Mathematical study of the influence of canine distemper virus on tigers: an eco-epidemic dynamics with incubation delay

Gupta, Jyoti; Dhar, Joydip; Sinha, Poonam

doi:10.1007/s12215-021-00667-x

Cited by 4 publications

(6 citation statements)

References 30 publications

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“…Considering the parameter values specified in [7,28,[46][47][48], we set the following parameters value are: α = 2.5, β = 0.5, r = 4, d 1 = 0.07, d = 0.02, K = 100, α 1 = 0.6, b = 50, b 1 = 20. These values fall within the observed range, except where model solutions were not obtained.…”

Section: Analysis Of Sensitivitymentioning

confidence: 99%

Eco-epidemic Dynamics with Infected Communicable Infection from Prey to Predator: Effect of Recovery Delay for Predator

Rajawat,

Dhar,

Sinha

2024

Preprint

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In this paper, the system including communicable infection from prey to predator , represented by the growing rate of the prey as a healing of a predator’s, has been utilized to develop and analyze a four-dimensional, non-linear eco-epidemic model. In the context of the analysis, the exploration of all potential equilibrium points, along with an examination of their local stability conditions, has been conducted both with and without considering time delays. Additionally, the confirmation of the model’s positivity and boundedness has been carried out. The positive and negative impact of the proposed model on the prey-predator population has been investigated aided by sensitivity analysis where the presence and validence of Bifurcation were elucidated by the numerical studies. The parameters were identified which explained the influence of disease and recovery delay over the model population. A right base for the perception of the behavioural effects of the prey-predator on eco-epidemiology has been prepared through the theoretical result. Based on the analytical result furthermore, numerical simulations were done so that the authenticity of the author’s numerical analytical approach using parameter values may be verified.

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Section: Analysis Of Sensitivitymentioning

confidence: 99%

Eco-epidemic Dynamics with Infected Communicable Infection from Prey to Predator: Effect of Recovery Delay for Predator

Rajawat,

Dhar,

Sinha

2024

Preprint

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“…The infectious disease dynamics influence the population size of its host and interacting species. A number of researcher incorporated disease in prey and predator [17][18][19][20][21][22][23][24]. Some authors assumed that healthy prey needs more handling time for predators than infected ones [24].…”

Section: Introductionmentioning

confidence: 99%

“…A number of researcher incorporated disease in prey and predator [17][18][19][20][21][22][23][24]. Some authors assumed that healthy prey needs more handling time for predators than infected ones [24]. A variety of researchers in population dynamics incorporated gestation time lags in their research and analyzed the gestation delay's effects on the prey-predator dynamics [25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Effect of multiple gestation delays in a prey–predator food chain system with infected class of prey

Gupta,

Dhar,

Sinha

2024

SeMA

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This article investigates a tri-trophic food chain model with the epidemic at the bottom level (prey) and gestation delays for the next two levels( the intermediate predator and top predator). The steady states' positivity, boundedness, existence, and stability have been analyzed. The study of Hopf bifurcation has been carried out for different steady states. It is shown that when the gestation delay for intermediate predator τ 1 is absent, the interior equilibrium is locally stable for gestation delays of top predators τ 2 ∈ (0, τ + 20 ) and performs Hopf bifurcation for all τ 2 > τ + 20 . Further, in the presence both the delay τ 1 and τ 2 , the system becomes unstable when τ 1 , τ 2 crosses their critical values τ ++ 10 , τ ++ 20

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“…There exists a large volume of literature on ecological models with time delays present in the governing equations. Time-delayed eco-epidemiological models have been investigated in [25,38,12,4,13,29,51]. Qi and Zhao [38] formulated a delayed fractional eco-epidemic model with an extended feedback controller.…”

mentioning

confidence: 99%

“…Several models [25,38,12,4,13,29,51] were studied earlier with a disease in prey, but there are not enough results on models with a disease in the predator population. To fill the research gap, we have constructed a delayed eco-epidemiological model where the predator population is affected by an infectious disease.…”

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confidence: 99%

A brief discussion about a predator-prey model including disease in predators with the delay effect

Das,

Chakraborty

2023

NACO

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Prey-predator interactions in an ecosystem are greatly influenced by the gestation delay and disease. To analyze the complex dynamics of the prey-predator interaction, we have proposed a three-tire delayed eco-epidemic model including disease in the predator population. During the study of this model, we establish the positivity and boundedness of the proposed model and also find all possible equilibrium points with their local and global stability condition in absence and presence of gestation delay. Analytical and numerical studies explain the existence of Transcritical and Hopf-bifurcations. Using sensitivity analysis, we examine the positive and negative impact of all model parameters and identify the most significant parameters. The main objective is to understand how disease and gestation delay influence the populations of this proposed model and also examine the combined effect of both gestation delay and disease infection rate. Furthermore, we incorporate the disease transmission delay and explore the combined effect of both gestation delay and disease transmission delay on the solutions of the proposed system. Numerically, we have demonstrated that the system experiences only steady and periodic behavior under the influence of gestation delay, but under the combined impact of both gestation delay and disease transmission delay, the system undergoes stable, one-periodic, two-periodic, and chaotic regimes.

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Mathematical study of the influence of canine distemper virus on tigers: an eco-epidemic dynamics with incubation delay

Cited by 4 publications

References 30 publications

Eco-epidemic Dynamics with Infected Communicable Infection from Prey to Predator: Effect of Recovery Delay for Predator

Eco-epidemic Dynamics with Infected Communicable Infection from Prey to Predator: Effect of Recovery Delay for Predator

Effect of multiple gestation delays in a prey–predator food chain system with infected class of prey

A brief discussion about a predator-prey model including disease in predators with the delay effect

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