An estimation method of probability of infection using Reed - Frost model^{†}

Eunjin Eom^{1} · Jinseub Hwang^{2} · Boseung Choi^{3}

Received December 30, 2016; Revised January 5, 2017; Accepted January 12, 2017.

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

- Abstract
- SIR model (Kermack and McKendrik, 1927) is one of the most popular method to explain the spread of disease, In order to construct SIR model, we need to estimate transition rate parameter and recovery rate parameter. If we don’t have any information of the two rate parameters, we should estimate using observed whole trajectory of pandemic of disease. Thus, with restricted observed data, we can’t estimate rate parameters. In this research, we introduced Reed-Frost model (Andersson and Britton, 2000) to calculate the probability of infection in the early stage of pandemic with the restriction of data. When we have an initial number of susceptible and infected, and a final number of infected, we can apply Reed - Frost model and we can get the probability of infection. We applied the Reed - Frost model to the Vibrio cholerae pandemic data from Republic of the Cameroon and calculated the probability of infection at the early stage. We also construct SIR model using the result of Reed - Frost model.
**Keywords**: Epidemic model, Reed - Frost model, SIR model, vibrio cholerae.