Open AccessMSEICR Fractional Order Mathematical Model of The Spread Hepatitis B
Author(s) -
Suriani Suriani,
Syamsuddin Toaha,
Kasbawati Kasbawati
Publication year - 2020
Publication title -
jurnal matematika, statistika dan komputasi/jurnal matematika statistik dan komputasi
Language(s) - English
Resource type - Journals
eISSN - 2614-8811
pISSN - 1858-1382
DOI - 10.20956/jmsk.v17i2.10994
Subject(s) - equilibrium point , order (exchange) , stability (learning theory) , value (mathematics) , mathematics , eigenvalues and eigenvectors , fractional calculus , object (grammar) , computer science , mathematical analysis , statistics , physics , economics , finance , quantum mechanics , machine learning , artificial intelligence , differential equation
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.