Mathematical Model of Dengue Hemorrhagic Fever with Aedes albopictus Mosquitos as Vector

Abstract

Dengue Hemorrhagic Fever (DHF) is an acute febrile illness caused by a dengue virus. This virus has four serotypes, i.e. Dengue I - IV. The dengue virus is transmitted by various species of Aedes mosquitoes. Mathematical model can be used to study the spread of the disease. The mathematical model discussed in this paper is SEIR model. The main vector of the disease is mosquito of the Aedes albopictus type. In the SEIR model, an analysis is performed to assess the stability of the equilibrium point and numerical simulations. There are two equilibrium points obtained. The first equilibrium point is a disease-free equilibrium (DFE), which is stable, given the basic reproductive number ℜ < 1. The second equilibrium point is called an endemic point, which stability is guaranteed if the value ℜ > 1. The numerical simulations show that increasing mosquitoes mortality rate makes the number of exposed susceptible humans decrease. Furthermore, increase in the average bite of infected mosquito will increase the number of exposed susceptible humans. For the mosquito population, increasing mosquitoes mortality rate will decrease the number of exposed susceptible mosquitoes. Finally, increase in the average bite of infected mosquito will increase the number of exposed susceptible mosquitoes.

Demam Berdarah Dengue (DBD) merupakan penyakit demam akut yang disebabkan oleh virus Dengue. Virus ini memiliki empat serotype virus, yaitu Dengue I – IV (Gubler 1998). Virus ini ditularkan oleh berbagai nyamuk spesies Aedes. Nyamuk ini merupakan vektor yang sangat efisien, sehingga penyakit ini menjadi wabah (epidemi). Berbagai program pengendalian epidemi DBD menjadi prioritas utama WHO dan departemen kesehatan di banyak negara selama ini. Di Indonesia, upaya ini terbilang belum berhasil karena adanya berbagai kendala baik secara teknis maupun non-teknis. Sehubungan dengan banyaknya kendala tersebut, perlu adanya suatu penelitian dan pemikiran yang dilakukan. Pemodelan Matematika dapat membantu memahami dan mengidentifikasi hubungan penyebaran penyakit DBD dengan berbagai parameter epidemiologi. Model matematik yang dimaksud diantaranya ialah model Susceptible, Infected, Recovered (SIR) dan model Susceptible, Exposed, Infected, Recovered (SEIR).