Communication in Biomathematical Sciences

Dr Fractional Order Optimal Control Model for Tuberculosis with Drug Resistance and Treatment Delay: Mathematical Modeling Approach

2026-01-07T19:04:41+07:00

Tuberculosis (TB) continues to pose a major global public health challenge, especially with the emergence of drug-resistant strains and challenges associated with delayed treatment. In this study, we formulate and analyze a novel fractional order mathematical model to investigate the transmission dynamics of TB incorporating drug resistance and treatment delay. The model is governed by a system of Caputo fractional differential equations to capture the memory and hereditary properties inherent in TB progression. Time-dependent optimal control strategies, including public awareness, prompt treatment, and second-line drug therapy, are introduced to minimize the burden of infectious and drug-resistant cases while reducing associated costs. We establish the positivity, boundedness, existence and uniqueness of the fractional model’s solutions. The reproduction number R₀ is derived and used to examine the local stability of the infection-free equilibrium. Furthermore, we perform sensitivity analysis to assess the impact of key parameters, and numerical simulations are conducted using Grunwald-Letnikov approximation method. The results reveal the significance of timely treatment initiation and continuous awareness campaigns in controlling TB, especially in the presence of drug-resistant strains. The study provides a strong foundation for designing efficient public health interventions and contributes to the growing literature on fractional-order epidemiological modeling

Impacts of Global Warming and Harvesting on a Three-Species Intraguild Prey-Predator System with Variable Carrying Capacity

2026-01-05T17:22:46+07:00

Intraguild predation (IGP) represents a complex ecological interaction in which two species compete for a shared resource while one species preys upon the other. Understanding such dynamics is essential for predicting community stability under environmental and anthropogenic disturbances. A novel three-species intraguild predation model incorporating the effects of global warming, biotic resource dependence, and selective harvesting is considered. The prey and predator populations are assumed to exhibit modified logistic growth, where their intrinsic growth rates are regulated by warming-sensitive terms, and their carrying capacities depend dynamically on a renewable biotic resource. The resource itself evolves according to a feedback mechanism reflecting both regeneration and depletion through species consumption. A constant-effort harvesting strategy is applied to the predator population, coupling ecological and economic dynamics within a unified framework.
The model is formulated as a system of nonlinear ordinary differential equations, and analytical investigations are performed to determine the existence and stability of equilibria using linearization and Jacobian matrix techniques. Further, the study explores Hopf bifurcation conditions, illustrating how warming intensity and harvesting effort jointly influence population persistence and oscillatory behavior. The results reveal that excessive warming or overharvesting can destabilize the system, leading to species extinction or periodic fluctuations, whereas balanced parameter regimes support stable coexistence of all three species. This work offers significant theoretical and ecological insights by bridging climate–ecological feedbacks and bioeconomic factors within intraguild systems. The proposed framework enhances understanding of ecosystem resilience under climate change and exploitation pressures and provides a foundation for developing sustainable resource management and conservation policies in the face of global environmental uncertainty. This work suggests a novel intraguild predation model that concurrently takes into account the dependence on renewable resources, selective predator harvesting, and growth regulated by global warming. The carrying capacities of both prey and predator dynamically evolve through a shared biotic resource that is influenced by species consumption, in contrast to current IGP frameworks. Novel dynamical behaviours, such as coexistence collapse and the appearance of Hopf bifurcation, are caused by the combined influence of warming intensity and harvesting effort. Overall, the model offers new insights into ecosystem resilience under environmental change by integrating ecological interactions, extraction pressure, and climate consequences in a unique way. The analytical findings are validated through Python and Mathematica.

Dynamics and Optimal Control of Tuberculosis Model with Vaccination and Incomplete Treatment: An Implementation to Tuberculosis Data

2026-01-02T17:36:27+07:00

Vaccination is an intervention frequently used to anticipate TB transmission. When TB infection occurs,
treatment failure becomes an important issue to be examined. Hence, in this paper, we propose a TB epidemic
model incorporating vaccination and imperfect treatment. The proposed model involves six human population
classes: susceptible, vaccinated, exposed, infectious treated at home, infectious treated in the hospital, and
recovered. The fundamental properties of the model have been investigated, including the existence, uniqueness,
nonnegativity, and boundedness of the solution. The model has two equilibrium points: the disease-free
equilibrium and the endemic equilibrium. The disease-free equilibrium is locally and globally asymptotically
stable if the basic reproduction number is less than unity. Conversely, the endemic equilibrium is asymptotically
stable. The stability of each equilibrium point has been confirmed through numerical simulations. The proposed
model has also been applied to TB data from the USA, South Korea, and South Africa via parameter estimation.
The parameter estimation results show that the model solution is able to capture the TB data trends with a
very high R-squared value. We also propose an optimal control problem with hospitalization rate control and
educational campaign proportion control. The objective of this control is to minimize TB cases with minimal
control costs. The problem has been solved analytically using Pontryagin’s Minimum Principle and verified
through numerical simulations. The simulations show that the simultaneous implementation of both controls
is the best strategy compared to implementing the two controls separately.

MULTISCALE SIMULATION OF NEURONAL DYNAMICS VIA AN EXTENDED HODGKIN–HUXLEY FRAMEWORK

2025-12-25T02:56:53+07:00

The Hodgkin–Huxley (HH) model is a central element in computational neuroscience, since it provides
a detailed biophysical foundation to describe the electrical excitability of the neuronal membrane. Here we report
a thorough foundation for an HH-based model with memorized dynamics for a capacitive memory term through
Cole–Cole-type RC-ladder circuits, an M-type potassium current for spike-frequency adaptation, and a calcium
current for plateau depolarizations. The equations of motion, including those for the viscous interactions, make up
a ten-dimensional nonlinear system of ODEs, and are integrated numerically employing the standard Runge–Kutta
routine. Furthermore, we augment the model with spatial diffusion to turn it into a hybrid PDE–ODE system
capable of describing the traveling waves on a 1D axon. Simulations show that with memory and adaptive currents,
spiking thresholds and the inter-spike intervals will be completely changed, having more realistic neuronal
dynamics. The outcome confirms that the model can adequately simulate biological action potentials while computationally
stable in stiff ionic kinetics. This model offers a biologically plausible and computationally efficient
means to simulate multiscale neuronal processes.