Browsing by Author "Anuj Kullu"

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Bifurcation Analysis of a Discrete-Time Tumor Model with Crowley-Martin Functional Response and its Optimal Control Theory
(Springer Science and Business Media Deutschland GmbH, 2025) Itishree Jena; Kaushik Dehingia; Anuj Kullu; Anupam Priyadarshi
Functional response is vital in understanding and controlling disease dynamics through mathematical modeling. This study introduces the Crowley-Martin (C-M) functional response in tumor-host cell interaction dynamics, which accounts for the handling time of healthy host cells in destroying tumor cells and the magnitude of interference among these cells. When both interference and handling time of healthy host cells in destroying tumor cells are zero, tumor cells are eradicated effectively. As these parameters increase, the system shifts to a state of coexistence. The complex dynamics of the model are explored by discretize the continuous model using Euler’s method. The local stability and bifurcation of the model for different parameter values are studied, and appropriate conditions are established. Numerical simulations validate the theoretical results of Flip and Neimark-Sacker bifurcation, revealing complex dynamical behaviors, including chaotic patterns, which suggest disease progression. Based on the chaos appearing in the bifurcation diagrams, we propose an optimal control strategy to control tumor cell growth by introducing chemotherapy drugs. © The Author(s), under exclusive licence to Shiraz University 2025.
ERADICATION OF SCHISTOSOMIASIS THROUGH PUBLIC HEALTH AWARENESS AND APPLICATION OF APPROPRIATE MOLLUSCICIDES TO CONTROL SNAIL POPULATION: AN INTERVENTION STRATEGY
(World Scientific, 2025) Anuj Kullu; Anupam Priyadarshi; Itishree Jena; Nitin Sharma; Parvaiz Ahmad Naik; Sania Qureshi
Schistosomiasis is assumed to be one of the deadliest and overlooked endemic diseases found in tropical and sub-tropical regions, which is increasing at a concerning rate annually. The World Health Organization (WHO) has introduced a new roadmap for neglected tropical diseases from 2021 to 2030, with the elimination of schistosomiasis from all endemic countries as a global objective. In this paper, we develop a compartment model to represent the disease transmission and to understand the impact of parameters including public health awareness, number of parasite eggs, miracidia emergence rate, snail control parameter, and efficacy of pesticides on the dynamics of disease transmission. The basic reproduction number, R0 is calculated using the next-generation matrix method, which serves as a crucial indicator of infection risks. The local stability of disease-free equilibrium and endemic equilibrium is established analytically using R0. Through sensitivity analysis, the key parameters are identified that significantly affect R0. Based on our model analysis, we hypothesize that massive public health awareness along with moderate snail control with efficacious molluscicides (pesticides) is the most sustainable intervention strategy to eradicate the disease from the tropical and sub-tropical regions. © 2025 World Scientific Publishing Company.
Unraveling memory effects and chaos control in a fractional-order tri-trophic food web: insights from iso-spike patterns in bi-parametric plane
(Springer Science and Business Media B.V., 2025) Anuj Kullu; Prajjwal Gupta; Anupam Priyadarshi
Trophic interactions play a crucial role in the functioning of ecological communities. It influences the species coexistence, biodiversity, and ecosystem stability. Traditional integer-order differential models have been widely used to study these ecosystem dynamics but often overlook the critical role of memory effects and long-range interactions in ecological processes. This study introduces a fractional-order tri-trophic intraguild predation (IGP) model that integrates Caputo derivative to incorporate memory effects in the predator–prey dynamics. The model applies Leslie-Gower and Holling type-II functional responses to describe realistic predation behaviors. A key contribution of this work is the introduction of iso-spike method, a new computational approach to visualize and analyze periodic behaviors in fractional-order ecological systems. It maps the frequency and structure of periodic spikes across a bi-parametric space and identifies shrimp-shaped periodic islands—a distinctive feature in bifurcation diagrams. These islands demarcate regions where chaotic dynamics transition into stable periodic behavior due to the influence of memory. The analysis through one-parameter bifurcation diagrams and two-parameter iso-spike diagram reveals that lower fractional orders (stronger memory) induce point stability, suppressing chaotic oscillations, while higher fractional orders (weaker memory) allow chaotic dynamics to persist. These findings suggest that memory effects, represented by fractional-order derivatives, can play a pivotal role in stabilizing ecological systems. Our simulations are performed on the PARAM SHIVAY supercomputing facility (80 cores, 768 GB RAM), which provide a computationally efficient framework for large-scale exploration of dynamic regimes across extensive parameter spaces. This approach not only advances the field of fractional-order modeling but also has significant implications for real-world ecological management. By integrating memory effects through fractional calculus and employing the iso-spike method, this study opens new avenues for modeling ecological systems with complex feedback loops, long-range dependencies, and memory-driven dynamics. The findings show that fractional-order models can better understand and manage ecosystem stability and resilience against environmental changes. © The Author(s), under exclusive licence to Springer Nature B.V. 2025.