Communication in Biomathematical Sciences

A STUDY ON QUADRATIC CONVECTION OF DARCY-FORCHHEIMER CASSON VISCOELASTIC FLOW OVER A STRETCHING SURFACE

Kranthi Kumar, Baby Rani , Papa Rao

The non-linear convective Darcy-Forchheimer Casson liquid over-stretching porous bed in presences momentum slip examined by numerically. Permeability porous media fill the domain. In addition, the thermal conductivity supposed to the variable as well the Brinkman extended Darcy-Forchheimer model is applied to simulate the present case. The leading equations of preserving momentum, conservation energy are nonlinear partial differential equations and coupled due to non-linear Bossiness approximation. Using similarity transformation technique, the transport equations and the respective conditions at the boundary are converted will be in ordinary differential equations and The differential equations obtained via this process have all been solved with help of the 4th order R-K scheme along with the shooting method. Fluid velocity reduced with the rise of Farchheimer parameter and as an impact of inertial force, fluid temperature boosted.

Modelling the Dynamics of Some Common Reported Offenses in Ghana Incorporating Skills training and Employment.

Criminal activities be it minor or serious hugely affects national development and stability of most developing countries. Crime and violence activities of which unemployment is among the causes impose immense social and economic costs worldwide especially in Sub-Saharan Africa. Increase in crime (minor or serious) triggered by high unemployment rate is an issue to policy makers globally. This calls for an innovative modelling intervention framework for effective policy implementation to combat crime in Ghana. In this study, a crime model is formulated that analyze the dynamics of minor and serious offenses in Ghana by incorporating skills training and employment as mitigating (control) tools for crime. The model investigate fundamental modelling concepts like crime reproduction number, sensitivity analysis, crime-free and crime endemic equilibrium points. To support the theoretical aspect, simulations are conducted. From the simulation it is observed that intervention in areas of skilled training and employment by governments will help in reducing criminal activities (minor or serious) in a population.

Mathematical Modeling of Anemia Prevalence Due to Climate-Induced Nutritional Decay

Rifah Tasnia, Shantunu Mondal, Md. Haider Ali Biswas

Anemia is a non-communicable disease afflicting a large portion of the global population. Anemia is the result of a poor hemoglobin concentration in red blood cells. Pregnant women, females in postpartum, and newborns are disproportionately affected by anemia. The human body consumes minerals from a diverse array of food items. Despite the latest agrotechnological developments in large-scale food production, the nutritional scarcity of food items has substantially paved the path of many hazardous diseases e.g., anemia. The nutritional deterioration in the food chain is attributed to a confluence of climate hazards. Elevated carbon dioxide in the atmosphere, soil depletion, soil erosion, etc. are the prime suspects behind this catastrophic incident. A mathematical model captures the essence of the dynamic behavior of natural phenomena. This study has meticulously examined the correlation between nutritional loss and the anemia outbreak. One of its unique contributions is, that it has evaluated the vertical transmission (mother to infant) in the spread of anemia as a major factor. The study establishes evidence for the escalating nutritional degradation that demands sustainable interventions to avert the ongoing spread of anemia on a global scale.

Chapter 1:Mathematical Modeling of Neural–Glial Interactions Under Stress: Insights into Astrocyte, Oligodendrocyte, and Neuronal Dynamics in PTSD

Rifah Tasnia, Shantunu Mondal, Dr. Md. Haider Ali Biswas, Asep K. Supriatna

Post-traumatic stress disorder (PTSD) is characterized by dysregulated neural activity across interconnected brain regions, where stress-induced glucocorticoid signaling alters the dynamics of neuron–glia interactions. In this study, we developed a computational model to investigate neural cell frequency dysregulation in PTSD by formulating a system of nonlinear differential equations that couples astrocytes, oligodendrocytes, and neurons. A unique contribution of this work is the integration of the tripartite synapse framework, extended to explicitly capture astrocyte–oligodendrocyte–neuron interactions under stress modulation. The model incorporates oscillatory stress input, Hill-type nonlinearities, and multi-timescale adaptation to describe feedback mechanisms underlying glial–neuronal communication. Analytical and numerical simulations demonstrate how periodic stress exposure drives abnormal frequency responses, leading to maladaptive neural oscillations. Our findings highlight the critical role of glial modulation in stress-induced network dysfunction and provide a quantitative framework for exploring therapeutic interventions aimed at restoring normal neural frequency dynamics in PTSD.