Fear induced coexistence in eco-epidemiological systems with infected prey

Rajesh Das; Sourav Kumar Sasmal; Rajesh Das; Sourav Kumar Sasmal

doi:10.3934/mbe.2025107

Mathematical Biosciences and Engineering

2025, Volume 22, Issue 11: 2897-2922. doi: 10.3934/mbe.2025107

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Fear induced coexistence in eco-epidemiological systems with infected prey

Rajesh Das ¹,
Sourav Kumar Sasmal ^{1,2
,
,}

1.
Department of Applied Mathematics and Scientific Computing, IIT Roorkee, Uttarakhand 247667, India
2.
Mathematics, Faculty of Science, University of South Bohemia, Ceske Budejovice 37005, Czech Republic

Received: 10 April 2025 Revised: 04 September 2025 Accepted: 05 September 2025 Published: 17 September 2025

The combined effects of ecological and disease characteristics are examined in eco-epidemiological models, which incorporate infectious illnesses into interaction models. We assumed in this article that the prey population is somewhat infected, and the predator benefits more from eating susceptible prey than from feeding on infected prey. Infected and susceptible prey are equally competitive for resources, and the predator consumes both at the same rate. We employed polar blow-up and time-scale desingularization techniques to tackle the singularity caused by frequency-dependent disease transmission at the origin in our model. For simplicity, we considered the linear functional response for interactions between prey and predators. We aimed to determine the influence of fear of predation on the eco-epidemiological system. According to our findings, there are two ways in which predation fear might support the coexistence of three populations: stable coexistence and oscillatory coexistence. Furthermore, our finding remained unchanged if we eliminated two presumptions: that susceptible and infected prey compete equally for resources and that predators consume both prey at identical rates. We also compared the outcomes by taking into account the growth with positive density dependency (Allee effect) and arrived at the same conclusion.
- eco-epidemiological system,
- coexistence,
- fear effect,
- polar blow-up,
- time-scale desingularization,
- Hopf bifurcation
Citation: Rajesh Das, Sourav Kumar Sasmal. Fear induced coexistence in eco-epidemiological systems with infected prey[J]. Mathematical Biosciences and Engineering, 2025, 22(11): 2897-2922. doi: 10.3934/mbe.2025107

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Abstract

The combined effects of ecological and disease characteristics are examined in eco-epidemiological models, which incorporate infectious illnesses into interaction models. We assumed in this article that the prey population is somewhat infected, and the predator benefits more from eating susceptible prey than from feeding on infected prey. Infected and susceptible prey are equally competitive for resources, and the predator consumes both at the same rate. We employed polar blow-up and time-scale desingularization techniques to tackle the singularity caused by frequency-dependent disease transmission at the origin in our model. For simplicity, we considered the linear functional response for interactions between prey and predators. We aimed to determine the influence of fear of predation on the eco-epidemiological system. According to our findings, there are two ways in which predation fear might support the coexistence of three populations: stable coexistence and oscillatory coexistence. Furthermore, our finding remained unchanged if we eliminated two presumptions: that susceptible and infected prey compete equally for resources and that predators consume both prey at identical rates. We also compared the outcomes by taking into account the growth with positive density dependency (Allee effect) and arrived at the same conclusion.

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