PENERAPAN METODE REDUKSI GRAF UNTUK PENENTUAN RO PADA MODEL VECTOR-HOST

Abstract

The basic reproduction number Ro is defined as the number of new infections that occur after one initial infections is introduced into a susceptible population. In epidemiological models of infectious diseases, the basic reproduction number Ro is used as a threshold parameter to determine the condition for disease outbreaks and extinctions. There are many methods availables in literatures for basic reproduction number Ro calculations. In this paper, two methods for basic reproduction number Ro calculations, next generation matrix method and digraph reduction method were considered. Both methods applied to compartmental models that possess a desease free equilibrium point. For example, the next generation matrix method and the digraph reduction method were applied to vector-host model. Since the digraph reduction method avoids the direct calculation of a matrix inverse or determinants as in the next generation matrix method, the digraph reduction method can be practical for large systems and is a good alternative to the next generation matrix method.

Keyword: Basic reproduction number, next generation matrix method, digraph reduction method, vector-host model.