Persistence in epidemic metapopulations: quantifying the rescue effects for measles, mumps, rubella and whooping cough

Metapopulation rescue effects are thought to be key to the persistence of many acute immunizing infections. Yet the enhancement of persistence through spatial coupling has not been previously quantified. Here we estimate the metapopulation rescue effects for four childhood infections using global WHO reported incidence data by comparing persistence on island countries vs all other countries, while controlling for key variables such as vaccine cover, birth rates and economic development. The relative risk of extinction on islands is significantly higher, and approximately double the risk of extinction in mainland countries. Furthermore, as may be expected, infections with longer infectious periods tend to have the strongest metapopulation rescue effects. Our results quantitate the notion that demography and local community size controls disease persistence

Quasi-stationary distributions for the Domany-Kinzel stochastic cellular automaton

We construct the {\it quasi-stationary} (QS) probability distribution for the Domany-Kinzel stochastic cellular automaton (DKCA), a discrete-time Markov process with an absorbing state. QS distributions are derived at both the one- and two-site levels. We characterize the distribuitions by their mean, and various moment ratios, and analyze the lifetime of the QS state, and the relaxation time to attain this state. Of particular interest are the scaling properties of the QS state along the critical line separating the active and absorbing phases. These exhibit a high degree of similarity to the contact process and the Malthus-Verhulst process (the closest continuous-time analogs of the DKCA), which extends to the scaling form of the QS distribution.Comment: 15 pages, 9 figures, submited to PR

Mathematical explanation of the predictive power of the X-level approach reaction noise estimator method

The X-level Approach Reaction Noise Estimator (XARNES) method has been developed previously to study reaction noise in well mixed reaction volumes. The method is a typical moment closure method and it works by closing the infinite hierarchy of equations that describe moments of the particle number distribution function. This is done by using correlation forms which describe correlation effects in a strict mathematical way. The variable X is used to specify which correlation effects (forms) are included in the description. Previously, it was argued, in a rather informal way, that the method should work well in situations where the particle number distribution function is Poisson-like. Numerical tests confirmed this. It was shown that the predictive power of the method increases, i.e. the agreement between the theory and simulations improves, if X is increased. In here, these features of the method are explained by using rigorous mathematical reasoning. Three derivative matching theoremsare proven which show that the observed numerical behavior is generic to the method

A rationale for continuing mass antibiotic distributions for trachoma

BACKGROUND: The World Health Organization recommends periodic mass antibiotic distributions to reduce the ocular strains of chlamydia that cause trachoma, the world's leading cause of infectious blindness. Their stated goal is to control infection, not to completely eliminate it. A single mass distribution can dramatically reduce the prevalence of infection. However, if infection is not eliminated in every individual in the community, it may gradually return back into the community, so often repeated treatments are necessary. Since public health groups are reluctant to distribute antibiotics indefinitely, we are still in need of a proven long-term rationale. Here we use mathematical models to demonstrate that repeated antibiotic distributions can eliminate infection in a reasonable time period. METHODS: We fit parameters of a stochastic epidemiological transmission model to data collected before and 6 months after a mass antibiotic distribution in a region of Ethiopia that is one of the most severely affected areas in the world. We validate the model by comparing our predicted results to Ethiopian data which was collected biannually for two years past the initial mass antibiotic distribution. We use the model to simulate the effect of different treatment programs in terms of local elimination of infection. RESULTS: Simulations show that the average prevalence of infection across all villages progressively decreases after each treatment, as long as the frequency and coverage of antibiotics are high enough. Infection can be eliminated in more villages with each round of treatment. However, in the communities where infection is not eliminated, it returns to the same average level, forming the same stationary distribution. This phenomenon is also seen in subsequent epidemiological data from Ethiopia. Simulations suggest that a biannual treatment plan implemented for 5 years will lead to elimination in 95% of all villages. CONCLUSION: Local elimination from a community is theoretically possible, even in the most severely infected communities. However, elimination from larger areas may require repeated biannual treatments and prevention of re-introduction from outside to treated areas

The Role of Environmental Transmission in Recurrent Avian Influenza Epidemics

Avian influenza virus (AIV) persists in North American wild waterfowl, exhibiting major outbreaks every 2–4 years. Attempts to explain the patterns of periodicity and persistence using simple direct transmission models are unsuccessful. Motivated by empirical evidence, we examine the contribution of an overlooked AIV transmission mode: environmental transmission. It is known that infectious birds shed large concentrations of virions in the environment, where virions may persist for a long time. We thus propose that, in addition to direct fecal/oral transmission, birds may become infected by ingesting virions that have long persisted in the environment. We design a new host–pathogen model that combines within-season transmission dynamics, between-season migration and reproduction, and environmental variation. Analysis of the model yields three major results. First, environmental transmission provides a persistence mechanism within small communities where epidemics cannot be sustained by direct transmission only (i.e., communities smaller than the critical community size). Second, environmental transmission offers a parsimonious explanation of the 2–4 year periodicity of avian influenza epidemics. Third, very low levels of environmental transmission (i.e., few cases per year) are sufficient for avian influenza to persist in populations where it would otherwise vanish