Modelling and statistical inference of infectious diseases

Abstract

Emerging infectious diseases (EIDs) have been an enormous burden on public health all around the world. They share the property of rapid spread among countries and continents, which potentially cause enormous harm to human society. Using statistical inferential methods and mathematical models, researchers have been succeeding in exploring the underlying dynamics of EIDs, as well as foresting their future trends. With reported cases of Infuenza A/H1N1 and A/H3N2 from January 2010 and July 2017 from World Health Organization, we explored and verifed the anti-phase temporal pattern of these two subtypes both in Hong Kong and North Temperate Zone, which indicates a high prevalence of A/H1N1 coincides with a low prevalence of A/H3N2 and vice versa. By constructing a statistical metric, i.e., weekly case ratio of infuenza B over infuenza A, we showed a strong positive correlation with the activity of B/Victoria in China, abnormality of extremely high ratio accompanied by unusual low vaccine effective in the United States, as well as revealed the global pattern of infuenza activity by computing the statistical correlation of the ratios between countries and regions. We investigated heterogeneities in demographic information of tuberculosis (TB) notifcations and estimate the effects of age and period (historical trend) on TB and drug-resistant (DR)-TB across cities in Shandong from 2006-2017 and from 2004-2017, respectively, by age-period-cohort (APC) models. We observed a drastic shift from transmitted TB to reactivated TB, especially among women. We forecast the future trend of TB from 2018-2027 and of DR-TB from 2018-2023 and predicted 1.5-3.5 multi-drug-resistant (MDR)-TB cases per population of 100 thousand by the end of 2023. Furthermore, using mathematical models (a plug-and-play likelihood-based inference framework), we ftted a susceptible-exposed-infectious-recovered-susceptible (SEIRS) model of camels to the reported human cases with a constant proportion of human cases from camels (i.e., either 25% or 12%). We considered two scenarios: (i) the transmission rate among camels is time-varying with a constant spill-over rate from camels to human or (ii) the spill-over rate is time-varying with a constant transmission rate among camels. Our estimated loss-of-immunity rate and prevalence of Middle East respiratory syndrome coronavirus infections among camels mostly matched with previous serological or virological studies, shedding light on this issue. We recommended including dromedary camels in animal surveillance and control of Middle East respiratory syndrome coronavirus in Saudi Arabia which could help reduce their sporadic introductions to humans. "Phylodynamics" indicates methods or frameworks that make the statistical inferences from both epidemiological and phylogenetic data. By Coalescent Theory, phylodynamics has become a hot topic recently, while theoretical studies that clarify its feasibility and practical studies that explore the inconsistency and its impact on inference are lacking. We utilized the integrated framework via iterated fltering method within the plug-and-play simulation based scheme and estimated the parameters of interest and their 95% confidence intervals through a global search for the maximum likelihood. We found failures in estimating, which is probably caused by inappropriate likelihood expression and is consistent with previous studies. We then discussed the inconsistency between coalescent theory and stochastic models, as well as its theoretical proof.