MSEICR Fractional Order Mathematical Model of The Spread Hepatitis B

Abstract

This research aims to develop the MSEICR model by reviewing fractional orders on the spread of Hepatitis B by administering vaccinations and treatment, and analyzing fractional effects by numerical simulations of the MSEICR mathematical model using the method Grunwald Letnikov. Researchers use qualitative methods to achieve the object of research. The steps are to determine the MSEICR model by reviewing the fractional order, looking for endemic equilibrium points for each non-endemic and endemic equilibrium point, determining the equality of characteristics and eigenvalues ​​of the Jacobian matrix. Next, look for values  ​​(Basic Reproductive Numbers), analyze stability around non-endemic and endemic equilibrium points and complete numerical simulations. From the simulation provided, it is known that by giving a fractional alpha value of and  , the greater the value of the fractional order parameters used, the movement of the solution graphs is getting closer to the equilibrium point. If given and still endemic, whereas if and  the value  is increased to non-endemic, then the number of hepatitis B sufferers will disappear.