Compositional modelling of immune response and virus transmission dynamics.

Transmission models for infectious diseases are typically formulated in terms of dynamics between individuals or groups with processes such as disease progression or recovery for each individual captured phenomenologically, without reference to underlying biological processes. Furthermore, the construction of these models is often monolithic: they do not allow one to readily modify the processes involved or include the new ones, or to combine models at different scales. We show how to construct a simple model of immune response to a respiratory virus and a model of transmission using an easily modifiable set of rules allowing further refining and merging the two models together. The immune response model reproduces the expected response curve of PCR testing for COVID-19 and implies a long-tailed distribution of infectiousness reflective of individual heterogeneity. This immune response model, when combined with a transmission model, reproduces the previously reported shift in the population distribution of viral loads along an epidemic trajectory. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Estimating the resources required in the roll-out of universal access to antiretroviral treatment in Zimbabwe.

OBJECTIVES: To develop projections of the resources required (person-years of drug supply and healthcare worker time) for universal access to antiretroviral treatment (ART) in Zimbabwe. METHODS: A stochastic mathematical model of disease progression, diagnosis, clinical monitoring and survival in HIV infected individuals. FINDINGS: The number of patients receiving ART is determined by many factors, including the strategy of the ART programme (method of initiation, frequency of patient monitoring, ability to include patients diagnosed before ART became available), other healthcare services (referral rates from antenatal clinics, uptake of HIV testing), demographic and epidemiological conditions (past and future trends in incidence rates and population growth) as well as the medical impact of ART (average survival and the relationship with CD4 count when initiated). The variations in these factors lead to substantial differences in long-term projections; with universal access by 2010 and no further prevention interventions, between 370 000 and almost 2 million patients could be receiving treatment in 2030-a fivefold difference. Under universal access, by 2010 each doctor will initiate ART for up to two patients every day and the case-load for nurses will at least triple as more patients enter care and start treatment. CONCLUSIONS: The resources required by ART programmes are great and depend on the healthcare systems and the demographic/epidemiological context. This leads to considerable uncertainty in long-term projections and large variation in the resources required in different countries and over time. Understanding how current practices relate to future resource requirements can help optimise ART programmes and inform long-term public health planning.

Using tests for recent infection to estimate incidence: problems and prospects for HIV.

Tests for recent infection (TRIs), such as the BED assay, provide a convenient way to estimate HIV incidence rates from cross-sectional survey data. Controversy has arisen over how the imperfect performance of a TRI should be characterised and taken into account. Recent theoretical work is providing a unified framework within which to work with a variety of TRI- and epidemic-specific assumptions in order to estimate incidence using imperfect TRIs, but suggests that larger survey sample sizes will be required than previously thought. This paper reviews the framework qualitatively and provides examples of estimator performance, identifying the characteristics required by a TRI to estimate incidence reliably that should guide the future development of TRIs.

Role of widows in the heterosexual transmission of HIV in Manicaland, Zimbabwe, 1998-2003.

BACKGROUND: AIDS is the main driver of young widowhood in southern Africa. METHODS: The demographic characteristics of widows, their reported risk behaviours and the prevalence of HIV were examined by analysing a longitudinal population-based cohort of men and women aged 15-54 years in Manicaland, eastern Zimbabwe. The results from statistical analyses were used to construct a mathematical simulation model with the aim of estimating the contribution of widow behaviour to heterosexual HIV transmission. RESULTS: 413 (11.4%) sexually experienced women and 31 (1.2%) sexually experienced men were reported to be widowed at the time of follow-up. The prevalence of HIV was exceptionally high among both widows (61%) and widowers (male widows) (54%). Widows were more likely to have high rates of partner change and engage in a pattern of transactional sex than married women. Widowers took partners who were a median of 10 years younger than themselves. Mathematical model simulations of different scenarios of sexual behaviour of widows suggested that the sexual activity of widow(er)s may underlie 8-17% of new HIV infections over a 20-year period. CONCLUSIONS: This combined statistical analysis and model simulation suggest that widowhood plays an important role in the transmission of HIV in this rural Zimbabwean population. High-risk partnerships may be formed when widowed men and women reconnect to the sexual network.

The role of testing and counselling for HIV prevention and care in the era of scaling-up antiretroviral therapy.

OBJECTIVE: HIV Testing and Counselling (TC) programmes are being scaled-up as part of efforts to provide universal access to antiretroviral treatment (ART). METHODS AND FINDINGS: Mathematical modelling of TC in Zimbabwe shows that if universal access is to be sustained, TC must include prevention counselling that enables behaviour change among infected and uninfected individuals. The predicted impact TC is modest, but improved programmes could generate substantial reductions in incidence, reducing need for ART in the long-term. CONCLUSIONS: TC programmes that focus only on identifying those in need of treatment will not be sufficient to bring the epidemic under control.

Interpreting declines in HIV prevalence: impact of spatial aggregation and migration on expected declines in prevalence.

BACKGROUND: Declines in the prevalence of HIV might occur due to natural epidemic dynamics rather than changes in risk behaviour. Determining the cause of an observed decline is important in understanding the epidemiology of HIV. OBJECTIVE: To explore how patterns of recruitment and interactions between subpopulations in different areas influence the predicted decline in the prevalence of HIV in the absence of reductions in risk behaviour. METHODS: A deterministic mathematical model of the heterosexual transmission of HIV in high prevalence endemic settings incorporating various patterns of recruitment to high-risk behaviour groups, population growth and migration was solved numerically. The possibility that apparent trends are generated or obscured through aggregating data from across areas experiencing different epidemics is also considered. RESULTS: Declines in the prevalence of HIV can occur even if individuals do not change behaviour, raising the possibility that epidemic downturns could be wrongly attributed to interventions. This effect is greatest when individuals do not enter higher risk groups to compensate for reductions in size caused by deaths from AIDS and when migration is non-random with respect to risk or infectious status and migration patterns change as the epidemic matures. In contrast, aggregating prevalence data from subregions with different epidemic profiles tends to mask declines in prevalence. CONCLUSIONS: Interpreting surveillance data is important in understanding widespread responses to HIV epidemics. The results show that understanding patterns of adoption of risk behaviours and patterns of migration is important in interpreting declines in the prevalence of HIV.

Measuring effectiveness in community randomized trials of HIV prevention.

BACKGROUND: Complicated HIV transmission dynamics make it unclear how to design and interpret results from community-randomized controlled trials (CRCT) of interventions to prevent infection. METHODS: Mathematical modelling was used to investigate the effectiveness of interventions to prevent HIV transmission aimed at high-risk groups and factors related to the chance of recording a statistically significant result. RESULTS: Behaviour change by high-risk groups can substantially reduce HIV incidence in the whole population, although its effect is sensitive to the structure of the sexual network and the phase of the epidemic. There is a delay between the behaviour change happening and its full effect being realized in the low-risk group and this can pull the measured incidence rate ratio towards one and reduce the chance of recording a statistically significant result in a CRCT. Our simulations suggest that only with unrealistically favourable study conditions would a statistically significant result be likely with 5 years follow-up or less. Small differences in the epidemiological parameters between communities can lead to misleading incidence rate ratios. Behaviour change independent of the intervention can increase the epidemiological impact of the intervention and the chance of recording a statistically significant result. CONCLUSIONS: HIV prevention interventions, especially those targeted at high-risk groups may take longer to work at the population level and need more follow-up time in a CRCT to generate statistically significant results. Mathematical modelling can be used in the design and analysis of CRCTs to understand how the impact of the intervention could develop and the implications this has for statistical power.

Behaviour change in generalised HIV epidemics: impact of reducing cross-generational sex and delaying age at sexual debut.

BACKGROUND: Sexual behavioural change is essential to prevent HIV infections in Africa and statistical analysis of risk factors at the individual-level may be used to design interventions. The importance of reducing cross-generational sex (young women having sex with older men) and delaying age at first sex on the spread of HIV at the population-level has been presumed but not scientifically investigated and quantified. METHODS: A mathematical model of heterosexual spread of HIV was developed to predict the population-level impact of reducing cross-generational sex and delaying sexual debut. RESULTS: The impact of behaviour change on the spread of HIV is sensitive to the structure and reaction of the sexual network. Reducing cross-generational sex could have little impact on the risk of infection unless it is accompanied by a reduction in the number of risky sexual contacts. Even peer-to-peer sexual mixing can support high endemic levels of HIV. The benefit of delaying sexual debut is comparatively small and is reduced if males continue to prefer young partners or if young women spend more time unmarried. In Manicaland, Zimbabwe, if older men were to use condoms as frequently as young men, the reduction in risk of infection could exceed that generated by a two-year delay in first sex. CONCLUSIONS: At the individual-level avoiding sex with older partners and delaying sexual debut can decrease the risk of infection but at the population-level these interventions may do little to limit the spread of HIV without wider-ranging behavioural changes throughout the sexual network.

Declines in HIV prevalence can be associated with changing sexual behaviour in Uganda, urban Kenya, Zimbabwe, and urban Haiti.

OBJECTIVE: To determine whether observed changes in HIV prevalence in countries with generalised HIV epidemics are associated with changes in sexual risk behaviour. METHODS: A mathematical model was developed to explore the relation between prevalence recorded at antenatal clinics (ANCs) and the pattern of incidence of infection throughout the population. To create a null model a range of assumptions about sexual behaviour, natural history of infection, and sampling biases in ANC populations were explored to determine which factors maximised declines in prevalence in the absence of behaviour change. Modelled prevalence, where possible based on locally collected behavioural data, was compared with the observed prevalence data in urban Haiti, urban Kenya, urban Cote d'Ivoire, Malawi, Zimbabwe, Rwanda, Uganda, and urban Ethiopia. RESULTS: Recent downturns in prevalence observed in urban Kenya, Zimbabwe, and urban Haiti, like Uganda before them, could only be replicated in the model through reductions in risk associated with changes in behaviour. In contrast, prevalence trends in urban Cote d'Ivoire, Malawi, urban Ethiopia, and Rwanda show no signs of changed sexual behaviour. CONCLUSIONS: Changes in patterns of HIV prevalence in urban Kenya, Zimbabwe, and urban Haiti are quite recent and caution is required because of doubts over the accuracy and representativeness of these estimates. Nonetheless, the observed changes are consistent with behaviour change and not the natural course of the HIV epidemic.

Why large-scale climate indices seem to predict ecological processes better than local weather.

Large-scale climatic indices such as the North Atlantic Oscillation are associated with population dynamics, variation in demographic rates and values of phenotypic traits in many species. Paradoxically, these large-scale indices can seem to be better predictors of ecological processes than local climate. Using detailed data from a population of Soay sheep, we show that high rainfall, high winds or low temperatures at any time during a 3-month period can cause mortality either immediately or lagged by a few days. Most measures of local climate used by ecologists fail to capture such complex associations between weather and ecological process, and this may help to explain why large-scale, seasonal indices of climate spanning several months can outperform local climatic factors. Furthermore, we show why an understanding of the mechanism by which climate influences population ecology is important. Through simulation we demonstrate that the timing of bad weather within a period of mortality can have an important modifying influence on intraspecific competition for food, revealing an interaction between climate and density dependence that the use of large-scale climatic indices or inappropriate local weather variables might obscure.