This study aims to analyze the dynamics of Lassa fever transmission and its impact on the brain and spinal cord then devise and analyze preventive actions. The stability of the infection-free equilibrium point is evaluated; the model’s precision is examined using empirical data; and all parameters are estimated and fitted. Subsequently, the basic reproductive number is determined, and subpopulation trends are observed over time. Sensitivity analysis is conducted to identify critical drivers influencing transmission dynamics. Two-dimensional plots visualize the impact of crucial parameters on the reproductive number. Through a comprehensive literature review and case analysis, an association between Lassa fever and various disabilities is established, including conditions such as encephalitis, hearing loss, ataxia, neuropsychiatric manifestations, meningitis, seizures, and coma. Solutions are devised and analyzed to enhance early detection, treatment, and mitigation of disease.

This study presents a mathematical model for simulating heat transfer in a multi-layer diving suit embedded with phase change materials (PCMs) under hydrostatic pressure. The model incorporates nonlinear thermal conductivity and diffusivity that vary with depth-induced pressure, alongside internal metabolic heat generation. A moving boundary problem is formulated using a one-dimensional Stefan model to capture latent heat effects in the PCM layer. The system is solved using a finite difference scheme for time-dependent regions and a boundary value solver for steady-state analysis. Results demonstrate that pressure-dependent thermal resistance enhances insulation at greater depths, while the PCM layer stabilizes internal temperatures near the melting point. The developed model provides a framework for optimizing thermally adaptive protective systems through rigorous mathematical formulations.

This paper describes the model development process in detail, including the formulation of equations and parameters based on existing knowledge of hair cycle dynamics and immune system interactions. Various analyses are conducted to gain insights into the behaviour of the model. Illustrative simulations are performed to observe the temporal dynamics of the disease progression under different conditions. Sensitivity analysis using eFAST (Extended Fourier Amplitude Sensitivity Test) is employed to identify the most influential parameters affecting the length of the anagen phase in hair follicles affected by alopecia areata. The findings of the study shed light on the complex dynamics of alopecia areata and contribute to a deeper understanding of the disease mechanisms. The model provides a valuable tool for studying autoimmune hair loss diseases and may have implications for the diagnosis and treatment of such conditions. By simulating the immune response and its effects on hair follicles, the model offers insights into potential treatment strategies that can target immune dysregulation. The temporal mathematical model presented in this dissertation provides a comprehensive framework for investigating alopecia areata and understanding its underlying dynamics. The integration of hair cycle dynamics and immune system interactions enhances our knowledge of the disease and opens avenues for future advancements in diagnosis and treatment approaches.

This paper describes the model development process in detail, including the formulation of equations and parameters based on existing knowledge of hair cycle dynamics and immune system interactions. Various analyses are conducted to gain insights into the behavior of the model. Illustrative simulations are performed to observe the temporal dynamics of the disease progression under different conditions. Sensitivity analysis using eFAST (Extended Fourier Amplitude Sensitivity Test) is employed to identify the most influential parameters affecting the length of the anagen phase in hair follicles affected by alopecia areata. The findings of the study shed light on the complex dynamics of alopecia areata and contribute to a deeper understanding of the disease mechanisms. The model provides a valuable tool for studying autoimmune hair loss diseases and may have implications for the diagnosis and treatment of such conditions. By simulating the immune response and its effects on hair follicles, the model offers insights into potential treatment strategies that can target immune dysregulation. The temporal mathematical model presented in this dissertation provides a comprehensive framework for investigating alopecia areata and understanding its underlying dynamics. The integration of hair cycle dynamics and immune system interactions enhances our knowledge of the disease and opens avenues for future advancements in diagnosis and treatment approaches.