The purpose of time series analysis via mechanistic models is to reconcile the known or hypothesized structure of a dynamical system with observations collected over time. We develop a framework for constructing nonlinear mechanistic models and carrying out inference. Our framework permits the consideration of implicit dynamic models, meaning statistical models for stochastic dynamical systems which are specified by a simulation algorithm to generate sample paths. Inference procedures that operate on implicit models are said to have the plug-and-play property. Our work builds on recently developed plug-and-play inference methodology for partially observed Markov models. We introduce a class of implicitly specified Markov chains with stochastic transition rates, and we demonstrate its applicability to open problems in statistical inference for biological systems. As one example, these models are shown to give a fresh perspective on measles transmission dynamics. As a second example, we present a mechanistic analysis of cholera incidence data, involving interaction between two competing strains of the pathogen Vibrio cholerae. 1. Introduction. A

Infectious bursal disease virus (IBDV) is a birnavirus causing immunosuppressive disease in chickens. Emergence of the very virulent form of IBDV (vvIBDV) in the late 1980s dramatically changed the epidemiology of the disease. In this study, we investigated the phylogenetic origins of its genome segments and estimated the time of emergence of their most recent common ancestors. Moreover, with recently developed coalescence techniques, we reconstructed the past population dynamics of vvIBDV and timed the onset of its expansion to the late 1980s. Our analysis suggests that genome segment A of vvIBDV emerged at least 20 years before its expansion, which argues against the hypothesis that mutation of genome segment A is the major contributing factor in the emergence and expansion of vvIBDV. Alternatively, the phylogeny of genome segment B suggests a possible reassortment event estimated to have taken place around the mid-1980s, which seems to coincide with its expansion within approximately 5 years. We therefore hypothesize that the reassortment of genome segment B initiated vvIBDV expansion in the late 1980s, possibly by enhancing the virulence of the virus synergistically with its existing genome segment A. This report reveals the possible mechanisms leading to the emergence and expansion of vvIBDV, which would certainly provide insights into the scope of surveillance and prevention efforts regarding the disease. Infectious bursal disease (IBD) is an immunosuppressive disease of young chickens that causes considerable economic

Abstract. Strain replacement is the effect of substitution of a strain of higher prevalence in the population with another. Differential effectiveness of the vaccines is thought to be the mechanism responsible for the replacement effect. Recent theoretical study shows that differential effectiveness of the vaccine may not be necessary and other trade-off mechanisms can lead to it even when the vaccine is “perfect”. We suggest that the mechanism of strain replacement is the reciprocal effect of vaccination on the fitness of the strains as measured by their invasion reproduction numbers. This mechanism is responsible for the substitution of one strain with another to occur both when the vaccine is perfect and when it is imperfect. We review various well-known trade-off mechanisms and investigate whether they lead to replacement effect in conjunction with “perfect ” vaccination. We find that in contrast to imperfect vaccination which leads to replacement of a strain with larger intrinsic reproduction number with a strain with a lower intrinsic reproduction number, “perfect ” vaccination seems to have opposite effect on the intrinsic reproduction numbers.

Known human immunodeficiency virus (HIV) transmission histories are invaluable models for investigating the evolutionary and transmission dynamics of the virus and to assess the accuracy of phylogenetic reconstructions. Here we have characterized an HIV-1 transmission chain consisting of nine infected patients, almost all of whom were treated with antiviral drugs at later stages of infection. Partial pol and env gp41 regions of the HIV genome were directly sequenced from plasma viral RNA for at least one sample from each patient. Phylogenetic analyses in pol using likelihood methods inferred an evolutionary history not fully compatible with the known transmission history. This could be attributed to parallel evolution of drug resistance mutations resulting in the incorrect clustering of multidrug-resistant virus. On the other hand, a fully compatible phylogenetic tree was reconstructed from the env sequences. We were able to identify and quantify the molecular footprint of drug-selective pressure in pol using maximum likelihood inference under different codon substitution models. An increased fixation rate of mutations in the HIV population of the multidrug-resistant patient was demonstrated using molecular clock modeling. We show that molecular evolutionary analyses, guided by a known transmission history, can reveal the presence of confounding factors like natural selection and caution should be taken when accurate descriptions of HIV evolution are required. The evolution of human immunodeficiency virus (HIV)

statistics

which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Background: The analysis of genetic variation in populations of infectious agents may help us understand their epidemiology and evolution. Here we study a model for assessing the levels and patterns of genetic diversity in populations of infectious agents. The population is structured into many small subpopulations, which correspond to their hosts, that are connected according to a specific type of contact network. We considered different types of networks, including fully connected networks and scale free networks, which have been considered as a model that captures some properties of real contact networks. Infectious agents transmit between hosts, through migration, where they grow and mutate until elimination by the host immune system. Results: We show how our model is closely related to the classical SIS model in epidemiology and find that: depending on the relation between the rate at which infectious agents are eliminated by the immune system and the within host effective population size, genetic diversity increases with R0 or peaks at intermediate R0 levels; patterns of genetic diversity in this model are in general similar to those expected under the standard neutral model, but in a scale free network and for low values

environmental noise