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Bifurcation Analysis in a Dengue Disease Model with Two Virus Serotypes

Fajar Adi-Kusumo, Aurora N. Aini, A. I. Endrayanto, Gunardi

Abstract



Dengue disease is caused by the dengue virus which is classified into four distinct serotypes. The disease is endemic in more than 100 countries in the world. The serotypes which are closely related to each other antigenically are transmitted to the human by the infected female mosquitos. The human infected by the virus will never be infected again with the same serotypes in some period of time. There is a partial immunity for the human after they recovered form the disease. However, there are no cross-protective immunity with the other serotypes. It is possible for the human to be infected again by the same virus with different serotypes. We consider the dengue fever model with two infections from the different serotypes. The human who are recovered from the primary infection by a serotype are assumed to be susceptible with the other serotypes. We use numerical bifurcation analysis to study behavior of the system. We also show the effect of change of the value of parameters to the endemicity condition of the system.

Keywords


dengue, serotypes, two infection, bifurcation.

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