An SIR Estimation for Pandemic by influenza A During the Haj

In this study, a system of SIR models depended on effective contact rate of the disease and potential size of the community is developed for simulating patterns of pandemic by influenza A during the Haj. Indeed, we consider three different SIR models such that each of them is calibrated to simulate a separate part of the ceremony and then we link these models together to obtain system simulating whole the Haj ceremony. Considering different numerical values of effective contact rate and potential size of the community, we estimate the portion of susceptible hosts in the community and also the portion of total infection during the ceremony and portion of infective individuals at any time of the ceremony. Our goal is to suggest doable optimal situations keeping the pandemic under the control and the number of infected people as low as possible.