### DYNAMIC ANALYSIS OF A FRACTIONAL SVIR SYSTEM MODELING AN INFECTIOUS DISEASE

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#### Abstract

Infectious diseases spread by microorganisms, viruses and bacteria, which can be transmitted from individual to individual very quickly and adversely affect public health, need to be treated immediately. In order to eliminate the structures that are harmful to the body or to strengthen the immune system, which is the whole of cells, structures and processes, individuals are vaccinated and the disease is suppressed. Thus, communicable diseases are prevented from threatening public health significantly. This paper offers a nonlinear fractional order system for modeling the effects of vaccination on a SVIR infectious disease. To see the memory effect on the system parameters, the model defined by the ordinary differential equation is redefined with the Caputo fractional derivative. Afterwards, the stability analysis and explanations are given about the fractional infectious disease SVIR model, the existence and uniqueness of the system are made. When $R^{c}<1$, it is seen that the disease is under control by vaccination, through the figures obtained with the help of MATLAB for the fractional SVIR model.

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DOI: https://doi.org/10.22190/FUMI211020042O

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