Trade-off between fear level induced by predator and infection rate among prey species
- PDF / 1,046,575 Bytes
- 29 Pages / 439.37 x 666.142 pts Page_size
- 14 Downloads / 133 Views
Trade-off between fear level induced by predator and infection rate among prey species Dipesh Barman1 · Jyotirmoy Roy1 · Shariful Alam1 Received: 4 March 2020 © Korean Society for Informatics and Computational Applied Mathematics 2020
Abstract In this article, an eco-epidemic predator–prey model has been considered where the reproduction of susceptible class of prey is assumed to be affected by the induced fear from predators. The positivity and boundedness of solutions along with existence criterion of the non-negative equilibrium points and their local stability analysis have been performed. Hopf-bifurcation analysis with direction around the co-existence equilibrium point is also performed and it is found that the interference competition rate leads the system to Hopf bifurcation and increases the stable co-existence of all the populations. Furthermore, the predator’s induced fear and infection rate among prey species importantly determine the dynamical complexity of the system. Analytical outcomes of the model system suggest that density of infected prey is directly proportional to the level of fear induced by the predator. Extensive numerical simulations have been carried out to validate all the analytical findings. Finally, Hopf-bifurcation curves of co-dimension two are drawn (with special empathises on interference competition rate) to detect various generalised Hopf-bifurcation and zero Hopf-bifurcation points and stability region of the system. Keywords Eco-epidemic model · Fear factor · Hopf-bifurcation · Periodic solution · GH bifurcation · ZH bifurcation Mathematics Subject Classification 92D30 · 92D50 · 34C23
1 Introduction Trait-mediated indirect effects [38] of predators on prey species have got reasonable attention among the researchers during the past few years. Several studies [9,12,16, 26,27] established the fact that density-mediated lethal effects significantly affect the
B 1
Shariful Alam [email protected] Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, India
123
D. Barman et al.
fitness of prey populations. But, few other studies [6,8,30,36,39] suggest that traitmediated effects of fear of predation can dramatically change the total geometry of an ecosystem by altering the foraging behaviour, psychological transformation and basic reproduction rate of prey. These trait-mediated effects, especially fear effect may fluctuate as it is context-dependent. Several examples can be cited in this regard; for example perceived predation risk of garter snake submerge the foraging activity of salamander [23]; birds respond to predator’s sound by leaving their nest in search of safer area due to fear [8]. Due to exposer to predator cues, the live-bearing guppy has to weaken their swimming ability during late stage of pregnancy and circumvent predation risk by clipping brood incarceration time [13] is another classical example of trait-mediated effects. These indirect effects can be fatal for the survival of adults as well as reproductive success of
Data Loading...
