arXiv subjects

Kurnia Susvitasari

Publications and source records attributed to Kurnia Susvitasari.

3 recordsLinked to original sources

arXiv2018

Expected Time to Extinction of SIS Epidemic Model Using Quasy Stationary Distribution

We study that the breakdown of epidemic depends on some parameters, that is expressed in epidemic reproduction ratio number. It is noted that when $R_0 $ exceeds 1, the stochastic model have two different results. But, eventually the extinction will be reached even though the major epidemic occurs. The question is how long this process will reach extinction. In this paper, we will focus on the Markovian process of SIS model when major epidemic occurs. Using the approximation of quasi--stationary distribution, the expected mean time of extinction only occurs when the process is one step away from being extinct. Combining the theorm from Ethier and Kurtz, we use CLT to find the approximation of this quasi distribution and successfully determine the asymptotic mean time to extinction of SIS model without demography.

math.ST↗

arXiv2018

Stochastic Model of SIR Epidemic Modelling

Threshold theorem is probably the most important development of mathematical epidemic modelling. Unfortunately, some models may not behave according to the threshold. In this paper, we will focus on the final outcome of SIR model with demography. The behaviour of the model approached by deteministic and stochastic models will be introduced, mainly using simulations. Furthermore, we will also investigate the dynamic of susceptibles in population in absence of infective. We have successfully showed that both deterministic and stochastic models performed similar results when $R_0 \leq 1$. That is, the disease-free stage in the epidemic. But when $R_0 > 1$, the deterministic and stochastic approaches had different interpretations.

q-bio.PE↗

arXiv2018

Comparing the Behaviour of Deterministic and Stochastic Model of SIS Epidemic

Studies about epidemic modelling have been conducted since before 19th century. Both deterministic and stochastiic model were used to capture the dynamic of infection in the population. The purpose of this project is to investigate the behaviour of the models when we set the basic reproduction number, $R_0$. This quantity is defined as the expected number of contacts made by a typical infective to susceptibles in the population. According to the epidemic threshold theory, when $R_0 \leq 1$, minor epidemic occurs with probability one in both approaches, but when $R_0 > 1$, the deterministic and stochastic models have different interpretation. In the deterministic approach, major epidemic occurs with probability one when $R_0 > 1$ and predicts that the disease will settle down to an endemic equilibrium. Stochastic models, on the other hand, identify that the minor epidemic can possibly occur. If it does, then the epidemic will die out quickly. Moreover, if we let the population size be large and the major epidemic occurs, then it will take off and then reach the endemic level and move randomly around the deterministic's equilibrium.

q-bio.PE↗