using the Lyapunov method are investigated. The chance of occurrence of loc

We propose an intraguild predation ecological system consisting of a tri-trophic food web with a fear response for the basal prey and a Lotka–Volterra functional response for predation by both a specialist predator (intraguild prey) and a generalist predator (intraguild predator), which we call the superpredator. We prove the positivity, existence, uniqueness, and boundedness of solutions, determine all equilibrium points, prove global stability, determine local bifurcations, and illustrate our results with numerical simulations. An unexpected outcome of the prey's fear of its specialist predator is the potential eradication of the superpredator.

Using a mathematical model to simulate the interaction between prey and predator was suggested and researched. It was believed that the model would entail predator cannibalism and constant refuge in the predator population, while the prey population would experience predation fear and need for a predator-dependent refuge. This study aimed to examine the proposed model's long-term behavior and explore the effects of the model's key parameters. The model's solution was demonstrated to be limited and positive. All potential equilibrium points' existence and stability were tested. When possible, the appropriate Lyapunov function was utilized to demonstrate the equilibrium points' overall stability. The system's persistence requirements were spe

Taking into account the significance of food chains in the environment, it demonstrates the interdependence of all living things and has economic implications for people. Hunting cooperation, fear, and intraspecific competition are all included in a food chain model that has been developed and researched. The study tries to comprehend how these elements affect the behavior of species along the food chain. We first examined the suggested model's solution properties before calculating every potential equilibrium point and examining the stability and bifurcation nearby. We have identified the factors that guarantee the global stability of the positive equilibrium point using the geometric approach. Additionally, the circumstances that would gu

     The dynamical behavior of an ecological system of  two predators-one prey updated with incorporating prey refuge and Beddington –De Angelis functional response had been studied in this work, The essential mathematical features of the present model have been studied  thoroughly. The system has local and global stability when certain conditions are met.  had been  proved respectively.  Further, the system has no saddle node bifurcation but transcritical bifurcation and Pitchfork bifurcation are satisfied while the Hopf bifurcation does not occur. Numerical illustrations are performed  to validate the model's applicability under consideration. Finally, the results are included in the form of points in agreement with the obt

A modified Leslie-Gower predator-prey model with a Beddington-DeAngelis functional response is proposed and studied. The purpose is to examine the effects of fear and quadratic fixed effort harvesting on the system's dynamic behavior. The model's qualitative properties, such as local equilibria stability, permanence, and global stability, are examined. The analysis of local bifurcation has been studied. It is discovered that the system experiences a saddle-node bifurcation at the survival equilibrium point whereas a transcritical bifurcation occurs at the boundary equilibrium point. Additionally established are the prerequisites for Hopf bifurcation existence. Finally, using MATLAB, a numerical investigation is conducted to verify the va

Understanding the effects of fear, quadratic fixed effort harvesting, and predator-dependent refuge are essential topics in ecology. Accordingly, a modified Leslie–Gower prey–predator model incorporating these biological factors is mathematically modeled using the Beddington–DeAngelis type of functional response to describe the predation processes. The model’s qualitative features are investigated, including local equilibria stability, permanence, and global stability. Bifurcation analysis is carried out on the temporal model to identify local bifurcations such as transcritical, saddle-node, and Hopf bifurcation. A comprehensive numerical inquiry is carried out using MATLAB to verify the obtained theoretical findings and und

The food web is a crucial conceptual tool for understanding the dynamics of energy transfer in an ecosystem, as well as the feeding relationships among species within a community. It also reveals species interactions and community structure. As a result, an ecological food web system with two predators competing for prey while experiencing fear was developed and studied. The properties of the solution of the system were determined, and all potential equilibrium points were identified. The dynamic behavior in their immediate surroundings was examined both locally and globally. The system’s persistence demands were calculated, and all conceivable forms of local bifurcations were investigated. With the aid of MATLAB, a numerical simu

It is well known that the spread of cancer or tumor growth increases in polluted environments. In this paper, the dynamic behavior of the cancer model in the polluted environment is studied taking into consideration the delay in clearance of the environment from their contamination. The set of differential equations that simulates this epidemic model is formulated. The existence, uniqueness, and the bound of the solution are discussed. The local and global stability conditions of disease-free and endemic equilibrium points are investigated. The occurrence of the Hopf bifurcation around the endemic equilibrium point is proved. The stability and direction of the periodic dynamics are studied. Finally, the paper is ended with a numerical simul

Due to the fact that living organisms do not exist individually, but rather exist in clusters interacting with each other, which helps to spread epidemics among them. Therefore, the study of the prey-predator system in the presence of an infectious disease is an important topic because the disease affects the system's dynamics and its existence. The presence of the hunting cooperation characteristic and the induced fear in the prey community impairs the growth rate of the prey and therefore affects the presence of the predator as well. Therefore, this research is interested in studying an eco-epidemiological system that includes the above factors. Therefore, an eco-epidemiological prey-predator model incorporating predation fear and

It is proposed and studied a prey-predator system with a Holling type II functional response that merges predation fear with a predator-dependent prey's refuge. Understanding the impact of fear and refuge on the system's dynamic behavior is one of the objectives. All conceivable steady-states are investigated for their stability. The persistence condition of the system has been established. Local bifurcation analysis is performed in the Sotomayor sense. Extensive numerical simulation with varied parameters was used to explore the system's global dynamics. A limit cycle and a point attractor are the two types of attractors in the system. It's also interesting to note that the system exhibits bi-stability between these 2 types of attractors.

A modified Leslie-Gower predator-prey model with fear effect and nonlinear harvesting is developed and investigated in this study. The predator is supposed to feed on the prey using Holling type-II functional response. The goal is to see how fear of predation and presence of harvesting affect the model's dynamics. The system's positivity and boundlessness are demonstrated. All conceivable equilibria's existence and stability requirements are established. All sorts of local bifurcation occurrence conditions are presented. Extensive numerical simulations of the proposed model are shown in form of Phase portraits and direction fields. That is to guarantee the correctness of the theoretical results of the dynamic behavior of the system and t

Given that the Crimean and Congo hemorrhagic fever is one of the deadly viral diseases that occur seasonally due to the activity of the carrier “tick,” studying and developing a mathematical model simulating this illness are crucial. Due to the delay in the disease’s incubation time in the sick individual, the paper involved the development of a mathematical model modeling the transmission of the disease from the carrier to humans and its spread among them. The major objective is to comprehend the dynamics of illness transmission so that it may be controlled, as well as how time delay affects this. The discussion of every one of the solution’s qualitative attributes is included. According to the established basic reproductio

     In this paper, the aquatic food chain model, consisting of Phytoplankton, Zooplankton, and Fish, in the contaminated environment is proposed and studied. Modified Leslie–Gower model with Holling type IV functional response are used to describe the growth of Fish and the food transition throughout the food chain, respectively. The toxic substance affects directly the Phytoplankton and indirectly the other species. The local stability analysis of all possible equilibrium points is done. The persistence conditions of the model are established. The basin of attraction for each point is specified using the Lyapunov function. Bifurcation analysis near the coexistence equilibrium point is investigated. Detecting the existence of chao

The avoidance strategy of prey to predation and the predation strategy for predators are important topics in evolutionary biology. Both prey and predators adjust their behaviors in order to obtain the maximal benefits and to raise their biomass for each. Therefore, this paper is aimed at studying the impact of prey’s fear and group defense against predation on the dynamics of the food-web model. Consequently, in this paper, a mathematical model that describes a tritrophic Leslie-Gower food-web system is formulated. Sokol-Howell type of function response is adapted to describe the predation process due to the prey’s group defensive capability. The effects of fear due to the predation process are considered in the first two levels

In this study, the spreading of the pandemic coronavirus disease (COVID-19) is formulated mathematically. The objective of this study is to stop or slow the spread of COVID-19. In fact, to stop the spread of COVID-19, the vaccine of the disease is needed. However, in the absence of the vaccine, people must have to obey curfew and social distancing and follow the media alert coverage rule. In order to maintain these alternative factors, we must obey the modeling rule. Therefore, the impact of curfew, media alert coverage, and social distance between the individuals on the outbreak of disease is considered. Five ordinary differential equations of the first-order are used to represent the model. The solution properties of the system ar

In this paper, we established a mathematical model of an SI1I2R epidemic disease with saturated incidence and general recovery functions of the first disease I1. Considering the basic reproduction number, we obtained conditions for both disease-free and co-existing cases. The equilibrium points local stability is verified by using the Routh-Hurwitz criterion, while for the global stability, we used a suitable Lyapunov function to analyze the endemic spread of the positive equilibrium point. Moreover, we carried out the local bifurcation around both equilibrium points (disease-free and co-existing), where we obtained that the disease-free equilibrium point undergoes a transcritical bifurcation. We conduct numerical simulations that suppo

In this paper,  a Sokol-Howell prey-predator model involving strong Allee effect is proposed and analyzed. The existence, uniqueness, and boundedness are studied. All the five possible equilibria have been are obtained and their local stability conditions are established. Using Sotomayor's theorem, the conditions of local saddle-node and transcritical and pitchfork bifurcation are derived and drawn. Numerical simulations are performed to clarify the analytical results

      A food chain model in which the top predator growing logistically has been proposed and studied. Two types of Holling’s functional responses type IV and type II have been used in the first trophic level and second trophic level respectively, in addition to Leslie-Gower in the third level. The properties of the solution are discussed. Since the boundary dynamics are affecting the dynamical behavior of the whole dynamical system, the linearization technique is used to study the stability of the subsystem of the proposed model. The persistence conditions of the obtained subsystem of the food chain are established. Finally, the model is simulated numerically to understand the global dynamics of the food chain un

A prey-predator model with Michael Mentence type of predator harvesting and infectious disease in prey is studied. The existence, uniqueness and boundedness of the solution of the model are investigated. The dynamical behavior of the system is studied locally as well as globally. The persistence conditions of the system are established. Local bifurcation near each of the equilibrium points is investigated. Finally, numerical simulations are given to show our obtained analytical results.

In this paper, chaotic and periodic dynamics in a hybrid food chain system with Holling type IV and Lotka-Volterra responses are discussed. The system is observed to be dissipative. The global stability of the equilibrium points is analyzed using Routh-Hurwitz criterion and Lyapunov direct method. Chaos phenomena is characterized by attractors and bifurcation diagram. The effect of the controlling parameter of the model is investigated theoretically and numerically.

The aims of this paper is investigating the spread of AIDS both within-host, through the contact between healthy cells with free virus inside the body, and between-host, through sexual contact among individuals and external sources of infectious. The outbreak of AIDS is described by a mathematical model consisting of two stages. The first stage describes the within-host spread of AIDS and is represented by the first three equations. While the second stage describes the between-host spread of AIDS and represented by the last four equations. The existence, uniqueness and boundedness of the solution of the model are discussed and all possible equilibrium points are determined. The local asymptotic stability (LAS) of the model is studied, wh

    The relationship between prey and predator populations is hypothesized and examined using a mathematical model. Predation fear, cannibalism among the prey population, and a refuge reliant on predators are predicted to occur. This study set out to look at the long-term behavior of the proposed model and the effects of its key elements. The solution properties of the model were investigated. All potential equilibrium points' existence and stability were looked at. The system's persistence requirements were established. What circumstances could lead to local bifurcation near equilibrium points was uncovered. Suitable Lyapunov functions are used to study the system's overall dynamics. Numerical simulations were conducted to verify the