Estimation and forecasting of a lag 2 dynamic model for infectious diseases

Abstract

When a common infectious disease is first detected in a community, it may quickly spread out through air, water, public facilities and personal contacts. At a given time point, each infected individual may or may not infect other individuals in the community. Meanwhile, it is also possible that some individuals who carry the same disease travel into the community. In the present work, we discuss estimation and forecasting of an extension to the lag 1 longitudinal dynamic model for correlated data used by Oyet & Sutradhar (2011) for modelling the spread of infectious disease. The lag 1 model only allow individuals with infection at time point t–1 to cause new infections at time point t. Clearly, if at time point t–2, there is an individual who is still infected by the disease, it is also possible for this individual to infect others at time point t. The present model discussed in this work allows for such a possibility. During the modelling, we consider stationary and nonstationary covariates. We also extend the model to situations where unobservable community effect and the latent community effect is present. The regression parameter β and the parameter of latent community effect δ 2/γ are estimated by generalized quasi-likelihood (GQL) approach. The correlation parameters ρ1 and ρ2 are estimated by using method of moments. In each of the cases, we examined the accuracy of the estimates and forecasts through simulation studies.