# Mathematical modeling of epidemic surveillance

2019-09-16

Chen, Xi, Ph. D.

## Abstract

My thesis focus on three aspects of epidemic surveillance: Estimation of the probability and corresponding uncertainty analysis for disease to be imported into multiple geographic regions (Chapter 1); Estimation of the transmission of disease after local transmission established (Chapter 2); Prevalence and corresponding confidence interval estimation incorporating individual level test sensitivity and specificity (Chapter 3). The maximum entropy model, a commonly used species distribution model (SDM) normally combines observations of the species occurrence with environmental information to predict the geographic distributions of animal or plant species. However, it only produces point estimates for the probability of species existence. To understand the uncertainty of the point estimates, we analytically derived the variance of the outputs of the maximum entropy model from the variance of the input in chapter 1. We applied the analytic method to obtain the standard deviation of dengue importation probability and Aedes aegypti suitability. Dengue occurrence data and Aedes aegypti mosquito abundance data, combined with demographic and environmental data, were applied to obtain point estimates and the corresponding variance. To address the issue of not having the true distributions for comparison, we compared and contrasted the performance of the analytical expression with the bootstrap method and Poisson point process model which proved of equivalence of maximum entropy model with the assumption of independent point locations. Both Dengue importation probability and Aedes aegypti mosquito suitability examples show that the methods generate comparatively the same results and the analytic method we introduced is dramatically faster than the bootstrap method and directly apply to maximum entropy model. Infectious diseases such as influenza progress quickly potentially reaching large parts of populations. Accurately estimating the parameters of the infectious disease progression model can efficiently help health organization determine the progression and severity of the disease and response properly and quickly. In chapter 2, we studied the application of 2 basic particle filter methods popularly used — Bootstrap Filter and Auxiliary Particle Filter — in estimating the parameters in infectious disease progression models which are non-linear in nature. We propose a posterior particle filter algorithm and two single statistic posterior particle filter algorithms to enhance handling outliers in data. The posterior particle filter algorithm and the two single statistic posterior particle filter algorithms are shown to out-perform the traditional bootstrap and auxiliary particle filters in terms of accurately and consistently estimating the parameters in compartmental SIR models. Besides, we proposed a re-sampling algorithm and compare it with the current popularly used re- sampling algorithm to show the importance of the re-sampling algorithm in helping improving the consistency of the particle filters. Dengue is currently diagnosed using test algorithm determined by number of days after illness onset which cause the challenge of prevalence estimation as the sensitivity and specificity level of patients varies with different RNA and antibody level. In Chapter 3, we tried to address the challenge of adjusting the estimated prevalence and propose the way of estimating corresponding confidence interval incorporating the individual level sensitivity and specificity. We compared sensitivity, specificity for individual level benefits and average estimation errors and precision for surveillance purpose of both using single test and possible combination of multiple tests. Prevalence estimation adjustment can correct all test combinations. Using immunoassays targeting DENV nonstructural protein (NS1), the combination the NS1 and and IgM-capture immunoassays (ELISA) and the combination of NS1 and real-time reverse transcription polymerase chain reaction (RT-PCR) can statistically significant improving sensitivity of the tests without sacrificing the specificity and narrowing the confidence interval of prevalence estimation.