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All Journal Jurnal Mahasiswa Matematika Research Journal of Life Science Natural B

Marsudi, Marsudi

Brawijaya University

Author-ID : 2844184

Agriculture, Biological Sciences & Forestry Biochemistry, Genetics & Molecular Biology Environmental Science Mathematics Medicine & Pharmacology

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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

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

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.

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

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.

Co-Authors AGUS WIDODO Budiati, Lina Dikerianto, Goesta Endang Wahyu Handamari Firdaus, Muhammad Rizki Ganiswara H., Andrias Hady Rasikhun Hidayat, Noor Imam Nurhadi Purwanto Kurniawati, Anisa Fitria Kwardiniya Andawaningtyas Lestari, Retno Putri Mahmudah, Mahmudah Mubarok, Ahmad Husni Pratiwi, R. C. Putri, Anggita Oktaviana R., Rinang Dwi Ratno Bagus Edy Wibowo Rosyida, Indah Cahyani Rosyidah, Lailiyatul Sobri Abusini Tamrin, Ahmad Husni Tunjungsari, Meirdania Fitri Wahyu T.M., Mega Zuhriah, Aminatu

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