The degree of bio-threat associated with newly detected pathogen variants (genotypes) that are genetically similar to some known pathogens may be assessed in terms of the cross-immunity between the two variants under study. Perfect (lack of) cross-immunity between the two variants suggests that the newly detected pathogen and the known variant are identical (distinct) epidemiologically. New epidemiological models will be developed for estimating cross-immunity in a two-strain system that may allow for variable birth rate of the natural hosts, possibility of vertical transmission and finite number of contacts per subject per unit time. Similar to many popular epidemiological models, the proposed epidemiological models stipulate that the dynamics of the state vector follow some nonlinear partial differential equation (PDE). New computationally efficient estimation methods are proposed for estimating a PDE model. The development of the proposed methodologies will be guided by analysis of a real monitoring longitudinal data on prevalence of various Bartonella variants (genotypes) in a natural population of rodents (cotton rats).
The research team consists of two statisticians from two academic institutions and one epidemiologist from the CDC, who have worked closely together for a number of years. The proposed works will provide general tools for quantifying an epidemiological similarity between newly detected pathogen variant and known bacterial species, which contribute to the general problem on the assessment of bio-threat associated with newly detected variants. The proposed estimation methods can be generally applicable for estimating PDE models used in epidemiological studies, as well as in other fields, e.g. finance. A computer package implementing the proposed methods will be freely available to the public. The research team will continue to maintain the strong record of training PhD students in cross-disciplinary research.
A differential equation system based on the Susceptible-Infective-Recovered (SIR) model was proposed. The developed SIR system depends on proportions only and allows birth rate change over time. A conditional least squares method based on the unscented Kalman filter was proposed to analyze nonlinear differential equation system such as the SIR model. The proposed conditional least squares method enjoys asymptotic normality. In particular, the conditional least squares method based on the unscented Kalman filter was theoretically proven to provide a better approximation of nonlinear system than that based on the extended Kalman filter. The proposed method was applied to real bartonella disease data to evaluate cross-immunity. Partial cross-immunity was found among genetically similar bartonella variants. A nonparametric estimation for partially observed differential equation models was developed. This model was applied to real bartonella disease data, in which whether captured animals were infected or not was known. In other words, when the blood samples of the captured animals did not indicate infection, it was unknown whether they were susceptible to or recovered from bartonella disease. Methods for comparing survival quantiles were developed based on the pseudo-value technique for clustered survival data. Simulation studies showed that the proposed methods work satisfactorily for independent and clustered survival data. Although the conditional least squares method from this project was developed for differential equations in epidemiology, it can be used for nonlinear differential equation systems in engineering, and nonlinear time series models in economics and epidemiology. The developed survival quantile models can be used for independent and clustered survival data in biological science and clinics.
