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.

In this article, we study a fractional-order prey-predator model incorporating prey refuge and predator harvesting, employing a Holling type III functional response. The model’s dynamics are explored using the consumption number C 0 , providing a comprehensive understanding of its ecological implications. We establish the existence and uniqueness of the solution, ensuring the model’s mathematical robustness. Stability analysis is conducted to determine the conditions under which the system remains in equilibrium. Sensitivity analysis is performed to assess the importance of various parameters on the system’s behaviour with respect to the consumption number. Additionally, we investigate the occurrence of transcritical bifurcations, utilizing the prey refuge as a bifurcation parameter. Numerical simulations are carried out to illustrate the theoretical results and to provide deeper insights into the model’s dynamics. Our findings contribute to the understanding of fractional-order systems in ecological modelling and offer valuable perspectives on the management of predator-prey interactions in the presence of prey refuge and predator harvesting.

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.