(untitled) (Journal of Mathematical Modeling and Fractional Calculus, 2024)
The primary objective of this research is to examine the model of Marburg virus disease with therapy to prevent the infections from spreading throughout the community due to saliva, urine, and feces. A mathematical model is established using the created hypothesis for a healthy environment in order to examine the different rates of Marburg virus disease after taking control measures with treatment for different protection. The model is then converted into a fractional ordered model for continuous monitoring, including theoretical solutions, by using the Fractal Fractional operator. The model’s global stability is studied through Lyapunov derivative by equilibrium and endemic point of model. Both qualitative and quantitative analysis is done on a proposed model with the power law kernel, with particular focus on unique solutions, positivity, and boundedness. By using of fixed point theory and the Lipschitz condition, there is only one exact solution. By confirming the Lyapunov function globally, equilibrium points that are both endemic and disease-free are checked for stability. Numerical simulations are utilized to investigate the effects of the fractal fractional operator on the generalized form of the power law kernel using a two-step Lagrange polynomial approach for ongoing monitoring of the Marburg virus disease and treatment strategies. The simulations show how different parameters affect the illness. In order to simulate the actual behavior and management of Marburg virus disease produced by saliva, urine, and feces and to implement control measures for a healthy environment with a hypersensitive reaction (HR), simulations have been constructed. This type of research will be helpful in figuring out how diseases spread and in developing management strategies based on our verified results for human in community.