Many diseases exhibit subcritical transmission (i.e. 0

We explore the transmission process for sexually transmitted diseases (STDs). We derive the classical frequency-dependent incidence mechanistically from a pair-formation model, using an approximation that applies to populations with rapid pairing dynamics (such as core groups or non-pair-bonding animals). This mechanistic derivation provides a framework to assess how accurately frequency-dependent incidence portrays the pair-based transmission known to underlie STD dynamics. This accuracy depends strongly on the disease being studied: frequency-dependent formulations are more suitable for chronic less-transmissible infections than for transient highly transmissible infections. Our results thus support earlier proposals to divide STDs into these two functional classes, and we suggest guidelines to help assess under what conditions each class can be appropriately modelled using frequency-dependent incidence. We then extend the derivation to include situations where infected individuals exhibit altered pairing behaviour. For four cases of increasing behavioural complexity, analytic expressions are presented for the generalized frequency-dependent incidence rate, basic reproductive number (R0) and steady-state prevalence (i∞) of an epidemic. The expression for R0is identical for all cases, giving refined insights into determinants of invasibility of STDs. Potentially significant effects of infection-induced changes in contact behaviour are illustrated by simulating epidemics of bacterial and viral STDs. We discuss the application of our results to STDs (in humans and animals) and other infectious diseases.

Severe acute respiratory syndrome (SARS) has been transmitted extensively within hospitals, and healthcare workers (HCWs) have comprised a large proportion of SARS cases worldwide. We present a stochastic model of a SARS outbreak in a community and its hospital. For a range of basic reproductive numbers (R0) corresponding to conditions in different cities (but with emphasis on R0∼ 3 as reported for Hong Kong and Singapore), we evaluate contact precautions and case management (quarantine and isolation) as containment measures. Hospital-based contact precautions emerge as the most potent measures, with hospital-wide measures being particularly important if screening of HCWs is inadequate. For R0= 3, case isolation alone can control a SARS outbreak only if isolation reduces transmission by at least a factor of four and the mean symptom-onset-to-isolation time is less than 3 days. Delays of a few days in contact tracing and case identification severely degrade the utility of quarantine and isolation, particularly in high-transmission settings. Still more detrimental are delays between the onset of an outbreak and the implementation of control measures; for given control scenarios, our model identifies windows of opportunity beyond which the efficacy of containment efforts is reduced greatly. By considering pathways of transmission in our system, we show that if hospital-based transmission is not halted, measures that reduce community-HCW contact are vital to preventing a widespread epidemic. The implications of our results for future emerging pathogens are discussed.

Population-level analyses often use average quantities to describe heterogeneous systems, particularly when variation does not arise from identifiable groups. A prominent example, central to our current understanding of epidemic spread, is the basic reproductive number, R(0), which is defined as the mean number of infections caused by an infected individual in a susceptible population. Population estimates of R(0) can obscure considerable individual variation in infectiousness, as highlighted during the global emergence of severe acute respiratory syndrome (SARS) by numerous 'superspreading events' in which certain individuals infected unusually large numbers of secondary cases. For diseases transmitted by non-sexual direct contacts, such as SARS or smallpox, individual variation is difficult to measure empirically, and thus its importance for outbreak dynamics has been unclear. Here we present an integrated theoretical and statistical analysis of the influence of individual variation in infectiousness on disease emergence. Using contact tracing data from eight directly transmitted diseases, we show that the distribution of individual infectiousness around R(0) is often highly skewed. Model predictions accounting for this variation differ sharply from average-based approaches, with disease extinction more likely and outbreaks rarer but more explosive. Using these models, we explore implications for outbreak control, showing that individual-specific control measures outperform population-wide measures. Moreover, the dramatic improvements achieved through targeted control policies emphasize the need to identify predictive correlates of higher infectiousness. Our findings indicate that superspreading is a normal feature of disease spread, and to frame ongoing discussion we propose a rigorous definition for superspreading events and a method to predict their frequency.

The population dynamics of infectious disease is a mature field in terms of theory and to some extent, application. However for microparasites, the theory and application of models of the dynamics within a single infected host is still an open field. Further, connecting across the scales - from cellular to host level, to population level - has potential to vastly improve our understanding of pathogen dynamics and evolution. Here, we highlight seven challenges in the following areas: transmission bottlenecks, heterogeneity within host, dynamic fitness landscapes within hosts, making use of next-generation sequencing data, capturing superinfection and when and how to model more than two scales.

Evolution is a key aspect of the biology of many pathogens, driving processes ranging from immune escape to changes in virulence. Because evolution is inherently subject to feedbacks, and because pathogen evolution plays out at scales ranging from within-host to between-host and beyond, evolutionary questions provide special challenges to the modelling community. In this article, we provide an overview of five challenges in modelling the evolution of pathogens and their hosts, and point to areas for development, focussing in particular on the issue of linking theory and data.

Recognition is a prerequisite for non-random association amongst individuals. We explore how non-random association patterns (i.e. who spends time with whom) affect disease dynamics. We estimated the amount of time individuals spent together per month using radio-tracking data from African buffalo and incorporated these data into a dynamic social network model. The dynamic nature of the network has a strong influence on simulated disease dynamics particularly for diseases with shorter infectious periods. Cluster analyses of the association data demonstrated that buffalo herds were not as well defined as previously thought. Associations were more tightly clustered in 2002 than 2003, perhaps due to drier conditions in 2003. As a result, diseases may spread faster during drought conditions due to increased population mixing. Association data are often collected but this is the first use of empirical data in a network disease model in a wildlife population.

Many disease systems exhibit complexities not captured by current theoretical and empirical work. In particular, systems with multiple host species and multiple infectious agents (i.e., multi-host, multi-agent systems) require novel methods to extend the wealth of knowledge acquired studying primarily single-host, single-agent systems. We outline eight challenges in multi-host, multi-agent systems that could substantively increase our knowledge of the drivers and broader ecosystem effects of infectious disease dynamics.

Studying the emergence of novel infectious agents involves many processes spanning host species, spatial scales, and scientific disciplines. Mathematical models play an essential role in combining insights from these investigations and drawing robust inferences from field and experimental data. We describe nine challenges in modelling the emergence of novel pathogens, emphasizing the interface between models and data.