Computing human to human Avian influenza R0 via transmission chains and parameter estimation

Abstract

The transmission of avian influenza between humans is extremely rare, and it mostly affects individuals who are in contact with infected family member. Although this scenario is uncommon, there have been multiple outbreaks that occur in small infection clusters in Asia with relatively low transmissibility, and thus are too weak to cause an epidemic. Still, subcritical transmission from stuttering chain data is vital for determining whether avian influenza is close to the threshold of R0 > 1. In this article, we will explore two methods of estimating R0 using transmission chains and parameter estimation through data fitting. We found that R0 = 0.2205 when calculating the R0 using the maximum likelihood method. When we computed the reproduction number for human to human transmission through differential equations and fitted the model to data from the cumulative cases, cumulative deaths, and cumulative secondary cases, we estimated R0 = 0.1768. To avoid violating the assumption of the least square method, we fitted the model to incidence data to obtain R0 = 0.1520. We tested the structural and practical identifiability of the model, and concluded that the model is identifiable under certain assumptions. We further use two more methods to estimate R0: by the R0 definition which gives an overestimate of 0.28 and by Ferguson approach which yields R0 = 0.1586. We conclude that R0 for human to human transmission was about 0.2.