Probabilistic modeling of genome evolution and disease spread of tuberculosis

Abstract

In the second part, we study the transmission dynamics of TB disease. Based on the DNA fingerprints of the MTBC, TB patients can be clustered in to small groups. This allows us to investigate the dynamics at the individual level. Since immigrants make the majority of TB cases in the United States, we focus our anal- ysis on immigrant TB patients. We propose a model to estimate the probability of an immigrant entering the country latently infected with TB versus he/she being infected after entry, given the entry and diagnosis time of the immigrant patients within the cluster. The transmission routes among the patients increase exponen- tially with the size of the cluster. The fact that individuals outside the cluster could also infect someone within the cluster further complicates the dynamics. We use Mean Field approximations to simplify the complicated transmission routs among patients and the effects of the individuals outside the cluster. The performance of the model is evaluated with Receiver Operating Characteristic (ROC) analysis on simulated data. Finally, we apply our model to the patient data collected from New York City.

Tuberculosis (TB) remains one of the leading causes of mortality worldwide. It is caused by Mycobacterium tuberculosis complex (MTBC). The development of the DNA fingerprinting technologies in the past decade has enriched the information available for scientific research and TB control. The genetic dissimilarities among different strains of MTBC will result in different fingerprinting data. With this information, TB patient isolates can be grouped into small clusters, which greatly facilitates TB control and surveillance. Spacer Oligonucleotide Types (Spoligotypes) and Mycobacterial Interspersed Repetitive Units - Variable Number Tandem Repeats (MIRU-VNTR) are two of the popular biomarkers used for DNA fingerprinting worldwide. MIRU-VNTR typing records the numbers of the tandem repetitive units at several specific loci in MTBC genome, which are collectively referred as MIRU. This thesis studies TB from two aspects: 1)micro-level exploring the evolution prop- erties of MIRU based on our assumptions ; 2)macro-level, proposing mathematical model to capture the transmission dynamics within a TB cluster.

In the past decade, MIRU is gaining popularity in TB research and control. Compared to Spoligotypes, MIRU is relatively less studied. Understanding the char- acteristics of MIRU is crucial to fully harness its power as a TB analysis tool. In the first part of this thesis, we take advantage of the characteristics of Spoligotypes to infer the mutation directions of MTBC and analyze the mutations in MIRU. A Markov Chain of the repeat numbers of MIRU at each locus is built based the mu- tations found in the data. We compute and compare the stationary distributions of repeat numbers at different loci. An error analysis is done to investigate the errors produced at each stage of our study: from inferring the probability transition matri- ces of the Markov Chains to computing the corresponding stationary distributions. We also study the distance between the current distribution of the repeat numbers and the stationary ones. Finally, we analyze the rates of each locus reaching its stationary distribution through theoretical computations and simulations.