Deterministic and stochastic analysis of an eco-epidemiological model

Abstract

Chronic wasting disease (CWD) is a contagious prion disease among the deer family that has the potential to disrupt the ecosystems where deer occur in abundance. To understand the dynamics of this emerging infectious disease, we consider a simple eco-epidemic model where the host population is infected by CWD. Boundedness of the system is established. The structure of equilibria and their linearized stability are investigated. The persistence condition is discussed. By constructing a suitable Lyapunov function, we discuss the global stability of the endemic equilibrium. Local bifurcation (transcritical) around the boundary equilibria is developed. Sufficient conditions for the existence of Hopf-bifurcation are derived. Further, we have also introduced white type of noise into the system to investigate stochastic stability. This suggests that the deterministic model is robust with respect to stochastic perturbation. Some numerical simulations are performed to validate our results.

Study of a fractional‐order model of chronic wasting disease

“…Study of chronic wasting disease (CWD) is very important topic from theoretical as well as ecological point of view. There has been lot of work done on integer‐order models describing CWD . In integer‐order model, Sharp and Pastor studied the effect of carrying capacity on the system, and they observed stable limit cycle when carrying capacity crosses a critical value, but other parameter like disease transmission rate is not focused so much in their work.…”

“…There has been lot of work done on integer-order models describing CWD. 2,7,12 In integer-order model, Sharp and Pastor 12 studied the effect of carrying capacity on the system, and they observed stable limit cycle when carrying capacity crosses a critical value, but other parameter like disease transmission rate is not focused so much in their work. From literature survey, the dynamics of a fractional-order modelling CWD has not studied before.…”

“…In most of the cases, the disease spreads indirectly via environmental contamination, though some literature shows that the disease transmitted through direct transmission . There are several works on chronic wasting disease which may be found in . Other disease model studied in can be applicable to the chronic wasting disease for better understanding the system.…”

“…2,3 There are several works on chronic wasting disease which may be found in. [4][5][6][7] Other disease model studied in [8][9][10][11] can be applicable to the chronic wasting disease for better understanding the system. In 2006, Miller et al 2 developed a chronic wasting disease model by considering well-known susceptible-infected-recover (SIR) models in human.…”

Stability and bifurcation analysis of a diffusive modified Leslie-Gower prey-predator model with prey infection and Beddington DeAngelis functional response

“…Anderson and May [2] were the pioneers for investigating the invasion, persistence, and spread of infectious diseases by formulating an eco-epidemiological prey-predator model. At recent times, many researchers have proposed and studied epidemic and eco-epidemiological models [3] , [4] , [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] . For example, Shaikh et al [6] have investigated the dynamics of an eco-epidemiological system with disease in competitive prey species.…”