Complex dynamics of a predator–prey–parasite system: An interplay among infection rate, predator's reproductive gain and preference

Wave of chaos in a spatial eco-epidemiological system: Generating realistic patterns of patchiness in rabbit–lynx dynamics

“…We will denoteλ + =λ 2 andλ − =λ 3 . Since a [3] 13 < 0 and a [3] 31 > 0, the real parts ofλ 2 andλ 3 will be of the same sign as that of a [3] 11 . Now, if K < K cr = c1(δ+ω4) (ω4−δ) , then a [3] 11 > 0 and two eigenvalues of J (E 3 ) will be positive; hence the proof follows from Sotomayor [58].…”

“…One of the eigenvalues of J (E 3 ) will be zero if and only if det J (E 3 ) = −a [3] 13 a [3] 22 a [3] 31 = 0, i.e. a [3] 22 = 0, since (a [3] 13 , a [3] 31 ) ̸ = (0, 0). This gives β = β * =…”

“…If predators feed upon both susceptible rabbit (S) and infected rabbit (I) of a single species, then selectivity or preference of the predators to susceptible and infected preys plays significant role in the system dynamics [23]. In this case traditional type II functional response should be replaced by multiple-prey type II, which can be mathematically represented by ω 1 S/(S + b 1 I + c 1 ) and ω 2 S/(S + b 1 I + c 1 ) for susceptible and infected rabbits, respectively [3,9,12]. The parameter b 1 measures the selectivity/preference of the predator to infected rabbit over the susceptible one or vice-versa.…”

“…c 1 Prey per unit area Represents the half saturation constant that measures the extent to which the environment provides protection to susceptible and infected rabbit population. b 1 Dimensionless Vulnerability of infected rabbit relative to susceptible rabbit ω 2 Prey per predator per day Maximum predation rate of the infected rabbit population ω 3 Per day Conversion rate of the infected rabbit population to predator population a Per day Total death rate of the infected rabbit population from causes other than predation δ Per day Total death rate of Iberian lynx population To proceed, we next introduce spatial variations to the model system (2.2). We assume that both prey and predator populations perform active movement in x and y directions which has been ignored in previous studies and is biologically relevant.…”

“…As a result, many models have been proposed and studied to investigate the mechanism of disease transmission [3,11,45,54,71]. Roy and Upadhyay [54] designed a spatial eco-epidemiological model with simple law of mass action and Holling type II functional response to understand the extinction dynamics of endangered lynx cat species.…”