Longitudinal modeling of infectious disease

摘要

When individuals in a community develop an infectious disease, it may quickly spread through personal contacts. Modeling the progression of such a disease is equivalent to modeling a branching process in which an infected person may infect others in a small time interval. It is also possible for some immigrants to enter the community with the disease and thus contribute to an increase in the number of infections. There exist various modeling approaches for dealing with this type of infectious disease data collected over a long period of time. However, there are certain infectious diseases which require very quick remedy by health professionals to prevent it from spreading further due to the dangerous nature of the disease. Such interventions require an understanding of the pattern of the disease in a short period of time. As a result, the spread of such infectious diseases only occur over a short period of time. The modeling of this type of infections that last only for a short period of time across several communities or countries is not, however, adequately discussed in the literature. In this paper, we develop a branching process with immigration to model this type of infectious disease data collected over a short period of time and provide consistent estimates of the parameters involved in the proposed model. We note that the model and inferences exploited in this paper are also applicable to infectious disease data obtained over a long period of time. We discuss a generalization of the proposed model under the assumption that the data may be affected by unobservable random community effects.