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28 results on '"Roy, Parimita"'

18. Untangling the role of tri-trophic food chain model in sustaining quokka population.

Author

Jain, Sanjoli and Roy, Parimita

Subjects
*BASIC reproduction number, *RED fox, *DINGO, *PREDATION, *ENDANGERED species, *FOOD chains
Abstract

The introduction of predators like red fox and dingoes in the 1930s took a big toll on the quokka population. This paper is mainly concerned with designing conservation policies for quokka population (an endangered species). For this purpose, we designed a reaction–diffusion tri-tropic food chain model consisting quokka and its two predators, red fox and dingoes. We have shown the global existence, non-negativity and uniform boundedness for the designed spatiotemporal model. Existence and stability analysis of the equilibrium points for the model is done. We applied the prevalent idea of basic reproduction number with its origin from epidemiology to the food chain model, to deduce a condition for extinction and persistence of predator population. Natural systems exhibit an amazing diversity of structures in both living and non-living systems. We found that in the presence of diffusion, the model has the potential of exhibiting Turing instability generating beautiful patterns. Numerical results reveal that quokka tends to avoid places resided by dingoes. Our research aims at finding a solution for the current quokka extinction problem by showing the effect of presence of alternative food for dingoes and prohibiting the external factor causing death of quokka population. [ABSTRACT FROM AUTHOR]

Published
2022
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28. Existence of global attractor in reaction–diffusion model of obesity-induced Alzheimer's disease and its control strategies.

Author

Upadhyay, Ranjit Kumar, Pradhan, Debasish, Parshad, Rana D., and Roy, Parimita

Subjects
*ALZHEIMER'S disease, *NEUROFIBRILLARY tangles, *PANCREATIC beta cells, *EXERCISE therapy, *DISEASE management
Abstract

Evidence suggests that obesity, diabetes, and aging notably increase susceptibility to dementia-related conditions such as Alzheimer's disease (AD). This article explores the correlations between obesity, diabetes, and AD. It introduces a diffusion-driven model encompassing variables like glucose dynamics, insulin levels, beta cells, microglia, cytokines, amyloid- β plaques, neurofibrillary tangles (τ plaques), neurodegeneration, and cognitive decline. The study includes stability analysis (local and global), examining boundedness and long-time behavior via showing the existence of a global attractor for the diffusion-driven model. A global sensitivity analysis, utilizing the Partial Rank Correlation Coefficient (PRCC), identifies factors sensitively impacting A β plaque growth, τ plaques, and neurodegeneration. The deterministic model solution illustrates spatiotemporal dynamics, revealing a link between obesity and Alzheimer's, which is characterized by distinct patchy patterns. While Alzheimer's has no cure, employing optimal control techniques can help alleviate its effects and enhance affected individuals' quality of life. An optimal control problem for AD management is developed, optimizing multiple aspects of disease management. The study highlights the efficacy of long-term healthy lifestyle practices and customized anti-amyloid therapy in significantly delaying obesity-induced AD progression. This research sheds light on the connection between obesity and Alzheimer's, underscoring the negative impact of pro-inflammatory microglia on cognitive decline while proposing control strategies. • A model of obesity-led Alzheimer's disease is proposed with its spatial version. • The spatial model examines toxic microglia's role in disease onset and progression. • PRCC uncovers the critical factors driving the growth of A β and τ -plaques. • Simulation of the spatial model produces the disease's patchy pattern of spread. • We suggest optimal control for AD using anti-amyloid beta therapy with exercise. [ABSTRACT FROM AUTHOR]

Published
2025
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