Analysis of symmetries in models of multi-strain infections

In mathematical studies of the dynamics of multi-strain diseases caused by antigenically diverse pathogens, there is a substantial interest in analytical insights. Using the example of a generic model of multi-strain diseases with cross-immunity between strains, we show that a significant understanding of the stability of steady states and possible dynamical behaviours can be achieved when the symmetry of interactions between strains is taken into account. Techniques of equivariant bifurcation theory allow one to identify the type of possible symmetry-breaking Hopf bifurcation, as well as to classify different periodic solutions in terms of their spatial and temporal symmetries. The approach is also illustrated on other models of multi-strain diseases, where the same methodology provides a systematic understanding of bifurcation scenarios and periodic behaviours. The results of the analysis are quite generic, and have wider implications for understanding the dynamics of a large class of models of multi-strain diseases

School Absenteeism As an Adjunct Surveillance Indicator: Experience during the Second Wave of the 2009 H1N1 Pandemic in Quebec, Canada

A school absenteeism surveillance system was implemented in the province of Quebec, Canada during the second wave of the 2009 H1N1 pandemic. This paper compares this surveillance approach with other available indicators.All (3432) elementary and high schools from Quebec were included. Each school was required to report through a web-based system any day where the proportion of students absent for influenza-like illness (ILI) exceeded 10% of current school enrolment.Between October 18 and December 12 2009, 35.6% of all schools met the 10% absenteeism threshold. This proportion was greater in elementary compared to high schools (40% vs 19%) and in smaller compared to larger schools (44% vs 22%). The maximum absenteeism rate was reached the first day of reporting or within the next two days in 55% and 31% of schools respectively. The first reports and subsequent peak in school absenteeism provincially preceded the peak in paediatric hospitalization by two and one weeks, respectively. Trends in school surveillance otherwise mirrored other indicators.During a pandemic, school outbreak surveillance based on a 10% threshold appears insufficient to trigger timely intervention within a given affected school. However, school surveillance appears well-correlated and slightly anticipatory compared to other population indicators. As such, school absenteeism warrants further evaluation as an adjunct surveillance indicator whose overall utility will depend upon specified objectives, and other existing capacity for monitoring and response

Global Patterns in Seasonal Activity of Influenza A/H3N2, A/H1N1, and B from 1997 to 2005: Viral Coexistence and Latitudinal Gradients

Despite a mass of research on the epidemiology of seasonal influenza, overall patterns of infection have not been fully described on broad geographic scales and for specific types and subtypes of the influenza virus. Here we provide a descriptive analysis of laboratory-confirmed influenza surveillance data by type and subtype (A/H3N2, A/H1N1, and B) for 19 temperate countries in the Northern and Southern hemispheres from 1997 to 2005, compiled from a public database maintained by WHO (FluNet). Key findings include patterns of large scale co-occurrence of influenza type A and B, interhemispheric synchrony for subtype A/H3N2, and latitudinal gradients in epidemic timing for type A. These findings highlight the need for more countries to conduct year-round viral surveillance and report reliable incidence data at the type and subtype level, especially in the Tropics

Genetic Diversity in the SIR Model of Pathogen Evolution

We introduce a model for assessing the levels and patterns of genetic diversity in pathogen populations, whose epidemiology follows a susceptible-infected-recovered model (SIR). We model the population of pathogens as a metapopulation composed of subpopulations (infected hosts), where pathogens replicate and mutate. Hosts transmit pathogens to uninfected hosts. We show that the level of pathogen variation is well predicted by analytical expressions, such that pathogen neutral molecular variation is bounded by the level of infection and increases with the duration of infection. We then introduce selection in the model and study the invasion probability of a new pathogenic strain whose fitness (R0(1+s)) is higher than the fitness of the resident strain (R0). We show that this invasion probability is given by the relative increment in R0 of the new pathogen (s). By analyzing the patterns of genetic diversity in this framework, we identify the molecular signatures during the replacement and compare these with those observed in sequences of influenza A

Immune Boosting Explains Regime-Shifts in Prevaccine-Era Pertussis Dynamics

Understanding the biological mechanisms underlying episodic outbreaks of infectious diseases is one of mathematical epidemiology’s major goals. Historic records are an invaluable source of information in this enterprise. Pertussis (whooping cough) is a re-emerging infection whose intermittent bouts of large multiannual epidemics interspersed between periods of smaller-amplitude cycles remain an enigma. It has been suggested that recent increases in pertussis incidence and shifts in the age-distribution of cases may be due to diminished natural immune boosting. Here we show that a model that incorporates this mechanism can account for a unique set of pre-vaccine-era data from Copenhagen. Under this model, immune boosting induces transient bursts of large amplitude outbreaks. In the face of mass vaccination, the boosting model predicts larger and more frequent outbreaks than do models with permanent or passively-waning immunity. Our results emphasize the importance of understanding the mechanisms responsible for maintaining immune memory fo

School closures during the 2009 influenza pandemic: national and local experiences

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A Minimal Model for Multiple Epidemics and Immunity Spreading

Pathogens and parasites are ubiquitous in the living world, being limited only by availability of suitable hosts. The ability to transmit a particular disease depends on competing infections as well as on the status of host immunity. Multiple diseases compete for the same resource and their fate is coupled to each other. Such couplings have many facets, for example cross-immunization between related influenza strains, mutual inhibition by killing the host, or possible even a mutual catalytic effect if host immunity is impaired. We here introduce a minimal model for an unlimited number of unrelated pathogens whose interaction is simplified to simple mutual exclusion. The model incorporates an ongoing development of host immunity to past diseases, while leaving the system open for emergence of new diseases. The model exhibits a rich dynamical behavior with interacting infection waves, leaving broad trails of immunization in the host population. This obtained immunization pattern depends only on the system size and on the mutation rate that initiates new diseases

Influenza A Gradual and Epochal Evolution: Insights from Simple Models

The recurrence of influenza A epidemics has originally been explained by a “continuous antigenic drift” scenario. Recently, it has been shown that if genetic drift is gradual, the evolution of influenza A main antigen, the haemagglutinin, is punctuated. As a consequence, it has been suggested that influenza A dynamics at the population level should be approximated by a serial model. Here, simple models are used to test whether a serial model requires gradual antigenic drift within groups of strains with the same antigenic properties (antigenic clusters). We compare the effect of status based and history based frameworks and the influence of reduced susceptibility and infectivity assumptions on the transient dynamics of antigenic clusters. Our results reveal that the replacement of a resident antigenic cluster by a mutant cluster, as observed in data, is reproduced only by the status based model integrating the reduced infectivity assumption. This combination of assumptions is useful to overcome the otherwise extremely high model dimensionality of models incorporating many strains, but relies on a biological hypothesis not obviously satisfied. Our findings finally suggest the dynamical importance of gradual antigenic drift even in the presence of punctuated immune escape. A more regular renewal of susceptible pool than the one implemented in a serial model should be part of a minimal theory for influenza at the population level

Spatial clustering in the spatio-temporal dynamics of endemic cholera

<p>Abstract</p> <p>Background</p> <p>The spatio-temporal patterns of infectious diseases that are environmentally driven reflect the combined effects of transmission dynamics and environmental heterogeneity. They contain important information on different routes of transmission, including the role of environmental reservoirs. Consideration of the spatial component in infectious disease dynamics has led to insights on the propagation of fronts at the level of counties in rabies in the US, and the metapopulation behavior at the level of cities in childhood diseases such as measles in the UK, both at relatively coarse scales. As epidemiological data on individual infections become available, spatio-temporal patterns can be examined at higher resolutions.</p> <p>Methods</p> <p>The extensive spatio-temporal data set for cholera in Matlab, Bangladesh, maps the individual location of cases from 1983 to 2003. This unique record allows us to examine the spatial structure of cholera outbreaks, to address the role of primary transmission, occurring from an aquatic reservoir to the human host, and that of secondary transmission, involving a feedback between current and past levels of infection. We use Ripley's K and L indices and bootstrapping methods to evaluate the occurrence of spatial clustering in the cases during outbreaks using different temporal windows. The spatial location of cases was also confronted against the spatial location of water sources.</p> <p>Results</p> <p>Spatial clustering of cholera cases was detected at different temporal and spatial scales. Cases relative to water sources also exhibit spatial clustering.</p> <p>Conclusions</p> <p>The clustering of cases supports an important role of secondary transmission in the dynamics of cholera epidemics in Matlab, Bangladesh. The spatial clustering of cases relative to water sources, and its timing, suggests an effective role of water reservoirs during the onset of cholera outbreaks. Once primary transmission has initiated an outbreak, secondary transmission takes over and plays a fundamental role in shaping the epidemics in this endemic area.</p