APLIKASI MODEL EPIDEMIK SEIAR-SEI PADA PENYEBARAN PENYAKIT MALARIA DENGAN INFEKSI ASIMTOMATIK DAN SUPER INFEKSI

Authors

  • Stella Maryana Belwawin

DOI:

https://doi.org/10.20956/jmsk.v15i2.5715

Keywords:

Malaria, asymptomatic infection, super infection, basic reproduction number, rule of descrates

Abstract

Abstract

This aim of this study is to determine the point of equilibrium and analyze the stability of SEIAR-SEI model on malaria disease with asymptomatic infection, super infection and the effect of the mosquito's life cycle. This study also aim is to measure the sensitivity of the spread of malaria to the parameters of asymptomatic infections, the rate of treatment, and the rate of birth of mosquitoes through the magnitude of . The method in this research is deductively, through several stage, such as  determination of disease-free equilibrium point and endemic equilibrium point, determination of basic reproduction number (), analyze of the basic reproduction number sensitivity of the spread of malaria to the parameters of asymptomatic infections, the rate of treatment, and the rate of birth of mosquitoes. The endemic equilibrium point was obtained using rule of Descartes. The result show that the change in the value of parameter , , and  has effect on the basic reproduction number (). Treatment factors in the human population influence the elimination of malaria in a population. Whereas asymptomatic infection factors and the birth rate of adult mosquitoes influence the increase in malaria infection.

 

Keywords:  Malaria, asymptomatic infection, super infection, basic reproduction number, rule of descrates.

 

Abstrak

Penelitian ini bertujuan menentukan titik keseimbangan dan menganalisis kestabilan dari model SEIAR_SEI pada penyakit malaria dengan pengaruh infeksi asimtomatik, super infeksi, dan siklus hidup nyamuk. Penelitian ini juga bertujuan mengukur tingkat sensitivitas penyebaran penyakit malaria terhadap parameter infeksi asimtomatik, laju pengobatan, serta laju kelahiran nyamuk.melalu besaran .  Metode yang digunakan dalam penelitian ini adalah metode deduktif dengan langkah-langkah : menentukan titik keseimbangan bebas penyakit dan endemik dan menentukan bilangan reproduksi dasar ). Analisis sensitivitas bilangan reproduksi dasar dilakukan terhadap parameter infeksi asimtomatik, pengobatan, dan laju kelahiran nyamuk. Tititk keseimbangan endemik diperoleh dengan aturan descrates. Hasil yang diperoleh menunjukkan parameter , , dan  berpengaruh terhadap bilangan reproduksi dasar (). Faktor pengobatan berpengaruh terhadap eliminasi penyakit malaria. Sedangkan faktor infeksi asimtomatik dan laju kelahiran nyamuk dewasa berpengaruh terhadap peningkatan infeksi penyakit malaria.

 

Kata kunci: Malaria, Infeksi Asimtomatik, Super Infeksi, Bilangan Reproduksi Dasar, Aturan Descrates .

 

References

. Cai Liming dkk,, 2017. Optimal Control of a Malaria Model with Asymptomatic Class and Superinfection, doi/ 10.1016/j.mbs.2017.03.00.

. Diekmann O. dkk. 1990. On the Definition and the Computation of the Basic Reproduction Rasio R_0 in Models for Infectious Disease. J. Math. Biol. Vol 28: 365-382.

. Lindblade K.A. dkk,, 2013. The silent threat: asymptomatic parasitemia and malaria transmission, Expert Rev. Anti. Infect. Ther., 11(6), , p.623-639.

. Kemenkes R.I., 2016. Eliminasi Malaria Indonesia, www.malaria.id , diakses tanggal 3 Mei 2018.

. Traore Bakary, 2017. A Mathematical Model of Malaria Transmission with Structured Vektor Pupolation and Seasonality, DOI/10.1155/2017/6754097

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Published

2018-12-20

Issue

Vol. 15 No. 2 (2019): JMSK Vol. 15, No. 2, January 2019

Section

Research Articles

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