In this paper, we investigate with a time fractional‐order derivative in three‐species predator‐prey model the presence of prey social behavior. A new approximation for interaction behavior has been considered. For analysis, study divided into two principal parts. First all, local stability equilibria and existence Hopf bifurcation. Then, numerical Caputo fractional operator is utilized to approximate solution model. An excellent agreement seen between results theoretical predictions.

As the COVID-19 is still spreading in more than 180 countries, according to WHO. There a need understand dynamics of this infection and predict its impact on public health capacity. This work aims forecast progress disease three countries from different continents: The United States America, Arab Emirates Algeria. existing data shows that fatality high elderly people with comorbidity. Therefore, we consider an age-structured model. Our model also takes into two main components (a) number...

Abstract In this research, we discuss the influence of an infectious disease in evolution ecological species. A computational predator-prey model fractional order is considered. Also, assume that there a non-fatal developed prey population. Indeed, it considered predators have cooperative hunting. This situation occurs when pair or group animals coordinate their activities as part hunting behavior to improve chances making kill and feeding. model, then shift role standard derivatives...

This research is concerned to study the global threshold dynamics of a hybrid viral infection model, with assumption that all parameters are space dependent. The considered model contains three principal equations, first an ordinary differential equation represents uninfected cells, age-structured modeled by transport for infected-cells, and diffusive studies evolution virus. challenging mathematical aspect this lies in fact partially degenerate solution map not compact. Also, understanding...

We propose a general model to investigate the effect of distinct dispersal coefficients infected and susceptible hosts in pathogen dynamics. The mathematical challenge lies fact that investigated is partially degenerate solution map not compact. spatial heterogeneity parameters diffusion induce infection low-risk regions. In fact, as increases, reproduction particles decreases. dynamics governed by value basic number R 0 . If ≤ 1, then extinct, for > 1 persist, there at least one positive...

To study the consumption of heroin in a heterogeneous environment, we propose and analyze spatiotemporal model with distributed delay. Using spectral theory, determine basic reproduction number , which serves threshold role. If then addiction‐free steady state is globally asymptotically stable while if there at least one addictive state. Moreover, when dispersal coefficients zero, only state, it stable; both diffusions susceptible addicted individuals are present, cannot identify temporal...

In this paper, we study the influence of nonlocal interspecific competition prey population on dynamics diffusive predator‐prey model with social behavior. Using linear stability analysis, conditions for positive constant steady state at which undergoes Hopf bifurcation, T‐H bifurcation (Turing‐Hopf bifurcation) are investigated. The Turing patterns occur in presence and cannot be found original system. For determining dynamical behavior near point, normal form has been used. Some graphical...

Abstract The behavior of any complex dynamic system is a natural result the interaction between components that system. Important examples these systems are biological models describe characteristics interactions certain organisms in environment. study requires use precise and advanced computational methods mathematics. In this paper, we discuss prey–predator model includes two competitive predators one prey with generalized functional. primary presumption construction competition on only...

The current paper deals with the transmission of MERS-CoV model between humans populace and camels, which are suspected to be primary source for infection. effect time disease is explored using a non-linear fractional order in sense Caputo operator this paper. considered analyzed qualitative theory, uniqueness solution discussed by Banach contraction principle. Stability analysis investigated aid Ulam-Hyres (UH) its generalized version. Finally, we show numerical results help...

The present paper is dealt with a predator-prey model in which the growth of prey population influenced by Allee effect while predator species are contended following Crowley-Martin type response function. proposed comprehensively analyzed terms stability and manifestation bifurcation system. system unveils bi-stability together existence separatrix. In view eminence spatial ecology, dynamical complexity emanating from induction reaction-diffusion also investigated profoundly. results...

We are concerned with a reaction-diffusion predator–prey model under homogeneous Neumann boundary condition incorporating prey refuge (proportion of both the species) and harvesting species in this contribution. Criteria for asymptotic stability (local global) bifurcation subsequent temporal system thoroughly analyzed around unique positive interior equilibrium point. For partial differential equation (PDE), conditions diffusion-driven instability Turing region two-parameter space...

In this paper, we study a mathematical model investigating the impact of unreported cases COVID-19 in three North African countries: Algeria, Egypt, and Morocco. To understand how population respects restriction mobility implemented each country, use Google Apple’s reports. These reports help to quantify effect movement restrictions on evolution active infection cases. We also approximate number infected unreported, proportion those that need hospitalization, estimate end epidemic wave....

In this paper, we investigate a predator–prey model with herd behavior and cross-diffusion subject to the zero flux boundary conditions. First, temporal of has been investigated, where Hopf bifurcation obtained. Then, by analyzing characteristic equation it proved that generate complex dynamics such as bifurcation, Turing instability, even Turing–Hopf bifurcation. Further, impact prey shape on spatiotemporal patterns discussed. Furthermore, computing normal form associated point, near point...

In this research, we investigate the influence of predator harvesting on predator–prey interaction in presence prey social behavior using a reaction–diffusion system subject to Neumann boundary conditions. It has been proved that investigated model can undergo Hopf, Turing–Hopf bifurcation, which indicates possibility having homogenous/nonhomogeneous periodic solution under some conditions parameters. The stability these solutions is studied normal form center manifold theory. obtained...