Dynamic analysis of a fractional svir system modeling an infectious disease

Abstract

Infectious diseases that spread by microorganisms, viruses and bacteria that can be transmitted very quickly from person to person and have negative effect on public health should be treated as soon as possible. In order to eliminate structures that are harmful to the body, or strengthen the immune system, which is the totality of cells, structures and processes, individuals are vaccinated and that way the disease is suppressed. Is this manner, infectious diseases are prevented from significantly threatening public health. This paper presents the vaccination effect on an infectious disease modeled by a fractional order SVIR system. The model discussed is defined in terms of the Caputo derivative. The existence and uniqueness of the solutions of the system are handled and stability analysis at the equilibrium numerical solutions of the system are obtained by the Adams Bashforth Moulton method. The results obtained are interpreted according to the reproduction number R-c, which is a threshold parameter for the disease to become epidemic or not. For this purpose, the dependencies of numerical solutions on problem parameters are displayed graphically by Matlab software.