Understanding the dynamics of infectious diseases using mathematical modeling is essential for developing prevention and control measures. Hepatitis B is still a major public health issue in many places, including Kenya, where the high incidence of illness presents serious difficulties. In this article, the existence and uniqueness of solutions for a fractional hepatitis B model in the Caputo sense were explored. Furthermore, using the Adams-type Predictor-Corrector method, numerical simulations of the fractional order model are carried out. The outcomes show how well the suggested control strategies work to stop the spread of hepatitis B virus.

Infectious illnesses like hepatitis place a heavy cost on global health, and precise mathematical models must be created in order to understand and manage them. The Adomian decomposition method (ADM) and an optimal control strategy are utilized to solve a fractional-order hepatitis model in this research. By adding fractional derivatives to account for memory effects and non-integer order dynamics, the fractional-order model expands the conventional compartmental model to take into account the complexity of hepatitis dynamics. The fractional-order hepatitis model is resolved using the ADM, a powerful and effective analytical approach. This approach offers a series solution that converges quickly, enabling the model’s precise analytical solution to be derived. To identify crucial criteria and enhance control mechanisms for the management of hepatitis, an optimal solution strategy is also introduced. The optimization procedure tries to lessen the disease’s spread and its negative effects on public health. We can find the best interventions, immunization schedules, and treatment regimens to effectively reduce the hepatitis pandemic by integrating the ADM solution with an optimization framework. The findings of this study show that the suggested method may be used to solve the fractional-order hepatitis model and optimize control measures. The analytical solution produced by ADM offers important insights into the underlying dynamics of hepatitis transmission, and the optimization process produces suggestions that public health professionals and politicians may put into practice. In the end, this research presents a promising direction for improving disease control efforts in a fractional-order context and contributes to a deeper understanding of hepatitis epidemiology. The importance of this method is that it gives solutions that coincide with that obtained using the numerical approach.

This study presents a comprehensive mathematical framework that applies fluid dynamics to model the spatial spread of infectious diseases with low mortality rates. By treating susceptible, infected, and treated population densities as fluids governed by a system of partial differential equations, the study simulates the epidemic’s spatial dynamics. The Monotone Upwind Scheme for Conservation Laws is employed to enhance the accuracy of numerical solutions, providing a high-resolution approach for capturing disease transmission patterns. The model’s analogy between fluid flow and epidemic propagation reveals critical insights into how diseases disperse geographically, influenced by factors like human mobility and environmental conditions. Numerical simulations show that the model can predict the evolution of infection and treatment population densities over time, offering practical applications for public health strategies. Sensitivity analysis of the reproduction number highlights the influence of key epidemiological parameters, guiding the development of more efficient disease control measures. This work contributes a novel perspective to spatial epidemiology by integrating principles of fluid dynamics, aiding in the design of targeted interventions for controlling disease outbreaks.

Inefficient heat transfer rates have resulted in high energy consumption costs in heat exchanger systems. In this study, unsteady MHD(Magneto-hydrodynamics) Nanofluid flow (Silver-water) through a divergent conduit with chemical reaction and radiation is investigated. The chemical reactions taking place within the Nanofluid are considered to be of first order with the radiation effects being in a steady state. The governing partial differential equations have been transformed into ordinary differential equations using similarity transformations. The resulting system of non-linear ordinary differential equations is then solved using the spectral collocation method and implemented in MATLAB software. The results for velocity, temperature, and concentration profiles are presented graphically and discussed. It was observed that increasing the Reynolds number and Hartmann number led to an increase in the velocity profile. Increasing the Eckert number and Joule heating parameter increased the temperature profile while increasing the radiation parameter led to a decrease in the temperature of the Nanofluid. The concentration of the Nanofluid increased with an increase in the Soret number and Chemical reaction parameter while the concentration decreased with an increase in the Schmidt number. The findings have practical applications in designing and optimizing heat exchangers by maximizing heat transfer thus contributing to the sustainability of geothermal power generation in the energy industry.