# MODEL SIRS PADA PENYEBARAN PENYAKIT DIARE AKUT PADA BALITA DI PROVINSI JAMBI

## Abstract

This study aims to obtain a SIRS mathematical model on the spread of acute diarrheal disease in infants, find out the equilibrium point of the model and test the stability of these points. It is assumed that the birth rate and natural death rate are considered the same, the population is homogeneous, there is one population that is toddlers, there is only diarrheal disease in the population, and infected individuals can recover from the disease will become vulnerable again and there is no rotela immunization in infants. Based on the obtained disease-free equilibrium point, the stability criteria are tested around the disease-free and endemic equilibrium point as seen from its basic reproductive number. The disease-free equilibrium point is asymptotic stable if the basic reproductive number is less than one and unstable if the basic reproduction number is more than one. Whereas the endemic equilibrium point is stable asymptotically if the reproduction number has more than one base. The results obtained from the disease free equilibrium point are .. As for the endemic equilibrium point of the disease . Basic reproduction numbers for disease-free equilibrium points are: and .The basic reproduction number for the endemic equilibrium point of the disease is equal to: ) or . This means that the disease-free equilibrium point has R_0 <1 then the system is stable Local asymptotic means that in the under five population in Jambi Province no one is infected and no one can transmit acute diarrheal disease and the endemic equilibrium point of the disease has so the local asymptotic stable system means that every infected individual can transmit acute diarrheal disease to an average of one individual is vulnerable so that within a certain period of time the disease spreads in the population.

Keywords: Stability, SIRS model, disease free equilibrium point and endemic equilibrium point.

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## References

Enatsu, Y., Messina, E., Nakata, Y., Muroya, Y., Russo, E., & Vecchio, A., 2000,Global Dynamics of a Delayed SIRS Epidemic Models With a Wide Class of Non linear Incidence Rates, Journal of Applied Mathematics And Computing.

Rost, G., & Wu, J. 2008. SEIR Epidemiological Model with Varying Infectivity and Infinite Delay.

Tri Onggo, IP. 2015. 92 Pengobatan mandiri dirumah anda. Yogyakarta; Bangkit.

Widowati dan Sutimin. 2007. Pemodelan Matematika. Semarang: Jurusan Matematika Fakultas MIPA Universitas Diponegoro.

Wiggins, Stephen. 2003. Introduction to Applied Nonlinear Dynamical System and Chaos: Second Edition. New York: Springer-Verlag.