Articles
<![CDATA[On the Reproduction Ratio of Dengue Incidence in Semarang, Indonesia 2015-2018 ]]>
<![CDATA[Puspita, Juni Wijayanti]]>;
<![CDATA[Fakhruddin, Muhammad]]>;
<![CDATA[Fahlena, Hilda]]>;
<![CDATA[Rohim, Fatkhur]]>;
<![CDATA[Sutimin, Sutimin]]>
<![CDATA[ Communication in Biomathematical Sciences Vol 2, No 2 (2019) ]]>
Publisher : <![CDATA[Indonesian Bio-Mathematical Society ]]>
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DOI: 10.5614/cbms.2019.2.2.5
<![CDATA[Dengue is one of the mosquito-borne diseases caused by dengue viruses (DENV), which has become endemic in most tropical and subtropical countries, including Indonesia. Since there is a lot of dengue incidence on children of age less than fourteen years old in Semarang, Indonesia, it is the interest here to analyze the different rates of infection among different age groups. A SIR-UV mathematical model with age structure in human the population is constructed to describe dengue transmission in Semarang from 2015 to 2018. In this study, we separated the human population into four age classes: children (0-4 years), youngster (5-14 years), productive adults (15-60 years) and non-productive adults (over 60 years). We use Particle Swarm Optimization to obtain optimal parameters for the transmission rates based on the yearly incidence. The basic reproduction ratio (R0) is derived from the Next Generation Matrix and is evaluated by using the optimal parameters for data Semarang in 2015-2018. Numerical simulation results show that the number of dengue incidence is in a good agreement with the actual data in Semarang for 2015-2018.]]>
<![CDATA[Modeling CD4+ T cells and CTL response in HIV-1 infection with antiretroviral therapy ]]>
<![CDATA[Sutimin, Sutimin]]>;
<![CDATA[Sunarsih, Sunarsih]]>;
<![CDATA[Tjahjana, R. Heru]]>
<![CDATA[ Communication in Biomathematical Sciences Vol 1, No 2 (2018) ]]>
Publisher : <![CDATA[Indonesian Bio-Mathematical Society ]]>
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DOI: 10.5614/cbms.2018.1.2.3
<![CDATA[The majority of an immune system infected by HIV (Human Immunodeficiency Virus) is CD4+ T cells. The HIV-1 transmission through cell to cell of CD4+ T cells supports the productive infection. On the other hand, infected CD4+ T cells stimulate cytotoxic T-lymphocytes cells to control HIV-1 infection. We develop and analyze a mathematical model incorporating the infection process through cell to cell contact of CD4+ T cells, CTL compartment and the combination of RTI and PI treatments. By means of the alternative reproduction ratio, it is analyzed the stability criteria and the existence of endemic equilibrium. Numerical simulations are presented to study the implication of the combination of RTI and PI therapy. The results indicate that RTI drug shows more significant effect in reducing HIV-1 infection compared to PI drug.]]>
<![CDATA[ANALISIS BIFURKASI MODEL PERTUMBUHAN TUMOR DENGAN PERSAMAAN LOGISTIK WAKTU TUNDA ]]>
<![CDATA[Dewi, Febriana]]>;
<![CDATA[sutimin, sutimin]]>
<![CDATA[ MATEMATIKA Vol 14, No 1 (2011): JURNAL MATEMATIKA ]]>
Publisher : <![CDATA[MATEMATIKA ]]>
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<![CDATA[In this paper is being studied about the logistic tumor growth model with time delay. The mathematical model is in non-linear differential equation with time delay difficult to find the solution analytically, so here we analyze the behavior of the model through perturbation. The tumor growth model has two equilibriums (i.e.at and ). Because this growth model is non-linear hence to analyze the stability of each equilibrium point is done through the linearization method. By using a perturbation procedure, the equilibrium point is unstable and is stable. The equilibrium is stable for , unstable for  and Hopf bifurcation occurs at .]]>
<![CDATA[MODEL PERTUMBUHAN BIOMASSA RUMPUT LAUT GRACILLARIA DENGAN CARRYING CAPACITY BERGANTUNG WAKTU ]]>
<![CDATA[Zullaikah, Zullaikah]]>;
<![CDATA[sutimin, sutimin]]>
<![CDATA[ MATEMATIKA Vol 11, No 2 (2008): Jurnal Matematika ]]>
Publisher : <![CDATA[MATEMATIKA ]]>
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<![CDATA[In this journal, we will discuss concerning with a dynamical model of growth of seaweed biomass. The model will be applied in the biomass growth of Gracillaria seaweed. The dynamical model is developed from the simple logistic model by considering the influence of resource absorption of ecosystem which support the environment. We assume that the resource absorption changes time dependent. By this assume, we include that the carrying capacity as function of time. To analyze the stability of the model equation, here we use the linearization method of the expansion series  ]]>
<![CDATA[MODEL DINAMIK PERTUMBUHAN BIOMASSA UDANG WINDU DENGAN FAKTOR MORTALITAS BERGANTUNG WAKTU ]]>
<![CDATA[sulanjari, Sulanjari]]>;
<![CDATA[sutimin, sutimin]]>
<![CDATA[ MATEMATIKA Vol 11, No 3 (2008): JURNAL MATEMATIKA ]]>
Publisher : <![CDATA[MATEMATIKA ]]>
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<![CDATA[In this paper will be discussed the growth model of shrimp biomass. Biomass is total weight from population. The growth model of shrimp biomass is influenced by the growth model of weight and of population. The growth model of weight, here will be governed and based on Von Bertalanffy’s model. The growth model of number population based on the exponential model and it has been constructed by mortality formula. From the growth model of shrimp biomass will be predicted when accurate harvest time to know the optimal harvest product.  ]]>
<![CDATA[KLASIFIKASI INTERAKSI GELOMBANG PERMUKAAN BERTIPE DUA SOLITON ]]>
<![CDATA[sutimin, Sutimin]]>;
<![CDATA[Rusgiyono, Agus]]>
<![CDATA[ MATEMATIKA Vol 4, No 1 (2001): JURNAL MATEMATIKA ]]>
Publisher : <![CDATA[MATEMATIKA ]]>
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<![CDATA[Pada tulisan ini diselidiki, masalah klasifikasi interaksi gelombang bertipe dua soliton Kadomtsev-Petviashvilli (KP). Disini dianalisis berdasarkan parameter interaksi dua solusi soliton baik melalui harga eksak maupun proses pelimitan. Proses pelimitan ini dilakukan untuk mengetahui resonansi diantara dua soliton. Selanjutnya resonansi soliton ini dikaji untuk mendapatkan soliton yang baru.]]>
<![CDATA[ANALISIS KESTABILAN MODEL DINAMIK NITROGEN DAN HUBUNGANNYA DENGAN PERTUMBUHAN LOGISTIK ALGA ]]>
<![CDATA[widowati, widowati]]>;
<![CDATA[sutimin, sutimin]]>;
<![CDATA[ps, hermin]]>;
<![CDATA[is, Tarita]]>
<![CDATA[ MATEMATIKA Vol 12, No 3 (2009): JURNAL MATEMATIKA ]]>
Publisher : <![CDATA[MATEMATIKA ]]>
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<![CDATA[The nitrogen dynamics model  related to algae growth is proposed. The form of the model is nonlinear differential equation system. From these model, the stability of the equilibrium point is disscussed. The stability is analized through the eigen values of the Jacobian matrix that is obtained from linearized system. From the simulation results is found that ammonia-nitrogen, nitrite-nitrogen, and nitrate-nitrogen concentration will achieve to a certain value. The changed of ammonia-nitrogen, nitrite-nitrogen, and nitrate-nitrogen concentration are effected by the algae density. If the alga density increase then the ammonia-nitrogen and nitrite-nitrogen concentrations will increase but the nitrate concentration will decrease.  ]]>
<![CDATA[DEFORMASI INTERAKSI DUA PAKET GELOMBANG DARI PERSAMAAN IMPROVED KdV (IKdV ]]>
<![CDATA[Sutimin, Sutimin]]>
<![CDATA[ MATEMATIKA Vol 9, No 1 (2006): JURNAL MATEMATIKA ]]>
Publisher : <![CDATA[MATEMATIKA ]]>
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<![CDATA[Here, We will study the nonlinear two waves packet interaction. The two waves packet is modeled by Improved Koreteweg de-Vries (IKdV) equation. The primary amplitudes are modulated by two-soliton of the nonlinear Schrődinger (NLS) equation. In this paper, we analyzed the interaction patterns of the two waves packet at the peak interaction. We have shown here, that during under going to the interaction region, the deformation of amplitudes profile will be occurred. The large deformation is characterized by the ratio of the amplitudes parameter and the wave numbers of each wave packets. The symmetry interaction also can be analyzed by the characterization of the parameters.]]>
<![CDATA[REFORMULASI DARI SOLUSI 3-SOLITON UNTUK PERSAMAAN KORTEWEG-de VRIES ]]>
<![CDATA[mustikaningsih, Dian]]>;
<![CDATA[sutimin, sutimin]]>
<![CDATA[ MATEMATIKA Vol 5, No 2 (2002): Jurnal Matematika ]]>
Publisher : <![CDATA[MATEMATIKA ]]>
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<![CDATA[The solution of 3-soliton for Korteweg-de Vries (KdV) equation can be obtained by the Hirota Method. The reformulation of the 3-soliton solution was represented as the superposition of the solution of each individual soliton. Moreover, the asymptotic form of 3-soliton solution was obtained by limiting of the t parameter. The phase shift of each individual soliton are analysed in detail based its asymptotic form. The results of the analysis shown that the first soliton always have a phase shift called forward, the second soliton have some possibility (there is no phase shift, have a forward phase shift, or have a backward phase shift), and for the third soliton always have a phase shift called backward.]]>
<![CDATA[ANALISIS KESTABILAN PERSAMAAN DIFERENSI TAK LINIER ]]>
<![CDATA[Uswatun, Indah]]>;
<![CDATA[Sutimin, Sutimin]]>
<![CDATA[ JURNAL SAINS DAN MATEMATIKA Volume 18 Issue 4 Year 2010 ]]>
Publisher : <![CDATA[JURNAL SAINS DAN MATEMATIKA ]]>
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<![CDATA[ABSTRAK---Analisis kestabilan dari persamaan diferensi tak linier dilakukan melalui uji teorema yaitu dengan menyelidiki titik setimbang x *. Analisis kestabilan dari fungsi diferensi f dalam teorema teoremayang telah dikaji menunjukkan bahwa jika |f '(x*)| < 1 berarti titik setimbang stabil asimtotik, sedangkan jika |f '(x*)| > 1 maka titik setimbang tidak stabil, kemudian jika |f '(x*)| = 1, kestabilan dari titik setimbang belum bisa disimpulkan. Di sini akan dikaji kestabilan dari titik setimbang pada kasus dimana |f '(x*)| = 1. Kajian dilakukan dengan memperhitungkan faktor f ' '(x*) dan f ' ' '(x*) sehingga pada akhirnya dapat disimpulkan kestabilan dari titik setimbang x*. Analisis kestabilan juga dapat dilakukandengan diagram Cobweb. Untuk persamaan diferensi logistik, kestabilan titik setimbang bergantung pada nilai dari parameter ï .Kata kunci: kestabilan, persamaan diferensi, titik setimbang, diagram Cobweb.]]>
