Comparability of results from pair and classical model formulations for different sexually transmitted infections

How do biases in sex ratio and disease characteristics affect the spread of sexually transmitted infections?

The epidemiology of sexually transmitted infections (STIs) is inherently linked to host mating dynamics. Studies across many taxa show that adult sex ratio, a major determinant of host mating dynamics, is often skewed - sometimes strongly - toward males or females. However, few predictions exist for the effects of skewed sex ratio on STI epidemiology, and none when coupled with sex biased disease characteristics. Here we use mathematical modelling to examine how interactions between sex ratio and disease characteristics affect STI prevalence in males and females. Notably, we find that while overall disease prevalence peaks at equal sex ratios, prevalence per sex peaks at skewed sex ratios. Furthermore, disease characteristics, sex-biased or not, drive predictable differences in male and female STI prevalence as sex ratio varies, with higher transmission and lower virulence generally increasing differences between the sexes for a given sex ratio. Our work reveals new insights into how STI prevalence in males and females depends on a complex interaction between host population sex ratio and disease characteristics.

A dynamic power-law sexual network model of gonorrhoea outbreaks

Human networks of sexual contacts are dynamic by nature, with partnerships forming and breaking continuously over time. Sexual behaviours are also highly heterogeneous, so that the number of partners reported by individuals over a given period of time is typically distributed as a power-law. Both the dynamism and heterogeneity of sexual partnerships are likely to have an effect in the patterns of spread of sexually transmitted diseases. To represent these two fundamental properties of sexual networks, we developed a stochastic process of dynamic partnership formation and dissolution, which results in power-law numbers of partners over time. Model parameters can be set to produce realistic conditions in terms of the exponent of the power-law distribution, of the number of individuals without relationships and of the average duration of relationships. Using an outbreak of antibiotic resistant gonorrhoea amongst men have sex with men as a case study, we show that our realistic dynamic network exhibits different properties compared to the frequently used static networks or homogeneous mixing models. We also consider an approximation to our dynamic network model in terms of a much simpler branching process. We estimate the parameters of the generation time distribution and offspring distribution which can be used for example in the context of outbreak reconstruction based on genomic data. Finally, we investigate the impact of a range of interventions against gonorrhoea, including increased condom use, more frequent screening and immunisation, concluding that the latter shows great promise to reduce the burden of gonorrhoea, even if the vaccine was only partially effective or applied to only a random subset of the population.

The epidemiological models of Karl-Peter Hadeler

The most frequently cited articles out of KP Hadeler's 45 papers with epidemiological applications are summarized. Parasitic diseases which increase the death rate of the hosts proportional to the integer number of parasites present were described by integral equations for the generating function of the age- and time-dependent number of parasites. A model was derived for a population structured by the continuous level of parasitic infection.

Stimulated by the spread of AIDS a new class of epidemic models was developed which take into account explicitly the formation and separation of pairs. For predator-prey populations with parasitic infections threshold conditions for the persistence of the predator were derived. The interaction of epidemics and demography was analysed. Several epidemiological conditions led to backward bifurcations associated with multiple infective stationary states.

Pair formation models for sexually transmitted infections: A primer

For modelling sexually transmitted infections, duration of partnerships can strongly influence the transmission dynamics of the infection. If partnerships are monogamous, pairs of susceptible individuals are protected from becoming infected, while pairs of infected individuals delay onward transmission of the infection as long as they persist. In addition, for curable infections re-infection from an infected partner may occur. Furthermore, interventions based on contact tracing rely on the possibility of identifying and treating partners of infected individuals. To reflect these features in a mathematical model, pair formation models were introduced to mathematical epidemiology in the 1980's. They have since been developed into a widely used tool in modelling sexually transmitted infections and the impact of interventions. Here we give a basic introduction to the concepts of pair formation models for a susceptible-infected-susceptible (SIS) epidemic. We review some results and applications of pair formation models mainly in the context of chlamydia infection.

The Use of Mathematical Models of Chlamydia Transmission to Address Public Health Policy Questions: A Systematic Review

BACKGROUND

Mathematical models of chlamydia transmission can help inform disease control policy decisions when direct empirical evaluation of alternatives is impractical. We reviewed published chlamydia models to understand the range of approaches used for policy analyses and how the studies have responded to developments in the field.

METHODS

We performed a literature review by searching Medline and Google Scholar (up to October 2015) to identify publications describing dynamic chlamydia transmission models used to address public health policy questions. We extracted information on modeling methodology, interventions, and key findings.

RESULTS

We identified 47 publications (including two model comparison studies), which reported collectively on 29 distinct mathematical models. Nine models were individual-based, and 20 were deterministic compartmental models. The earliest studies evaluated the benefits of national-level screening programs and predicted potentially large benefits from increased screening. Subsequent trials and further modeling analyses suggested the impact might have been overestimated. Partner notification has been increasingly evaluated in mathematical modeling, whereas behavioral interventions have received relatively limited attention.

CONCLUSIONS

Our review provides an overview of chlamydia transmission models and gives a perspective on how mathematical modeling has responded to increasing empirical evidence and addressed policy questions related to prevention of chlamydia infection and sequelae.