The Effect of Susceptible Immigrants in a System Dynamic on the Spread of Malaria in Indonesia

Abstract

The spread of malaria is a serious public health problem, including in Indonesia. The mathematical model is formulated to describe the dynamic nature of the spread of malaria. The model used in this article is the SIR-SI model. This article discusses the stability of the fixed point analyzed using the Jacobian matrix and Routh-Hurwitz criteria, bifurcation analysis using the Castillo-Chaves and Song Theorem, and numerical simulation of the effect of the rate of susceptible immigrants on the dynamics of the malaria by using data on malaria cases in Indonesia. The results of the analysis show that the stability of the fixed point is related to the basic reproduction number determined by the next-generation matrix, and bifurcation occurs when the basic reproduction number is equal to one. The results of numerical simulations show that in order to suppress the spread of malaria, it is necessary to reduce the rate of susceptible immigrants.

Keywords

• basic reproduction number
• bifurcation
• malaria
• stability
• susceptible immigrants