Kestabilan Model SIS dengan Non-monotone Incidence Rate & Treatment

Mohammad Soleh

Abstract


Our paper proposed a non monoton incidence rate, logistic growth, migration, and under treatment for SIS model. The character of originally SIS model which using bilinear insience rate will cover by new model. An existences and stabilities of free disease state and endemic are investigated to explore the characteristic of model. The existence of equilibrium point is founded by solving differential equation of the model and their stability are explored by an eigen criteria. We obtained that only one free disease state and endemic which asimtotycal stable by condition.
Key words: Endemic state, Free Disease state, Non Monoton Incidence Rate, SIS Model, treatment.

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References


Alexander M.E, Moghadas S.M. Periodicity in an epidemic model with a generalized nonlinear

incidence. Mathematical Biosciences. 2004; vol. 189, no. 1, pp. 75–96,.

Capasso V, Serio G. A generalization of the Kermack-McKendrick deterministic epidemic model.

Mathematical Biosciences. 1978; vol. 42, no. 1-2, pp. 43–61, 1978.

Chufen Wu, Peixuan Weng, Stability Analysis of Age Structured SIS Models with General Incidence

Rate, Elsevier, 2009, 11(2010) 1826-1834.

Linear

nonmonoton

Seminar Nasional Teknologi Informasi, Komunikasi dan Industri (SNTIKI) 7 ISSN :2085-9902

Pekanbaru, 11 November 2015

Gajendra U, Gupta V.K, Singh B, Khandelwal R, and Neetu T. An Epidemic Model with Modified Non-monotonic Incidence Rate under treatment, Applied Mathematical Sciences.; 2012, Vol. 6, no. 24, 1159 – 1171.

H.W.Hetchote, the Mathematics Infectious Diseases, SIAM Revew, vol. 42, No. 4 (Dec 2000), pp. 599-653.

Hu, Z., Liu, S., Wang, H., Backward Bifurcation of an Epidemic Model with Standard Incidence Rate and Treatment Rate, Mathematical Biosciences, Elsevier, 2006, pp. 58-71.

Hu, Z., Ma, W., Ruan, S., Analysis of SIR Epidemic Models with Nonlinear Incidence Rate and Treatment, Mathematical Biosciences, Elsevier, 2012, pp. 12-20.

Kar T.K., Ashim B. : Modeling and Analysis of an Epidemic Model with Non-monotonic Incidence Rate under Treatment, Journal of Mathematics Research. 2010; Vol 2, No. 1, 103-115.

Linda JS. Allen, an Introduction to Stochastic Epidemic Models, Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409- 1042, USA.

Perko L., Differential Equations and Dynamical System, Springer-Verlag, New York, 1991.

Sheikh, S., Modeling and Analysis of an SEIR Epidemic Model with a Limited Resource for Treatment, Global Journal of Science, 2012, vol. 12, ISSN: 2249-4626.

Soleh, M., Kestabilan Model SIS dengan Logistik dan Non Monotone Incidence Rates, Laporan Penelitian Individu Fakultas Sains & Teknologi UIN Suska Riau, 2013, Pekanbaru.

Soleh, M., Kestabilan Model SIS dengan Non Monotone Incidence Rate, Prosiding SNTIKI 4, 2012, Pekanbaru, ISSN : 2085-9902.

Soleh & Siregar, Kestabilan Equilibrium Model SIS dengan pertumbuhan logistik dan migrasi, Jurnal Sitekin, vol. 9 No. 2, 2012, Pekanbaru. ISSN 1693-2390.

Soleh & Helvi, Model SIS (Suspectible, Infectives, Suspectible) dengan Pertumbuhan Alami dan Proses Migrasi, Skripsi, 2011, Pekanbaru.

Wang, W., Ruan, S., Bifurcation in an Epidemic Model with Constant Removel Rate of the Infectives, 2004, J. Math. Anal. Appl. 291, 775-793.

Wang, W., Backward Bifurcation of an Epidemic Model with Treatment, Mathematical Biosciences, Elsevier, 2006, pp. 58-71.

Xiao D, Ruan S. Global analysis of an epidemic model with nonmonotone incidence rate. Mathematical Biosciences. 2007; vol. 208, no. 2, pp. 419–429.

Zhou, L., Fan, M., Dynamics of SIR Epidemic Model with Limited Medical Resource Revisited, Mathematical Biosciences, Elsevier, 2012, pp. 312-324.


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