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All Journal Pythagoras: Jurnal Matematika dan Pendidikan Matematika CAUCHY: Jurnal Matematika Murni dan Aplikasi Jurnal Mahasiswa Matematika Journal of Innovation and Applied Technology Natural B Jurnal POINTER BAREKENG: Jurnal Ilmu Matematika dan Terapan
Kwardiniya Andawaningtyas
Prodi Matematika Jurusan Matematika FMIPA Universitas Brawijaya
Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Education Energy Engineering Environmental Science Mathematics Mechanical Engineering Physics Transportation

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Journal : Natural B

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HIV/AIDS Dynamics Epidemic Analysis Through Age Group and Internal Competition Influence Marsudi Marsudi; Kwardiniya Andawaningtyas
Natural B, Journal of Health and Environmental Sciences Vol 1, No 1 (2011)
Publisher : Natural B, Journal of Health and Environmental Sciences

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (60.347 KB) | DOI: 10.21776/ub.natural-b.2011.001.01.9

Abstract

Transmission of HIV/AIDS in Indonesia has potential rounding into very hard. How situation of HIV/AIDS epidemics in Indonesia in future still is unclear. This research aims to analyze of HIV/AIDS epidemics dynamics with influence of age group and internal competition through the simple mathematics model. The SI compartment model is obtained by translating mechanism spreading of disease to be presented in the form of system of nonlinear differential equations. The model parameters obtained by estimation use data of HIV/AIDS in Indonesia from relevant literatures. The local and global stability for the equilibrium point is described use analysis of eigenvalues of Jacobian matrix and Lyapunov-LaSalle’s invariant principle. For the case of data of HIV/AIDS in Indonesia 2007, threshold values of infected reproduced ratio, R0= 0.000035 susceptible reproduced ratio, R1= 100.60235 and infection contact rate, R2=3.50192 The HIV/AIDS dynamics model with two age groups and internal competition has a unique disease-free equilibrium point. The disease-free equilibrium point E0*= (34258263.6455834, 0, 0) is locally asymptotically stable and global unstable.
Effect of Birth Rate Simulation and Vaccination on Dynamics Measles Epidemic Patterns Kwardiniya Andawaningtyas; Marsudi Marsudi
Natural B, Journal of Health and Environmental Sciences Vol 1, No 1 (2011)
Publisher : Natural B, Journal of Health and Environmental Sciences

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (75.689 KB) | DOI: 10.21776/ub.natural-b.2011.001.01.12

Abstract

The purpose of this research is to get description about influence of birth rates to the epidemic dynamics pattern of measles is presented as system of nonlinear differential equations. In this case, the epidemic dynamics of measles is of the form of the SEIR model with births which is obtained from four compartments: susceptible, exposed, infectious, and recovered. Then we analyze parameter model (α) to know the influence of change of birth rates to the epidemic dynamics pattern of measles. The changes of birth rates do not alter common pattern of epidemic measles, but the number of epidemic cycle, epidemic process, oscillation process, epidemic size, and time of epidemic convergent changes significantly. If the birth rate increases so does the epidemic cycle, but the epidemic process decreases, the oscillation is faster, and epidemic size converges to higher level value. If the birth rate decreases, the number of epidemic cycle decreases, epidemic process and oscillation take a longer, the epidemic size decreases with higher variance and converges to lower value.
Co-Authors A. Surbakti, Eka Abdul Rouf Alghofari Agustin, Rohmia Dwi Ani Budi Astuti Ardiyani, Evi Astiti, Medya Ning Dikerianto, Goesta Emilia S I Endang Wahyu Handamari Firdaus, Muhammad Rizki Haristyowati, Riska Karim, Corina Karim, Corina Khaqim, Luqman M., Atika Nabila Marsudi, Marsudi Masrukan, Eko Mila Kurniawaty Mubarok, Ahmad Husni Novita, Zella Octavia, Dyta Pramanta, Hermawan Rendy Pramudita, Riski Sa'adah, Umu Saifullah, Mohammad Dicky Setyowati, Nur Fitriana Shankar, Aldyan Shobah, Nuris Sobri Abusini Tendean, Nisa Yulianti Wuryasari Muharini Kusumawinahyu Yundari, Yundari Zuanisa, Rahma