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A Mathematical Model to Investigate the Long-Term Effects of the Lymphatic Filariasis Medical Treatment in Jati Sampurna, West Java
A.K. Supriatna1,*, H. Serviana2 & E. Soewono3
1Department of Mathematics, Universitas Padjadjaran Bandung
2Department of Mathematics, Universitas Islam Negeri Makassar
3Industrial and Financial Mathematics Group, Institut Teknologi Bandung
* Corresponding author: aksupriatna@bdg.centrin.net.id
Abstract. In this paper we discuss a mathematical model for the transmission of Lymphatic Filariasis disease in Jati Sampurna, West Java Indonesia. The model assumes that acute infected humans are infectious and treatment is given to a certain number of acute infected humans found from screening process. The treated acute individuals are assumed to be remain susceptible to the disease. The model is analyzed and it is found a condition for the existence and stability of the endemic equilibrium. A well known rule of thumb in epidemiological model, that is, the endemic equilibrium exists and stable if the basic reproduction number is greater than one, is shown. Moreover, it is also shown that if the level of screening n is sufficiently large, current medical treatment strategy will be able to reduce the long-term level of incidences. However, in practice it is not realistic and cannot eliminate the disease, in terms of reducing the basic reproduction number. The reproduction number can be reduced by giving additional treatments, such as reducing the biting rate and mosquito's density. This suggests that there should be a combination of treatment to eliminate the disease.
Keywords: Filariasis, mathematical model, basic reproduction number
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