On new systems of rabies virus using vaccination variable with modification

Area of Science:

• Epidemiology
• Mathematical Biology
• Fractional Calculus

Background:

• Compartmental models like SIR and SEIR are standard for disease modeling.
• Incorporating vaccination into these models is crucial for understanding transmission dynamics.
• Rabies modeling requires adaptation to account for vaccine effects.

Purpose of the Study:

• To develop novel dynamical systems for rabies virus transmission that include vaccination as a variable.
• To apply fractal-fractional calculus to these systems for enhanced analysis.
• To investigate the solvability and predict peak infection scenarios.

Main Methods:

• Modification of standard epidemiological models to include a vaccination variable, creating a five-dimensional system (RVT-Vaccination).
• Generalization of the RVT-Vaccination system using two- and three-dimensional fractal-fractional differential operators.
• Analysis of the systems' solvability using modified fractal-fractional integral operators.

Main Results:

• Development of two distinct fractal-fractional dynamical systems for rabies transmission with vaccination.
• Investigation of system solvability using advanced fractal-fractional operators.
• Estimation of peak infectious individuals and the timing of these peaks under various scenarios.

Conclusions:

• The proposed fractal-fractional models offer a novel approach to understanding rabies transmission dynamics with vaccination.
• The methodology provides tools to analyze system solvability and predict epidemic peaks.
• The study contributes to mathematical epidemiology by integrating vaccination and fractal-fractional calculus.