Modeling and Simulation, Applied Mathematics, Computational Mathematics, Ecology, Evolution, Behavior and Systematics
38
Scopus Publications
Scopus Publications
A fractional-order hepatitis B transmission model with Atangana–Baleanu derivative incorporating sociobehavioral and governmental interventions Randhir Singh Baghel Discover Public Health, 2026 Hepatitis B virus (HBV) remains a major global health challenge due to its high transmission potential, chronic progression, and significant morbidity. In this study, we formulate and analyze a novel fractional-order compartmental model for Hepatitis B dynamics, incorporating Atangana–Baleanu–Caputo (ABC) derivatives and a Beddington–DeAngelis-type incidence rate. The model accounts for preventive awareness efforts among susceptible individuals, as well as the suppressive impact of treatment on infected populations. Rigorous mathematical analysis is carried out, including the positively invariant region, existence and uniqueness of solutions, equilibrium points, local and global stability, and the computation of the basic reproduction number $${R}_{0}$$ using the next-generation matrix approach. Bifurcation analysis reveals the occurrence of a forward bifurcation at $${R}_{0}=1$$ , highlighting the transition from a disease-free state to an endemic state. A sensitivity analysis identifies key parameters influencing $${R}_{0}$$ , particularly the transmission rates from acutely and chronically infected individuals, and the rates of government-led awareness campaigns. Numerical simulations, based on a novel iterative scheme for fractional differential equations, demonstrate the significant role of memory effects in HBV transmission dynamics. Comparative results with the classical integer-order model show that the ABC fractional model more effectively captures the hereditary and long-term memory effects of the disease. The findings suggest that strengthening awareness efforts and improving their effectiveness are as critical as medical interventions in reducing Hepatitis B prevalence. This work provides both theoretical insights and practical guidance for policymakers, offering a comprehensive framework for the control and long-term management of Hepatitis B infection.
Delayed dynamics and detoxification in nutrient-phytoplankto-by-product systems: mechanisms driving bloom stability and oscillations Randhir Singh Baghel, Shrikant Verma, Narendra Khatri Scientific Reports, 2026 Phytoplankton blooms emerge from the interplay between nutrient availability, biomass growth, and inhibitory by-products such as toxins or exudates. Here, we develop a mechanistic nutrient–phytoplankton–by-product model that couples Beddington–DeAngelis nutrient uptake, by-product-mediated inhibition, and nutrient-dependent detoxification. Analytical results demonstrate that the system remains biologically feasible and bounded, and that a threshold condition governs bloom initiation. Linear stability and bifurcation analyses reveal how detoxification delays can trigger oscillatory bloom behaviour. Across ecologically realistic parameter regimes, the system tends to a stable coexistence state—either directly or through damped oscillations—rather than exhibiting repeated bloom–crash cycles. Global sensitivity analysis (PRCC and Sobol indices) highlights by-product production, inhibition strength, detoxification rate, toxin-linked mortality, and saturation effects as dominant regulators of stability and damping time. Introducing an explicit ecological delay exposes a critical threshold at which a Hopf bifurcation arises, converting the stable equilibrium into sustained oscillations. Numerical simulations confirm the transversality condition and indicate a supercritical onset. Collectively, these results provide a quantitative diagnostic for distinguishing transient from sustained bloom oscillations and identify measurable ecological processes—particularly detoxification and delayed feedback—that govern transitions between stable and oscillatory regimes.
Hybrid deterministic-stochastic modeling of epidemic spread: Analytical insights and numerical evidence from an Ornstein-Uhlenbeck SEIR framework Randhir Singh Baghel Chaos, 2026 Understanding how environmental variability influences infectious disease dynamics is fundamental to realistic epidemic modeling and control. In this work, we develop and analyze a hybrid deterministic–stochastic SEIR (susceptible–exposed–infectious–recovered) model in which the transmission and treatment rates evolve as mean-reverting Ornstein–Uhlenbeck (OU) stochastic processes. This formulation captures correlated environmental fluctuations that cause key epidemiological parameters to vary above and below their mean levels, bridging the gap between classical deterministic frameworks and realistic stochastic dynamics. We first establish the basic qualitative properties of the deterministic subsystem, including positivity, boundedness, and the existence of biologically feasible equilibria. A closed-form expression for the basic reproduction number R0 is derived, and local as well as global stability of the disease-free and endemic equilibria are rigorously characterized. Bifurcation analysis reveals rich nonlinear behavior, including transcritical, backward, saddle-node, and Hopf bifurcations, indicating the potential for bistability and self-sustained epidemic oscillations. The stochastic extension preserves positivity almost surely and admits analytical conditions for extinction, persistence, and stationary distributions. Numerical simulations demonstrate that environmental noise can induce or suppress outbreaks, alter epidemic amplitude and frequency, and even generate noise-driven periodic cycles. Global sensitivity analysis using partial rank correlation coefficients identifies the transmission rate β, treatment rate a, and noise intensity σβ as dominant factors shaping epidemic outcomes. The results collectively show that stochastic fluctuations are not minor disturbances but can fundamentally reshape epidemic thresholds and long-term behavior. This hybrid OU-driven framework provides a unified and biologically consistent approach for exploring epidemic dynamics under uncertainty, with direct relevance for designing robust and adaptive disease control strategies.
Fractal fractional modelling of fruit disease dynamics with memory and heterogeneity Randhir Singh Baghel, Siddharth Sandeep Huddar, Narendra Khatri Discover Applied Sciences, 2026 Fruit diseases pose a significant threat to agricultural productivity and food security, and their complex dynamics often involve memory effects, latent infection stages, and spatial heterogeneity that classical integer-order models poorly capture. In this study, we develop and analyse a fractal–fractional compartmental model for fruit disease dynamics that extends the standard SEIR-type framework by incorporating both the fractional order $$\:\alpha\:$$ (memory) and the fractal dimension $$\:\beta\:$$ (heterogeneity). We rigorously establish the existence and uniqueness of solutions for the proposed model in the Caputo sense and prove the positivity and boundedness of all state variables. The basic reproduction number $$\:{\mathcal{R}}_{0}$$ is derived as a threshold parameter, and a stability theorem for the disease-free equilibrium is presented. In addition, we investigate the Ulam–Hyers stability, demonstrating robustness with respect to small perturbations in initial data. Comprehensive numerical simulations are performed to assess the impact of varying $$\:\alpha\:$$ and $$\:\beta\:$$ on disease progression in susceptible, exposed, infected, and recovered compartments. The results show that decreasing $$\:\alpha\:$$ delays and reduces epidemic peaks, while varying $$\:\beta\:$$ spreads infection over time and modifies peak magnitudes, thereby reproducing a wide range of outbreak patterns observed in real orchards. These findings highlight the capacity of fractal–fractional models to provide a more realistic description of fruit disease dynamics and to serve as a decision-support tool for designing targeted intervention strategies. This work contributes both a novel mathematical framework and a comprehensive analytical and numerical analysis of its properties, bridging the gap between theoretical modelling and practical disease management. The approach opens new directions for incorporating optimal control, stochastic effects, and data-driven parameter estimation into plant epidemiology in future research.
Operational stability maps for climate-driven predator–prey dynamics: Distributed-order memory & hopf shifts Randhir Singh Baghel Franklin Open, 2026 We develop a distributed-order fractional predator-prey model that incorporates climate-driven thermal forcing, fear-mediated behavioural suppression, and memory-dependent vigilance dynamics. The model is governed by the distributed-order Caputo operatorCDt(μ)x(t)=∫01μ(α)CDtαx(t)dα,which captures a continuum of ecological memory scales. Temperature-dependent demographic rates r(T), a(T), and μ(T) modulate growth, predation, and mortality, while the dynamic fear variable f(t) reduces prey reproduction and encounter rates. We derive positivity, boundedness, and equilibrium conditions, and characterize the onset of oscillations via the Hopf bifurcation threshold G*. Stability analysis shows that distributed-order memory shifts Hopf boundaries and modifies invasion thresholds compared with the classical integer-order limit. A global sensitivity analysis using partial rank correlation coefficients (PRCC) and Sobol indices identifies temperature elasticities θr, θβ, and θμ as dominant drivers of the predator invasion number Ry, while fear suppression sp and low-order memory weights strongly influence G*. A climate-driven zooplankton-phytoplankton case study illustrates how warming and behavioural feedback jointly shape predator-prey resilience, highlighting scenarios in which distributed-order memory dampens oscillations and expands the region of stable coexistence.
Stochastic dynamics of nutrient-phytoplankton-by-product systems under environmental variability: Gaussian noise and feedback regulation Randhir Singh Baghel, Sarthak VP, Narendra Khatri Discover Applied Sciences, 2026 In this study, we develop and analyze a stochastic nutrient–phytoplankton–by-product model that captures the coupled effects of resource limitation, self-inhibition, and random environmental variability in aquatic ecosystems. Starting from a deterministic formulation, we establish the existence of positive equilibria and derive local stability conditions using the characteristic polynomial and Routh–Hurwitz criteria. Bifurcation analysis identifies parameter thresholds where steady states lose stability, leading to oscillatory or unstable nutrient–phytoplankton cycles. Extending the model into a stochastic framework with multiplicative Gaussian noise, we prove the existence of a unique positive global solution, demonstrate boundedness, and derive persistence and extinction criteria through Lyapunov and generator-based methods. Numerical simulations implemented using Higham’s higher-order stochastic scheme confirm the analytical results, showing that environmental fluctuations can induce transient blooms, damped oscillations, or stochastic collapses depending on parameter values. The results highlight how noise intensity and feedback regulation jointly shape long-term ecosystem stability, offering quantitative insight into how variability in nutrient supply and inhibitory by-products influences phytoplankton under fluctuating environmental conditions.
Leveraging Secure Federated Learning for Data-Driven Business Decisions Udit Mamodiya, Randhir Singh Baghel Adversarial AI and Data Poisoning in Federated Learning, 2026 In the age of data-based business, organizations depend more and more on wide analysis to inform strategic decisions. However, the growing concerns around data privacy, regulatory compliance, and inter-cooperation are significant challenges. This chapter explores how secure federated learning (SFL) provides a transformative approach to business strategy by enabling the training of machine learning models in collaboration with multiple entities without sharing sensitive data. We examine the underlying principles of federated education, differential privacy and encryption, and practical architectures for entertainment deployment. Through real-world examples, this chapter explains SFL.
DYNAMICAL STUDY OF TRI-TROPHIC HYBRID FOOD WEBS WITH SPATIAL EFFECT: A HIGHER ORDER ANALYSIS Dynamics of Continuous Discrete and Impulsive Systems Series A Mathematical Analysis, 2024
Spatiotemporal based predator-prey harvesting model for fishery with Beddington-DeAngelis type functional response and tax as the control entity Dynamics of Continuous Discrete and Impulsive Systems Series A Mathematical Analysis, 2019
Bifurcation and spatial pattern formation in spreading of disease with incubation period in a phytoplankton dynamics Electronic Journal of Differential Equations, 2012
