### Model Penyebaran Penyakit SIR Tipe Rantai Binomial dengan Kontak Random dan Waktu Penyembuhan Bernilai Tak Hingga

Ilham Asyifa Maulana Rosyid, Respatiwulan Respatiwulan, Sri Sulistijowati Handajani

#### Abstract

Susceptible-Infected-Recovered (SIR) epidemic model is an epidemic model that illustrates the pattern of disease spread with the characteristics of individuals who have recovered cannot be re-infected and have a permanent immune system. The binomial chain type epidemic model assumes that infection spreads in discrete time units and the number of the infected individuals follows a binomial distribution. This research aims to discuss  binomial chain type SIR epidemic model by simulating the model. The transition probability depends on  the number of infected individuals in the period   the number of individuals encountered, and  the transmission probability. This model also assumes an infinite recovery time ( = ∞). This situation illustrates that infected individuals remain contagious during the period of spread of the disease. This situation can arise when the causative agent of the disease has a long life. Then simulations are performed by giving different transmission probability  The results show that the greater transmission probability will cause the probability of a new individual being infected in the next period to be greater.

Keywords : SIR epidemic model, binomial chain, infinite recovery time

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#### References

Allen, L. J. S. An Introduction to Stochastic Epidemic Models. Lecture Notes in Mathematics, 81–130. 2008.

Halloran, M. E., Longini, I. M. and Struchiner, C. J. Binomial and Stochastic Transmission Models. Design and Analysis of Vaccine Studies. Statistics for Biology and Health. Springer, New York. 2010.

Hethcote, H. W. The Mathematics of Infectious Diseases. SIAM Rev. Vol. 42, No. 4, 599–653. 2000.

Tuckwell, H. C., and Williams, R. J. Some Properties of a Simple Stochastic Epidemic Model of SIR Type. Mathematical Biosciences, Vol. 208, No. 1, 76–97. 2007.

Herrhyanto, N. dan Gantini. Pengantar Statistika Matematis. Yrama Widya, Bandung. 2009.

Fine, P. E. M. A Comentary on the Reed-Frost Epidemic Model. American Journal of Epidemiology. No.106, 87-100. 1997.

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