Complexity in a predator-prey-parasite model with nonlinear incidence rate and incubation delay

Adak, Debadatta; Bairagi, Nandadulal

doi:10.1016/j.chaos.2015.09.028

Cited by 19 publications

(4 citation statements)

References 34 publications

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“…In recent past, eco-epidemiological models have received tremendous attention of modelers because these models consider the issues of ecology and epidemiology simultaneously. Various continuous-time models [18,19] and discrete-time models [20][21][22] have been proposed and analyzed considering different attributes of the eco-epidemiological system. In this paper, we consider an ecological system where prey population grows logistically and predator population feeds on it following type 2 response function.…”

Section: Discussionmentioning

confidence: 99%

Analysis of a fractional order eco‐epidemiological model with prey infection and type 2 functional response

Mondal

Lahiri

Bairagi

2017

Math Methods in App Sciences

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In this paper, we introduce fractional order into an ecoepidemiological model, where predator consumes disproportionately large number of infected preys following type 2 response function. We prove different mathematical results like existence, uniqueness, nonnegativity, and boundedness of the solutions of fractional order system. We also prove the local and global stability of different equilibrium points of the system. The results are illustrated with several examples. KEYWORDS ecological model, epidemic model, fractional order, global stability, local stability 6776

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Section: Discussionmentioning

confidence: 99%

Analysis of a fractional order eco‐epidemiological model with prey infection and type 2 functional response

Mondal

Lahiri

Bairagi

2017

Math Methods in App Sciences

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“…In our numerical simulations, we have selected a collection of biologically plausible hypothetical parameter values, which are outlined in Table 1 . Although these values are hypothetical in nature, they are drawn from existing literature sources 27 , 28 , 41 , 42 , 51 , 52 . Notably, these values closely resemble those found in these existing works.…”

Section: Optimal Controlmentioning

confidence: 99%

“…It’s important to note that the crowding effect is negligible when I is small, and in such cases, the two infection rates become equivalent. Subsequently, various other researchers 38 , 40 , 41 have adopted this incidence rate to analyze the dynamics of diverse epidemic models.…”

Section: Introductionmentioning

confidence: 99%

Treatment of infected predators under the influence of fear-induced refuge

Mondal,

Sarkar,

2023

Sci Rep

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In this research, we delve into the dynamics of an infected predator–prey system in the presence of fear and refuge, presenting a novel inclusion of treatment for infected individuals in this type of model. Through our analytical efforts, we establish a significant reproduction number that holds a pivotal role in determining disease extinction or persistence within the system. A noteworthy threshold value for this reproduction number delineates a boundary below which the infected population cannot endure in the system. It’s important to note that a range of reproduction numbers leads to both disease-free and endemic scenarios, yet the stability of these situations is contingent upon the initial population sizes. Furthermore, our investigation extends to the exploration of various types of bifurcation-namely, Backward, Saddle-node, and Hopf bifurcations. These findings unravel the intricate and diverse dynamics of the system. Of particular significance is the derivation of an optimal control policy for treatment, augmenting the practical utility of our work. The robustness of our analytical findings is fortified through meticulous verification via numerical simulations. These simulations not only bolster the credibility of our analytical results but also enhance their accessibility. Our study unveils that fear, refuge, and treatment possess individual capabilities to eradicate the disease from the system. Notably, increasing levels of fear and refuge exert a passive influence on the elimination of the infected population, whereas treatment wields an active influence-a crucial insight that bolsters the foundation of our model. Furthermore, our investigation uncovers a spectrum of system dynamics including bistability, one-period, two-period, and multi-period/chaotic behavior. These discoveries contribute to a profound enrichment of the system’s dynamic landscape.

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“…In system (1.1), bilinear incidence term is used to model the early stage of disease transmission ideally assumed that the susceptible and infected predators are homogeneous mixing. However as the infected transmission progressing, the mixing is no longer homogeneous, and the standard incidence term could better catch the transmission feature and lead to unexpected dynamics ( Adak & Bairagi, 2015 ; Dutta et al., 2022 ; Liu, 2011 ; Saha et al., 2018 ; Tan et al., 2022 ; Xu et al., 2020 ; Yang & Wang, 2019 ).…”

Section: Introductionmentioning

confidence: 99%

The effect of the fear factor on the dynamics of an eco-epidemiological system with standard incidence rate

Zhang

2024

Infectious Disease Modelling

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Complexity in a predator-prey-parasite model with nonlinear incidence rate and incubation delay

Cited by 19 publications

References 34 publications

Analysis of a fractional order eco‐epidemiological model with prey infection and type 2 functional response

Analysis of a fractional order eco‐epidemiological model with prey infection and type 2 functional response

Treatment of infected predators under the influence of fear-induced refuge

The effect of the fear factor on the dynamics of an eco-epidemiological system with standard incidence rate

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