M. Gabriela M. Gomes

Three-dimensional instability in flow over a backward-facing step

Results are reported from a three-dimensional computational stability analysis of flow over a backward-facing step with an expansion ratio (outlet to inlet height) of 2 at Reynolds numbers between 450 and 1050. The analysis shows that the first absolute linear instability of the steady two-dimensional flow is a steady three-dimensional bifurcation at a critical Reynolds number of 748. The critical eigenmode is localized to the primary separation bubble and has a flat roll structure with a spanwise wavelength of 6.9 step heights. The system is further shown to be absolutely stable to two-dimensional perturbations up to a Reynolds number of 1500. Stability spectra and visualizations of the global modes of the system are presented for representative Reynolds numbers.

Pertussis: increasing disease as a consequence of reducing transmission

Since the 1980s, the occurrence of pertussis cases in developed countries has increased and shifted towards older age groups. This resurgence follows 30 years of intense mass vaccination, and has been attributed primarily to three factors: (1) more effective diagnosis of the disease, (2) waning of vaccine-induced immunity, and (3) loss of vaccine efficacy due to the emergence of new Bordetella pertussis strains. Here we develop and analyse a mathematical model to assess the plausibility of these hypotheses. We consider that exposure to B pertussis through natural infection or vaccination induces an immune response that prevents severe disease but does not fully prevent mild infections. We also assume that these protective effects are temporary due to waning of immunity. These assumptions, describing the mode of action of adaptive immunity, are combined with a standard transmission model. Two distinct epidemiological scenarios are detected: under low transmission, most infections lead to severe disease; under high transmission, mild infections are frequent, boosting clinical immunity and maintaining low levels of severe disease. The two behaviours are separated by a reinfection threshold in transmission. As a result, the highest incidence of severe disease is expected to occur at intermediate transmission intensities--near the reinfection threshold--suggesting that pertussis resurgence may be induced by a reduction in transmission, independently of vaccination. The model is extended to interpret the outcomes of current control measures and explore scenarios for future interventions.

Prospects for Malaria Eradication in Sub-Saharan Africa

Background A characteristic of Plasmodium falciparum infections is the gradual acquisition of clinical immunity resulting from repeated exposures to the parasite. While the molecular basis of protection against clinical malaria remains unresolved, its effects on epidemiological patterns are well recognized. Accumulating epidemiological data constitute a valuable resource that must be intensively explored and interpreted as to effectively inform control planning. Methodology/Principal Finding Here we apply a mathematical model to clinical data from eight endemic regions in sub-Saharan Africa. The model provides a quantitative framework within which differences in age distribution of clinical disease are assessed in terms of the parameters underlying transmission. The shorter infectious periods estimated for clinical infections induce a regime of bistability of endemic and malaria-free states in regions of mesoendemic transmission. The two epidemiological states are separated by a threshold that provides a convenient measure for intervention design. Scenarios of eradication and resurgence are simulated. Conclusions/Significance In regions that support mesoendemic transmission, intervention success depends critically on reducing prevalence below a threshold which separates endemic and malaria-free regimes.

A Bayesian Framework for Parameter Estimation in Dynamical Models

Mathematical models in biology are powerful tools for the study and exploration of complex dynamics. Nevertheless, bringing theoretical results to an agreement with experimental observations involves acknowledging a great deal of uncertainty intrinsic to our theoretical representation of a real system. Proper handling of such uncertainties is key to the successful usage of models to predict experimental or field observations. This problem has been addressed over the years by many tools for model calibration and parameter estimation. In this article we present a general framework for uncertainty analysis and parameter estimation that is designed to handle uncertainties associated with the modeling of dynamic biological systems while remaining agnostic as to the type of model used. We apply the framework to fit an SIR-like influenza transmission model to 7 years of incidence data in three European countries: Belgium, the Netherlands and Portugal.

On the Final Size of Epidemics with Seasonality

We first study an SIR system of differential equations with periodic coefficients describing an epidemic in a seasonal environment. Unlike in a constant environment, the final epidemic size may not be an increasing function of the basic reproduction number ℛ0 or of the initial fraction of infected people. Moreover, large epidemics can happen even if ℛ0<1. But like in a constant environment, the final epidemic size tends to 0 when ℛ0<1 and the initial fraction of infected people tends to 0. When ℛ0>1, the final epidemic size is bigger than the fraction 1−1/ℛ0 of the initially nonimmune population. In summary, the basic reproduction number ℛ0 keeps its classical threshold property but many other properties are no longer true in a seasonal environment. These theoretical results should be kept in mind when analyzing data for emerging vector-borne diseases (West-Nile, dengue, chikungunya) or air-borne diseases (SARS, pandemic influenza); all these diseases being influenced by seasonality.

The role of weather on the relation between influenza and influenza-like illness.

Influenza epidemics, enabled by viral antigenic drift, occur invariably each winter in temperate climates. However, attempts to correlate the magnitude of virus change and epidemic size have been unsatisfactory. The incidence of influenza is not typically measured directly, but rather derived from the incidence of influenza-like illness (ILI), a clinical syndrome. Weather factors have been shown to influence the manifestation of influenza-like symptoms. We fitted an influenza transmission model to time series of influenza-like illness as monitored from 2003 to 2010 by two independent symptomatic surveillance systems (Influenzanet and EISN) in three European countries. By assuming that seasonality only acts upon the manifestation of symptoms, the model shows a significant correlation between the absolute humidity and temperature at the time of infection, and the proportion of influenza infections fulfilling the clinical ILI case definition, the so-called ILI factor. When a weather-dependent ILI factor is included in the model, the epidemic size of influenza-like illness becomes dependent not only on the susceptibility of the population at the beginning of the epidemic season but also on the weather conditions during which the epidemic unfolds. The combination reduces season-to-season variation in epidemic size and, interestingly, leads to a non-monotonic trend whereby the largest ILI epidemic occurs for moderate initial susceptibility.

How host heterogeneity governs tuberculosis reinfection

Recurrent episodes of tuberculosis (TB) can be due to relapse of latent infection or exogenous reinfection, and discrimination is crucial for control planning. Molecular genotyping of Mycobacterium tuberculosis isolates offers concrete opportunities to measure the relative contribution of reinfection in recurrent disease. Here, a mathematical model of TB transmission is fitted to data from 14 molecular epidemiology studies, enabling the estimation of relevant epidemiological parameters. Meta-analysis reveals that rates of reinfection after successful treatment are higher than rates of new TB, raising an important question about the underlying mechanism. We formulate two alternative mechanisms within our model framework: (i) infection increases susceptibility to reinfection or (ii) infection affects individuals differentially, thereby recruiting high-risk individuals to the group at risk for reinfection. The second mechanism is better supported by the fittings to the data, suggesting that reinfection rates are inflated through a population phenomenon that occurs in the presence of heterogeneity in individual risk of infection. As a result, rates of reinfection are higher when measured at the population level even though they might be lower at the individual level. Finally, differential host recruitment is modulated by transmission intensity, being less pronounced when incidence is high.

A Missing Dimension in Measures of Vaccination Impacts

Immunological protection, acquired from either natural infection or vaccination, varies among hosts, reflecting underlying biological variation and affecting population-level protection. Owing to the nature of resistance mechanisms, distributions of susceptibility and protection entangle with pathogen dose in a way that can be decoupled by adequately representing the dose dimension. Any infectious processes must depend in some fashion on dose, and empirical evidence exists for an effect of exposure dose on the probability of transmission to mumps-vaccinated hosts [1], the case-fatality ratio of measles [2], and the probability of infection and, given infection, of symptoms in cholera [3]. Extreme distributions of vaccine protection have been termed leaky (partially protects all hosts) and all-or-nothing (totally protects a proportion of hosts) [4]. These distributions can be distinguished in vaccine field trials from the time dependence of infections [5]. Frailty mixing models have also been proposed to estimate the distribution of protection from time to event data [6], [7], although the results are not comparable across regions unless there is explicit control for baseline transmission [8]. Distributions of host susceptibility and acquired protection can be estimated from dose-response data generated under controlled experimental conditions [9]–[11] and natural settings [12], [13]. These distributions can guide research on mechanisms of protection, as well as enable model validity across the entire range of transmission intensities. We argue for a shift to a dose-dimension paradigm in infectious disease science and community health.

Controlling Malaria Using Livestock-Based Interventions: A One Health Approach

Where malaria is transmitted by zoophilic vectors, two types of malaria control strategies have been proposed based on animals: using livestock to divert vector biting from people (zooprophylaxis) or as baits to attract vectors to insecticide sources (insecticide-treated livestock). Opposing findings have been obtained on malaria zooprophylaxis, and despite the success of an insecticide-treated livestock trial in Pakistan, where malaria vectors are highly zoophilic, its effectiveness is yet to be formally tested in Africa where vectors are more anthropophilic. This study aims to clarify the different effects of livestock on malaria and to understand under what circumstances livestock-based interventions could play a role in malaria control programmes. This was explored by developing a mathematical model and combining it with data from Pakistan and Ethiopia. Consistent with previous work, a zooprophylactic effect of untreated livestock is predicted in two situations: if vector population density does not increase with livestock introduction, or if livestock numbers and availability to vectors are sufficiently high such that the increase in vector density is counteracted by the diversion of bites from humans to animals. Although, as expected, insecticide-treatment of livestock is predicted to be more beneficial in settings with highly zoophilic vectors, like South Asia, we find that the intervention could also considerably decrease malaria transmission in regions with more anthropophilic vectors, like Anopheles arabiensis in Africa, under specific circumstances: high treatment coverage of the livestock population, using a product with stronger or longer lasting insecticidal effect than in the Pakistan trial, and with small (ideally null) repellency effect, or if increasing the attractiveness of treated livestock to malaria vectors. The results suggest these are the most appropriate conditions for field testing insecticide-treated livestock in an Africa region with moderately zoophilic vectors, where this intervention could contribute to the integrated control of malaria and livestock diseases.

Heterogeneity in susceptibility to infection can explain high reinfection rates

Heterogeneity in susceptibility and infectivity is inherent to infectious disease transmission in nature. Here we are concerned with the formulation of mathematical models that capture the essence of heterogeneity while keeping a simple structure suitable of analytical treatment. We explore the consequences of host heterogeneity in the susceptibility to infection for epidemiological models for which immunity conferred by infection is partially protective, known as susceptible-infected-recovered-infected (SIRI) models. We analyze the impact of heterogeneity on disease prevalence and contrast the susceptibility profiles of the subpopulations at risk for primary infection and reinfection. We present a systematic study in the case of two frailty groups. We predict that the average rate of reinfection may be higher than the average rate of primary infection, which may seem paradoxical given that primary infection induces life-long partial protection. Infection generates a selection mechanism whereby fit individuals remain in S and frail individuals are transferred to R. If this effect is strong enough we have a scenario where, on average, the rate of reinfection is higher than the rate of primary infection even though each individual has a risk reduction following primary infection. This mechanism may explain high rates of tuberculosis reinfection recently reported. Finally, the enhanced benefits of vaccination strategies that target the high-risk groups are quantified.