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NA Kurdhi
Department of Mathematics, University of Sebelas Maret
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ANALYSIS OF A VIRUS DYNAMICS MODEL WITH BEDDINGTON-DEANGELISH INFECTION RATE AND CTL IMMUNE RESPONSE Kurdhi, NA
Jurnal MIPA Vol 35, No 2 (2012): October 2012
Publisher : Jurnal MIPA

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Abstract

Penelitian ini menganalisis sebuah model dinamika virus dengan laju infeksi Beddington-DeAngelis dan respon imun CTL. Hal ini terbuktik bahwa pemecahan-pemecahan dengan nilai-nilai awal positif semuanya positif dan dibatasi. Stabilitas global titik ekuilibrium untuk model dinamika virus dieksplorasi dengan menggunakan fungsi Lyapunov. Dinamika global dari model ini ditentukan oleh nilai-nilai  bilangan reproduksi dasar R0. Hal ini membuktikan bahwa jika R0<1, terdapat keadaan tetap yang unik, keseimbangan bebas virus yang stabil asimtotik global. Jika R0>1, terdapat keadaan tetap lain, keseimbangan endemik yang stabil asimptotik secara global. Selain itu, kami menunjukkan bahwa respon CTL memiliki peran penting dalam pengendalian kepadatan partikel virus bebas dan sel yang terinfeksi. Simulasi-simulasi numerik disajikan untuk menggambarkan hasil-hasil. A virus dynamics model with Beddington-DeAngelis infection rate and CTL immune response is analyzed. It is proved that the solutions with positive initial values are all positive and bounded. The global stability of equilibrium points for dynamics virus model are explored by using appropriate Lyapunov functions. The global dynamics of the model are determined by the values of the basic reproduction number R0. It is proved that if R0<1, there is a unique steady state, the virus-free equilibrium, which is globally asymptotically stable. If R0>1 there is another steady state, the endemic equilibrium, which is globally asymptotically stable. In addition, we show that the CTL response have important role in controlling of the density of free virus particles and of infected cells. Numerical simulations are presented to illustrate the results.
ANALYSIS OF A VIRUS DYNAMICS MODEL WITH BEDDINGTON-DEANGELISH INFECTION RATE AND CTL IMMUNE RESPONSE Kurdhi, NA
Indonesian Journal of Mathematics and Natural Sciences Vol 35, No 2 (2012): October 2012
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

Penelitian ini menganalisis sebuah model dinamika virus dengan laju infeksi Beddington-DeAngelis dan respon imun CTL. Hal ini terbuktik bahwa pemecahan-pemecahan dengan nilai-nilai awal positif semuanya positif dan dibatasi. Stabilitas global titik ekuilibrium untuk model dinamika virus dieksplorasi dengan menggunakan fungsi Lyapunov. Dinamika global dari model ini ditentukan oleh nilai-nilai  bilangan reproduksi dasar R0. Hal ini membuktikan bahwa jika R0<1, terdapat keadaan tetap yang unik, keseimbangan bebas virus yang stabil asimtotik global. Jika R0>1, terdapat keadaan tetap lain, keseimbangan endemik yang stabil asimptotik secara global. Selain itu, kami menunjukkan bahwa respon CTL memiliki peran penting dalam pengendalian kepadatan partikel virus bebas dan sel yang terinfeksi. Simulasi-simulasi numerik disajikan untuk menggambarkan hasil-hasil. A virus dynamics model with Beddington-DeAngelis infection rate and CTL immune response is analyzed. It is proved that the solutions with positive initial values are all positive and bounded. The global stability of equilibrium points for dynamics virus model are explored by using appropriate Lyapunov functions. The global dynamics of the model are determined by the values of the basic reproduction number R0. It is proved that if R0<1, there is a unique steady state, the virus-free equilibrium, which is globally asymptotically stable. If R0>1 there is another steady state, the endemic equilibrium, which is globally asymptotically stable. In addition, we show that the CTL response have important role in controlling of the density of free virus particles and of infected cells. Numerical simulations are presented to illustrate the results.
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