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All Journal ACTA VETERINARIA INDONESIANA Jurnal Informatika Journal of Mathematical and Fundamental Sciences Milang Journal of Mathematics and Its Applications International Journal of Disaster Management Jurnal Matematika Integratif
Hadi Sumarno
Departemen Matematika, Fakultas Matematika Dan Ilmu Pengetahuan Alam, Institut Pertanian Bogor
Agriculture, Biological Sciences & Forestry Humanities Astronomy Chemistry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Electrical & Electronics Engineering Engineering Environmental Science Mathematics Mechanical Engineering Physics Social Sciences Transportation Veterinary

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Journal : Journal of Mathematical and Fundamental Sciences

 1 
Analysis of SIS-SI Stochastic Model with CTMC on the Spread of Malaria Disease Niswah Yanfa Nabilah Syams; Hadi Sumarno; Paian Sianturi
Journal of Mathematical and Fundamental Sciences Vol. 53 No. 2 (2021)
Publisher : Institute for Research and Community Services (LPPM) ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/j.math.fund.sci.2021.53.2.1

Abstract

Various mathematical models have been developed to describe the transmission of malaria disease. The purpose of this study was to modify an existing mathematical model of malaria disease by using a CTMC stochastic model. The investigation focused on the transition probability, the basic reproduction number (R0), the outbreak probability, the expected time required to reach a disease-free equilibrium, and the quasi-stationary probability distribution. The population system will experience disease outbreak if R0>1, whereas an outbreak will not occur in the population system if R0≤1. The probability that a mosquito bites an infectious human is denoted as k, while θ is associated with human immunity. Based on the numerical analysis conducted, k and θ have high a contribution to the distribution of malaria disease. This conclusion is based on their impact on the outbreak probability and the expected time required to reach a disease-free equilibrium.
An Analysis of CTMC Stochastic Models with Quarantine on the Spread of Tuberculosis Diseases Fatimatuzzahroh; Hadi Sumarno; Paian Sianturi
Journal of Mathematical and Fundamental Sciences Vol. 53 No. 1 (2021)
Publisher : Institute for Research and Community Services (LPPM) ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/j.math.fund.sci.2021.53.1.3

Abstract

The SIQRS epidemic model developed in this study is intended to analyze the spread characteristics of the infectious disease tuberculosis. It is a modification of the SIQR model developed by Cao et al., using a stochastic model called the Continuous Time Markov Chains (CTMC) approach. Further analysis of the SIQRS model was done to determine the transitional probability, the outbreak probability, the expected time until disease extinction and to simulate the effect of quarantine treatment on the expected time until disease extinction. Based on the simulation it can be concluded that a decrease of the healing rate together with an increase of the transmission rate changes the basic reproduction number (R0), the expected number of infected individuals (m), the time until disease extinction, and the outbreak probability. A disease outbreak will occur if both R0>1 and m>1 hold. Also, based on the simulation it was concluded that the decrease of the healing rate and the increase of the transmission rate cause increases of R0 and m. An increase of the quarantine rate reduces the expected time to disease extinction, R0 and m. As a consequence, the disease will gradually disappear from the system.
Co-Authors Ahmad Fajri Ali Kusnanto Ali Kusnanto Andri Hermawan Benediktus Nugroho Adi Wiyoto Cherry Galatia Ballangan Dadang Jaenudin Dadang Rahmat Nugraha Dini Dessya Luthfiani Euis Sunarti Fatimatuzzahroh I Gusti Putu Purnaba I Wayan Mangku Intan Islamia M Agus Setiadi Mutia Annisa N. K. Kutha Ardana Niswah Yanfa Nabilah Syams Paian Sianturi Paian Sianturi Ruhiyat Ruhiyat Sri Rahayu Yolwi Dyatma Yolwi Dyatma