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All Journal Research Journal of Life Science Natural B
Ratno Bagus Edy Wibowo
Department Of Mathematics, Faculty Of Mathematics And Natural Sciences, University Of Brawijaya
Agriculture, Biological Sciences & Forestry Biochemistry, Genetics & Molecular Biology Environmental Science Medicine & Pharmacology

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Mathematical model of HIV / AIDS Transmission with Health Education Marsudi Marsudi; Ratno Bagus Edy Wibowo
Natural B, Journal of Health and Environmental Sciences Vol 2, No 1 (2013)
Publisher : Natural B, Journal of Health and Environmental Sciences

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (87.368 KB) | DOI: 10.21776/ub.natural-b.2013.002.01.7

Abstract

In this research has been carried out the stability analysis of HIV/AIDS epidemic model with a public health educational through the expansion of the SI (susceptible-infected) model. In modeling of HIV/AIDS epidemic, the population is divided into six subpopulations: uneducated susceptible individuals, educated susceptible individuals, uneducated infected individuals without AIDS symptoms, educated infected individuals with AIDS symptoms, uneducated infected individuals with AIDS symptoms and educated infected individuals with AIDS symptoms. The disease-free equilibrium point of the HIV transmission model with education program is locally asymptotically stable if the basic reproduction number is less than unity and unstable if the basic reproduction number is greater than unity. The endemic equilibrium point is exist if the effective reproduction number is greater than unity and stability of endemic equilibrium point has been determined using the Center manifold theory. The center manifold theory can be used to analyze the stability near the disease-free equilibrium point (the effective reproduction number is equal to unity). The impact of a public health education on the spread of HIV/AIDS, the sensitivity analysis on effective reproduction numbers respect to all the parameters which drive the disease dynamics.  
Application of Optimal Control Strategies for the Spread of HIV in a Population Marsudi Marsudi; Noor Hidayat; Ratno Bagus Edy Wibowo
Research Journal of Life Science Vol 4, No 1 (2017)
Publisher : Lembaga Penelitian dan Pengabdian kepada Masyarakat, Universitas Brawijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (613.253 KB) | DOI: 10.21776/ub.rjls.2017.004.01.1

Abstract

This paper presents an application of optimal control theory to assess the effectiveness of control measures on the spread of HIV in a population.  This paper formulates and analyzes a deterministic mathematical model with use of condom, screening and therapy as control variables using optimal control theory and Pontryagin’s Maximum Principle. It formulates the appropriate optimal control problem and investigate the necessary conditions for the disease control in order to determine the role of unaware infectives in the spread of HIV using of condom, screening of unaware infective and antiretroviral therapy are used as the control items. The optimality system is derived and solved numerically.
Co-Authors Hidayat, Noor Marsudi, Marsudi