Starvation-recovery dynamics: insights via a nutritional state-structured model

Saiful Rahman Mondal; Saiful Rahman Mondal

doi:10.3934/math.20251161

AIMS Mathematics

2025, Volume 10, Issue 11: 26418-26445. doi: 10.3934/math.20251161

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Starvation-recovery dynamics: insights via a nutritional state-structured model

Saiful Rahman Mondal ^,

Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia

Received: 02 August 2025 Revised: 29 October 2025 Accepted: 05 November 2025 Published: 17 November 2025
MSC : 34B15, 34C60, 34D23, 35C07

This paper presents a nutritional state-structured model (NSM) to explore the dynamics of starvation and recovery in consumer-resource systems, focusing on full consumers ($F$), hungry consumers ($H$), and resources ($R$). The model employs a system of differential equations to capture ecological processes such as reproduction, starvation, and resource regeneration. Through bifurcation analysis, we identified critical thresholds, notably the starvation rate ($\sigma$) relative to the reproduction rate ($\lambda$), that dictate system stability, transitioning between extinction and coexistence equilibria. Parameter sensitive and numerical simulations revealed how parameter variations influence population persistence and resource sustainability, with $\sigma > \lambda$ promoting balanced ecosystems and $\lambda > \sigma$ leading to potential overexploitation. The analogue of the basic reproduction number ($\mathcal{R}_\mathrm{e}$) was derived using the next-generation matrix method, providing insights into the invasion dynamics and stability conditions of the system. This framework serves as a robust tool for analyzing eco-evolutionary interactions and assessing population persistence under resource-limited conditions. Finally, we demonstrated how higher fat reserves enhance competitive advantage, thereby driving the evolutionary trend toward larger body sizes as predicted by Cope's rule.
- starvation dynamics,
- resource replenishment,
- differential equations,
- ecological modeling
Citation: Saiful Rahman Mondal. Starvation-recovery dynamics: insights via a nutritional state-structured model[J]. AIMS Mathematics, 2025, 10(11): 26418-26445. doi: 10.3934/math.20251161

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Abstract

This paper presents a nutritional state-structured model (NSM) to explore the dynamics of starvation and recovery in consumer-resource systems, focusing on full consumers ($F$), hungry consumers ($H$), and resources ($R$). The model employs a system of differential equations to capture ecological processes such as reproduction, starvation, and resource regeneration. Through bifurcation analysis, we identified critical thresholds, notably the starvation rate ($\sigma$) relative to the reproduction rate ($\lambda$), that dictate system stability, transitioning between extinction and coexistence equilibria. Parameter sensitive and numerical simulations revealed how parameter variations influence population persistence and resource sustainability, with $\sigma > \lambda$ promoting balanced ecosystems and $\lambda > \sigma$ leading to potential overexploitation. The analogue of the basic reproduction number ($\mathcal{R}_\mathrm{e}$) was derived using the next-generation matrix method, providing insights into the invasion dynamics and stability conditions of the system. This framework serves as a robust tool for analyzing eco-evolutionary interactions and assessing population persistence under resource-limited conditions. Finally, we demonstrated how higher fat reserves enhance competitive advantage, thereby driving the evolutionary trend toward larger body sizes as predicted by Cope's rule.

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