A mathematical analysis of Hopf-bifurcation in a prey-predator model with nonlinear functional response

Abstract

In this paper, our aim is mathematical analysis and numerical simulation of a prey-predator model to describe the effect of predation between prey and predator with nonlinear functional response. First, we develop results concerning the boundedness, the existence and uniqueness of the solution. Furthermore, the Lyapunov principle and the Routh–Hurwitz criterion are applied to study respectively the local and global stability results. We also establish the Hopf-bifurcation to show the existence of a branch of nontrivial periodic solutions. Finally, numerical simulations have been accomplished to validate our analytical findings.

Mathematical analysis of the impact of the media coverage in mitigating the outbreak of COVID-19

“…When we consider the infected states and then linearising model (2) about , yields Setting , , , and considering an eigenvalue of the matrix , we then compute the characteristic polynomial as follows Consequently, where, Moreover, referring to the Routh–Hurwitz criterion, it then follows that: From above, since and then the disease-free equilibrium point of the model (2) is locally asymptotically stable [32] , [52] . □…”

Optimal control analysis of a COVID-19 and Tuberculosis (TB) co-infection model with an imperfect vaccine for COVID-19

“…Suppose now that we then have i.e In this case the population is decreasing and since the domain is compact, thus all the solutions remain there, [ 11 , 26 , 39 , 40 , 46 ]. …”

“…Of course, this study only concerns the parameters which appear in the expression of this threshold parameter. Knowing the different transmission parameters of TB and COVID-19 within an area, this study can help to choose the most appropriate and effective control measures [ 20 , 35 , 39 , 40 ]. The local sensitivity analysis that we carry out here allows us to evaluate the effect of a parameter on the basic reproduction number while keeping the other parameters as constant.…”

“…The local sensitivity analysis that we carry out here allows us to evaluate the effect of a parameter on the basic reproduction number while keeping the other parameters as constant. The method consists in calculating the sensitivity index of each parameter [ 35 , 39 , 40 ]. For example, the sensitivity index of with respect to is calculated as follows: Thus, From the values of our parameters, we obtain the sensitivity indices given in Table 1 and Fig.…”

A Complex Dynamic of an Eco-Epidemiological Mathematical Model with Migration

“…In most of the mathematical models, environment has been considered as homogeneous. However, in reality, environment is heterogeneous, and it can be considered as a set of different localities connected by migration [1,2]. In particular, for prey-predator population, infectious diseases coupled with prey-predator model produce a complex dynamic given the multitude of species living in the environment and interacting with each other.…”