Age-specific transmission dynamics of SARS-CoV-2 during the first 2 years of the pandemic

During its first 2 years, the SARS-CoV-2 pandemic manifested as multiple waves shaped by complex interactions between variants of concern, non-pharmaceutical interventions, and the immunological landscape of the population. Understanding how the age-specific epidemiology of SARS-CoV-2 has evolved throughout the pandemic is crucial for informing policy decisions. In this article, we aimed to develop an inference-based modeling approach to reconstruct the burden of true infections and hospital admissions in children, adolescents, and adults over the seven waves of four variants (wild-type, Alpha, Delta, and Omicron BA.1) during the first 2 years of the pandemic, using the Netherlands as the motivating example. We find that reported cases are a considerable underestimate and a generally poor predictor of true infection burden, especially because case reporting differs by age. The contribution of children and adolescents to total infection and hospitalization burden increased with successive variants and was largest during the Omicron BA.1 period. However, the ratio of hospitalizations to infections decreased with each subsequent variant in all age categories. Before the Delta period, almost all infections were primary infections occurring in naive individuals. During the Delta and Omicron BA.1 periods, primary infections were common in children but relatively rare in adults who experienced either reinfections or breakthrough infections. Our approach can be used to understand age-specific epidemiology through successive waves in other countries where random community surveys uncovering true SARS-CoV-2 dynamics are absent but basic surveillance and statistics data are available.

Estimation of introduction and transmission rates of SARS-CoV-2 in a prospective household study

Household studies provide an efficient means to study transmission of infectious diseases, enabling estimation of susceptibility and infectivity by person-type. A main inclusion criterion in such studies is usually the presence of an infected person. This precludes estimation of the hazards of pathogen introduction into the household. Here we estimate age- and time-dependent household introduction hazards together with within household transmission rates using data from a prospective household-based study in the Netherlands. A total of 307 households containing 1,209 persons were included from August 2020 until March 2021. Follow-up of households took place between August 2020 and August 2021 with maximal follow-up per household mostly limited to 161 days. Almost 1 out of 5 households (59/307) had evidence of an introduction of SARS-CoV-2. We estimate introduction hazards and within-household transmission rates in our study population with penalized splines and stochastic epidemic models, respectively. The estimated hazard of introduction of SARS-CoV-2 in the households was lower for children (0-12 years) than for adults (relative hazard: 0.62; 95%CrI: 0.34-1.0). Estimated introduction hazards peaked in mid October 2020, mid December 2020, and mid April 2021, preceding peaks in hospital admissions by 1-2 weeks. Best fitting transmission models included increased infectivity of children relative to adults and adolescents, such that the estimated child-to-child transmission probability (0.62; 95%CrI: 0.40-0.81) was considerably higher than the adult-to-adult transmission probability (0.12; 95%CrI: 0.057-0.19). Scenario analyses indicate that vaccination of adults can strongly reduce household infection attack rates and that adding adolescent vaccination offers limited added benefit.

Evolutionary implications of SARS-CoV-2 vaccination for the future design of vaccination strategies

Once the first SARS-CoV-2 vaccine became available, mass vaccination was the main pillar of the public health response to the COVID-19 pandemic. It was very effective in reducing hospitalizations and deaths. Here, we discuss the possibility that mass vaccination might accelerate SARS-CoV-2 evolution in antibody-binding regions compared to natural infection at the population level. Using the evidence of strong genetic variation in antibody-binding regions and taking advantage of the similarity between the envelope proteins of SARS-CoV-2 and influenza, we assume that immune selection pressure acting on these regions of the two viruses is similar. We discuss the consequences of this assumption for SARS-CoV-2 evolution in light of mathematical models developed previously for influenza. We further outline the implications of this phenomenon, if our assumptions are confirmed, for the future design of SARS-CoV-2 vaccination strategies.

The impact of variant and vaccination on SARS-CoV-2 symptomatology; three prospective household cohorts

OBJECTIVES

We compared age-stratified SARS-CoV-2 symptomatology of wild-type/Alpha vs Omicron BA.1/BA.2 variant infected individuals and the impact of COVID-19 booster vaccination on Omicron symptom burden.

METHODS

Data from three European prospective household cohorts were used (April 2020 to April 2021 and January to March 2022). Standardized outbreak protocols included (repeated) polymerase chain reaction testing, paired serology, and daily symptom scoring for all household members. Comparative analyses were performed on 346 secondary household cases from both periods.

RESULTS

Children <12 years (all unvaccinated) experienced more symptoms and higher severity scores during Omicron compared with wild-type/Alpha period (P ≤0.01). In adults, Omicron disease duration and severity were reduced (P ≤ 0.095). Omicron was associated with lower odds for loss of smell or taste (adjusted odds ratio [aOR]: 0.14; 95% CI 0.03-0.50) and higher but non-significant odds for upper respiratory symptoms, fever, and fatigue (aORs: 1.85-2.23). No differences were observed in disease severity or duration between primary vs booster series vaccinated adults (P ≥0.12).

CONCLUSION

The Omicron variant causes higher symptom burden in children compared with wild-type/Alpha and lower in adults, possibly due to previous vaccination. A shift in symptoms occurred with reduction in loss of smell/taste for Omicron. No additional effect of booster vaccination on Omicron symptom burden was observed.

The experienced positive and negative influence of HIV on quality of life of people with HIV and vulnerable to HIV in the Netherlands

This qualitative study aimed to explore the experienced influence of HIV on the quality of life (QoL) of people with HIV (PHIV) and key populations without but are vulnerable to HIV in the Netherlands. We conducted and thematically analyzed interviews with 29 PHIV and 13 participants from key populations without HIV (i.e., men who have sex with men). PHIV and key populations shared positive meaningful experiences regarding HIV, i.e., feeling grateful for ART, life, and the availability of PrEP, being loved and supported in the light of HIV, and providing support to the community. Negative predominant experiences regarding HIV were described by both PHIV and key populations as the negative effects of ART, challenges with regards to disclosing HIV, social stigmatization, and self-stigma. It remains important to support HIV community organizations in their efforts to reduce social stigmatization and to continue improving biomedical interventions for HIV.

Challenges for modelling interventions for future pandemics

Mathematical modelling and statistical inference provide a framework to evaluate different non-pharmaceutical and pharmaceutical interventions for the control of epidemics that has been widely used during the COVID-19 pandemic. In this paper, lessons learned from this and previous epidemics are used to highlight the challenges for future pandemic control. We consider the availability and use of data, as well as the need for correct parameterisation and calibration for different model frameworks. We discuss challenges that arise in describing and distinguishing between different interventions, within different modelling structures, and allowing both within and between host dynamics. We also highlight challenges in modelling the health economic and political aspects of interventions. Given the diversity of these challenges, a broad variety of interdisciplinary expertise is needed to address them, combining mathematical knowledge with biological and social insights, and including health economics and communication skills. Addressing these challenges for the future requires strong cross-disciplinary collaboration together with close communication between scientists and policy makers.

Time for change: Transitions between HIV risk levels and determinants of behavior change in men who have sex with men

As individual sexual behavior is variable over time, the timing of interventions might be vital to reducing HIV transmission. We aimed to investigate transitions between HIV risk levels among men who have sex with men (MSM), and identify determinants associated with behavior change. Participants in a longitudinal cohort study among HIV-negative MSM (Amsterdam Cohort Studies) completed questionnaires about their sexual behavior during biannual visits (2008-2017). Visits were assigned to different HIV risk levels, based on latent classes of behavior. We modelled transitions between risk levels, and identified determinants associated with these transitions at the visit preceding the transition using multi-state Markov models. Based on 7,865 visits of 767 participants, we classified three risk levels: low (73% of visits), medium (22%), and high risk (5%). For MSM at low risk, the six-month probability of increasing risk was 0.11. For MSM at medium risk, the probability of increasing to high risk was 0.08, while the probability of decreasing to low risk was 0.33. For MSM at high risk, the probability of decreasing risk was 0.43. Chemsex, erection stimulants and poppers, high HIV risk perception, and recent STI diagnosis were associated with increased risk at the next visit. High HIV risk perception and young age were associated with decreasing risk. Although the majority of MSM showed no behavior change, a considerable proportion increased HIV risk. Determinants associated with behavior change may help to identify MSM who are likely to increase risk in the near future and target interventions at these individuals, thereby reducing HIV transmission.

Quantifying heterogeneity in sexual behaviour and distribution of STIs before and after pre-exposure prophylaxis among men who have sex with men

Objectives: Pre-exposure prophylaxis (PrEP) use may influence sexual behaviour and transmission of STIs among men who have sex with men (MSM). We aimed to quantify the distribution of STI diagnoses among MSM in the Netherlands based on their sexual behaviour before and after the introduction of PrEP.Methods: HIV-negative MSM participating in a prospective cohort study (Amsterdam Cohort Studies) completed questionnaires about sexual behaviour and were tested for STI/HIV during biannual visits (2009-2019). We developed a sexual behaviour risk score predictive of STI diagnosis and used it to calculate Gini coefficients for gonorrhoea, chlamydia and syphilis diagnoses in the period before (2009 to mid-2015) and after PrEP (mid-2015 to 2019). Gini coefficients close to zero indicate that STI diagnoses are homogeneously distributed over the population, and close to one indicate that STI diagnoses are concentrated in individuals with a higher risk score.Results: The sexual behaviour risk score (n=630, n visits=10 677) ranged between 0.00 (low risk) and 3.61 (high risk), and the mean risk score increased from 0.70 (SD=0.66) before to 0.93 (SD=0.80) after PrEP. Positivity rates for chlamydia (4%) and syphilis (1%) remained relatively stable, but the positivity rate for gonorrhoea increased from 4% before to 6% after PrEP. Gini coefficients increased from 0.37 (95% CI 0.30 to 0.43) to 0.43 (95% CI 0.36 to 0.49) for chlamydia, and from 0.37 (95% CI 0.19 to 0.52) to 0.50 (95% CI 0.32 to 0.66) for syphilis comparing before to after PrEP. The Gini coefficient for gonorrhoea remained stable at 0.46 (95% CI 0.40 to 0.52) before and after PrEP.Conclusions: MSM engaged in more high-risk sexual behaviour and gonorrhoea diagnoses increased after PrEP was introduced. Chlamydia and syphilis diagnoses have become more concentrated in a high-risk subgroup. Monitoring the impact of increasing PrEP coverage on sexual behaviour and STI incidence is important. Improved STI prevention is needed, especially for high-risk MSM.

Controlling the pandemic during the SARS-CoV-2 vaccination rollout

There is a consensus that mass vaccination against SARS-CoV-2 will ultimately end the COVID-19 pandemic. However, it is not clear when and which control measures can be relaxed during the rollout of vaccination programmes. We investigate relaxation scenarios using an age-structured transmission model that has been fitted to age-specific seroprevalence data, hospital admissions, and projected vaccination coverage for Portugal. Our analyses suggest that the pressing need to restart socioeconomic activities could lead to new pandemic waves, and that substantial control efforts prove necessary throughout 2021. Using knowledge on control measures introduced in 2020, we anticipate that relaxing measures completely or to the extent as in autumn 2020 could launch a wave starting in April 2021. Additional waves could be prevented altogether if measures are relaxed as in summer 2020 or in a step-wise manner throughout 2021. We discuss at which point the control of COVID-19 would be achieved for each scenario.

The Rhythm of Risk: Sexual Behaviour, PrEP Use and HIV Risk Perception Between 1999 and 2018 Among Men Who Have Sex with Men in Amsterdam, The Netherlands

HIV risk perception plays a crucial role in the uptake of preventive strategies. We investigated how risk perception and its determinants changed between 1999 and 2018 in an open, prospective cohort of 1323 HIV-negative men who have sex with men (MSM). Risk perception, defined as the perceived likelihood of acquiring HIV in the past 6 months, changed over time: being relatively lower in 2008–2011, higher in 2012–2016, and again lower in 2017–2018. Irrespective of calendar year, condomless anal intercourse (AI) with casual partners and high numbers of partners were associated with higher risk perception. In 2017–2018, condomless receptive AI with a partner living with HIV was no longer associated with risk perception, while PrEP use and condomless AI with a steady partner were associated with lower risk perception. We showed that risk perception has fluctuated among MSM in the past 20 years. The Undetectable equals Untransmittable statement and PrEP coincided with lower perceived risk.

Model-based evaluation of school- and non-school-related measures to control the COVID-19 pandemic

The role of school-based contacts in the epidemiology of SARS-CoV-2 is incompletely understood. We use an age-structured transmission model fitted to age-specific seroprevalence and hospital admission data to assess the effects of school-based measures at different time points during the COVID-19 pandemic in the Netherlands. Our analyses suggest that the impact of measures reducing school-based contacts depends on the remaining opportunities to reduce non-school-based contacts. If opportunities to reduce the effective reproduction number (Re) with non-school-based measures are exhausted or undesired and Re is still close to 1, the additional benefit of school-based measures may be considerable, particularly among older school children. As two examples, we demonstrate that keeping schools closed after the summer holidays in 2020, in the absence of other measures, would not have prevented the second pandemic wave in autumn 2020 but closing schools in November 2020 could have reduced Re below 1, with unchanged non-school-based contacts.

[Forecasting the Pandemic: The Role of Mathematical Models]

N/a.

Short- and long-term impact of vaccination against cytomegalovirus: a modeling study

BACKGROUND

Infection with cytomegalovirus (CMV) is highly prevalent worldwide and can cause severe disease in immunocompromised persons and congenitally infected infants. The disease burden caused by congenital CMV infection is high, especially in resource-limited countries. Vaccines are currently under development for various target groups.

METHODS

We evaluated the impact of vaccination strategies and hygiene intervention using transmission models. Model parameters were estimated from a cross-sectional serological population study (n=5179) and a retrospective birth cohort (n=31,484), providing information on the age- and sex-specific CMV prevalence and on the birth prevalence of congenital CMV (cCMV).

RESULTS

The analyses show that vertical transmission and infectious reactivation are the main drivers of transmission. Vaccination strategies aimed at reducing transmission from mother to child (vaccinating pregnant women or women of reproductive age) can yield substantial reductions of cCMV in 20 years (31.7-71.4% if 70% of women are effectively vaccinated). Alternatively, hygiene intervention aimed at preventing CMV infection and re-infection of women of reproductive age from young children is expected to reduce cCMV by less than 2%. The effects of large-scale vaccination on CMV prevalence can be substantial, owing to the moderate transmissibility of CMV at the population level. However, as CMV causes lifelong infection, the timescale on which reductions in CMV prevalence are expected is in the order of several decades. Elimination of CMV infection in the long run is only feasible for a vaccine with a long duration of protection and high vaccination coverage.

CONCLUSIONS

Vaccination is an effective intervention to reduce the birth prevalence of cCMV. Population-level reductions in CMV prevalence can only be achieved on a long timescale. Our results stress the value of vaccinating pregnant women and women of childbearing age and provide support for the development of CMV vaccines and early planning of vaccination scenarios and rollouts.

Impact of self-imposed prevention measures and short-term government-imposed social distancing on mitigating and delaying a COVID-19 epidemic: A modelling study

BACKGROUND

The coronavirus disease (COVID-19) caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has spread to nearly every country in the world since it first emerged in China in December 2019. Many countries have implemented social distancing as a measure to "flatten the curve" of the ongoing epidemics. Evaluation of the impact of government-imposed social distancing and of other measures to control further spread of COVID-19 is urgent, especially because of the large societal and economic impact of the former. The aim of this study was to compare the individual and combined effectiveness of self-imposed prevention measures and of short-term government-imposed social distancing in mitigating, delaying, or preventing a COVID-19 epidemic.

METHODS AND FINDINGS

We developed a deterministic compartmental transmission model of SARS-CoV-2 in a population stratified by disease status (susceptible, exposed, infectious with mild or severe disease, diagnosed, and recovered) and disease awareness status (aware and unaware) due to the spread of COVID-19. Self-imposed measures were assumed to be taken by disease-aware individuals and included handwashing, mask-wearing, and social distancing. Government-imposed social distancing reduced the contact rate of individuals irrespective of their disease or awareness status. The model was parameterized using current best estimates of key epidemiological parameters from COVID-19 clinical studies. The model outcomes included the peak number of diagnoses, attack rate, and time until the peak number of diagnoses. For fast awareness spread in the population, self-imposed measures can significantly reduce the attack rate and diminish and postpone the peak number of diagnoses. We estimate that a large epidemic can be prevented if the efficacy of these measures exceeds 50%. For slow awareness spread, self-imposed measures reduce the peak number of diagnoses and attack rate but do not affect the timing of the peak. Early implementation of short-term government-imposed social distancing alone is estimated to delay (by at most 7 months for a 3-month intervention) but not to reduce the peak. The delay can be even longer and the height of the peak can be additionally reduced if this intervention is combined with self-imposed measures that are continued after government-imposed social distancing has been lifted. Our analyses are limited in that they do not account for stochasticity, demographics, heterogeneities in contact patterns or mixing, spatial effects, imperfect isolation of individuals with severe disease, and reinfection with COVID-19.

CONCLUSIONS

Our results suggest that information dissemination about COVID-19, which causes individual adoption of handwashing, mask-wearing, and social distancing, can be an effective strategy to mitigate and delay the epidemic. Early initiated short-term government-imposed social distancing can buy time for healthcare systems to prepare for an increasing COVID-19 burden. We stress the importance of disease awareness in controlling the ongoing epidemic and recommend that, in addition to policies on social distancing, governments and public health institutions mobilize people to adopt self-imposed measures with proven efficacy in order to successfully tackle COVID-19.

Impact of self-imposed prevention measures and short-term government-imposed social distancing on mitigating and delaying a COVID-19 epidemic: A modelling study

BACKGROUND

The coronavirus disease (COVID-19) caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has spread to nearly every country in the world since it first emerged in China in December 2019. Many countries have implemented social distancing as a measure to "flatten the curve" of the ongoing epidemics. Evaluation of the impact of government-imposed social distancing and of other measures to control further spread of COVID-19 is urgent, especially because of the large societal and economic impact of the former. The aim of this study was to compare the individual and combined effectiveness of self-imposed prevention measures and of short-term government-imposed social distancing in mitigating, delaying, or preventing a COVID-19 epidemic.

METHODS AND FINDINGS

We developed a deterministic compartmental transmission model of SARS-CoV-2 in a population stratified by disease status (susceptible, exposed, infectious with mild or severe disease, diagnosed, and recovered) and disease awareness status (aware and unaware) due to the spread of COVID-19. Self-imposed measures were assumed to be taken by disease-aware individuals and included handwashing, mask-wearing, and social distancing. Government-imposed social distancing reduced the contact rate of individuals irrespective of their disease or awareness status. The model was parameterized using current best estimates of key epidemiological parameters from COVID-19 clinical studies. The model outcomes included the peak number of diagnoses, attack rate, and time until the peak number of diagnoses. For fast awareness spread in the population, self-imposed measures can significantly reduce the attack rate and diminish and postpone the peak number of diagnoses. We estimate that a large epidemic can be prevented if the efficacy of these measures exceeds 50%. For slow awareness spread, self-imposed measures reduce the peak number of diagnoses and attack rate but do not affect the timing of the peak. Early implementation of short-term government-imposed social distancing alone is estimated to delay (by at most 7 months for a 3-month intervention) but not to reduce the peak. The delay can be even longer and the height of the peak can be additionally reduced if this intervention is combined with self-imposed measures that are continued after government-imposed social distancing has been lifted. Our analyses are limited in that they do not account for stochasticity, demographics, heterogeneities in contact patterns or mixing, spatial effects, imperfect isolation of individuals with severe disease, and reinfection with COVID-19.

CONCLUSIONS

Our results suggest that information dissemination about COVID-19, which causes individual adoption of handwashing, mask-wearing, and social distancing, can be an effective strategy to mitigate and delay the epidemic. Early initiated short-term government-imposed social distancing can buy time for healthcare systems to prepare for an increasing COVID-19 burden. We stress the importance of disease awareness in controlling the ongoing epidemic and recommend that, in addition to policies on social distancing, governments and public health institutions mobilize people to adopt self-imposed measures with proven efficacy in order to successfully tackle COVID-19.

Modelling the dynamics of population viral load measures under HIV treatment as prevention

In 2011 the Centers for Disease Control and Prevention (CDC) published guidelines for the use of population viral load (PVL), community viral load (CVL) and monitored viral load (MVL), defined as the average viral load (VL) of all HIV infected individuals in a population, of all diagnosed individuals, and of all individuals on antiretroviral treatment (ART), respectively. Since then, CVL has been used to assess the effectiveness of ART on HIV transmission and as a proxy for HIV incidence. The first objective of this study was to investigate how aggregate VL measures change with the HIV epidemic phase and the drivers behind these changes using a mathematical transmission model. Secondly, we aimed to give some insight into how well CVL correlates with HIV incidence during the course of the epidemic and roll out of ART. We developed a compartmental model for disease progression and HIV transmission with disease stages that differ in viral loads for epidemiological scenarios relevant to a concentrated epidemic in a population of men who have sex with men (MSM) in Western Europe (WE) and to a generalized epidemic in a heterosexual population in Sub-Saharan Africa (SSA). The model predicts that PVL and CVL change with the epidemic phase, while MVL stays constant. These dynamics are linked to the dynamics of infected subgroups (undiagnosed, diagnosed untreated and treated) in different disease stages (primary, chronic and AIDS). In particular, CVL decreases through all epidemic stages: before ART, since chronic population builds up faster than AIDS population and after ART, due to the build-up of treated population with low VL. The trends in CVL and incidence can be both opposing and coinciding depending on the epidemic phase. Before ART is scaled up to sufficiently high levels, incidence increases while CVL decreases. After this point, CVL is a useful indicator of changes in HIV incidence. The model predicts that during the ART scale-up HIV transmission is driven by undiagnosed and diagnosed untreated individuals, and that new infections decline due to the increase in the number of treated. Although CVL is not able to capture the contribution of undiagnosed population to HIV transmission, it declines due to the increase of people on ART too. In the scenarios described by our model, the present epidemic phase corresponds to declining trends in CVL and incidence.

Antigenic evolution of viruses in host populations

To escape immune recognition in previously infected hosts, viruses evolve genetically in immunologically important regions. The host’s immune system responds by generating new memory cells recognizing the mutated viral strains. Despite recent advances in data collection and analysis, it remains conceptually unclear how epidemiology, immune response, and evolutionary factors interact to produce the observed speed of evolution and the incidence of infection. Here we establish a general and simple relationship between long-term cross-immunity, genetic diversity, speed of evolution, and incidence. We develop an analytic method fusing the standard epidemiological susceptible-infected-recovered approach and the modern virus evolution theory. The model includes the factors of strain selection due to immune memory cells, random genetic drift, and clonal interference effects. We predict that the distribution of recovered individuals in memory serotypes creates a moving fitness landscape for the circulating strains which drives antigenic escape. The fitness slope (effective selection coefficient) is proportional to the reproductive number in the absence of immunity R₀ and inversely proportional to the cross-immunity distance a, defined as the genetic distance of a virus strain from a previously infecting strain conferring 50% decrease in infection probability. Analysis predicts that the evolution rate increases linearly with the fitness slope and logarithmically with the genomic mutation rate and the host population size. Fitting our analytic model to data obtained for influenza A H3N2 and H1N1, we predict the annual infection incidence within a previously estimated range, (4-7)%, and the antigenic mutation rate of U_b = (5 − 8) ⋅ 10⁻⁴ per transmission event per genome. Our prediction of the cross-immunity distance of a = (14 − 15) aminoacid substitutions agrees with independent data for equine influenza.

Spread of many RNA viruses in a population represents a competition between host immune responses and viral evolution. RNA viruses accumulate mutations in immunologically important regions to escape immune recognition in hosts previously exposed to infection, while the immune system responds by producing new memory cells. Despite recent advances in data collection and their analysis, it remains conceptually unclear how epidemiology, immune response, and evolutionary factors interact to produce the observed speed of evolution and its incidence. By combining the standard epidemiological approach with the modern theory of viral evolution, we predict a general relationship between long-term cross-immunity, antigenic diversity of virus, its evolution speed, infection incidence, and the time to the most recent common ancestor. We apply these theoretical findings to available data on influenza virus to determine two important parameters of its evolution and confirm the model. Current strategies of vaccination against influenza should take into account stochastic fluctuations in fitness effect of mutations predicted by the theory.

Impact of Heterogeneity in Sexual Behavior on Effectiveness in Reducing HIV Transmission with Test-and-Treat Strategy

The WHO’s early-release guideline for antiretroviral treatment (ART) of HIV infection based on a recent trial conducted in 34 countries recommends starting treatment immediately upon an HIV diagnosis. Therefore, the test-and-treat strategy may become more widely used in an effort to scale up HIV treatment and curb further transmission. Here we examine behavioural determinants of HIV transmission and how heterogeneity in sexual behaviour influences the outcomes of this strategy. Using a deterministic model, we perform a systematic investigation into the effects of various mixing patterns in a population of men who have sex with men (MSM), stratified by partner change rates, on the elimination threshold and endemic HIV prevalence. We find that both the level of overdispersion in the distribution of the number of sexual partners and mixing between population subgroups have a large influence on endemic prevalence before introduction of ART and on possible long term effectiveness of ART. Increasing heterogeneity in risk behavior may lead to lower endemic prevalence levels, but requires higher coverage levels of ART for elimination. Elimination is only feasible for populations with a rather low degree of assortativeness of mixing and requires treatment coverage of almost 80% if rates of testing and treatment uptake by all population subgroups are equal. In this case, for fully assortative mixing and 80% coverage endemic prevalence is reduced by 57%. In the presence of heterogeneity in ART uptake, elimination is easier to achieve when the subpopulation with highest risk behavior is tested and treated more often than the rest of the population, and vice versa when it is less. The developed framework can be used to extract information on behavioral heterogeneity from existing data which is otherwise hard to determine from population surveys.

HIV is endemic in populations of MSM in Western countries. As ART reduces transmission risk, increased testing and treatment rates are expected to lower HIV incidence. However, concerns are that in MSM populations changing risk behavior may counteract the impact of ART on transmission. Using a mathematical model, we investigated how heterogeneity in sexual behavior influences the possible effects of a test-and-treat strategy on HIV prevalence and in particular the prospects of eliminating HIV from these populations. We demonstrated that behavioral heterogeneity plays an important role in determining the impact of ART on reducing HIV transmission. Knowledge of behavioral heterogeneity is key in setting intervention goals in populations of MSM.

Conflicting Selection Pressures Will Constrain Viral Escape from Interfering Particles: Principles for Designing Resistance-Proof Antivirals

The rapid evolution of RNA-encoded viruses such as HIV presents a major barrier to infectious disease control using conventional pharmaceuticals and vaccines. Previously, it was proposed that defective interfering particles could be developed to indefinitely control the HIV/AIDS pandemic; in individual patients, these engineered molecular parasites were further predicted to be refractory to HIV’s mutational escape (i.e., be ‘resistance-proof’). However, an outstanding question has been whether these engineered interfering particles—termed Therapeutic Interfering Particles (TIPs)—would remain resistance-proof at the population-scale, where TIP-resistant HIV mutants may transmit more efficiently by reaching higher viral loads in the TIP-treated subpopulation. Here, we develop a multi-scale model to test whether TIPs will maintain indefinite control of HIV at the population-scale, as HIV (‘unilaterally’) evolves toward TIP resistance by limiting the production of viral proteins available for TIPs to parasitize. Model results capture the existence of two intrinsic evolutionary tradeoffs that collectively prevent the spread of TIP-resistant HIV mutants in a population. First, despite their increased transmission rates in TIP-treated sub-populations, unilateral TIP-resistant mutants are shown to have reduced transmission rates in TIP-untreated sub-populations. Second, these TIP-resistant mutants are shown to have reduced growth rates (i.e., replicative fitness) in both TIP-treated and TIP-untreated individuals. As a result of these tradeoffs, the model finds that TIP-susceptible HIV strains continually outcompete TIP-resistant HIV mutants at both patient and population scales when TIPs are engineered to express >3-fold more genomic RNA than HIV expresses. Thus, the results provide design constraints for engineering population-scale therapies that may be refractory to the acquisition of antiviral resistance.

A major obstacle to effective antimicrobial therapy campaigns is the rapid evolution of drug resistance. Given the static nature of current pharmaceuticals and vaccines, natural selection inevitably drives pathogens to mutate into drug-resistant variants that can resume productive replication. Further, these drug-resistant mutants transmit across populations, resulting in untreatable epidemics. Recently, a therapeutic strategy was proposed in which viral deletion mutants—termed therapeutic interfering particles (TIPs)—are engineered to only replicate by stealing their missing proteins from full-length viruses in co-infected cells. By stealing essential viral proteins, these engineered molecular parasites have been predicted to reduce viral levels in patients and viral transmission events across populations. Yet, a critical question is whether rapidly mutating viruses like HIV can evolve around TIP control by reducing production of the proteins that TIPs must steal in order to replicate (i.e., by ‘starving’ the TIPs). Here we develop a multi-scale model that tests whether TIP-starving HIV mutants can spread across populations to undermine TIP therapy campaigns at the population-scale. Strikingly, model results show that inherent evolutionary tradeoffs prevent these TIP-resistant HIV mutants from increasing in frequency (i.e., these TIP-resistant HIV mutants are continually outcompeted by TIP-sensitive mutants in both patients and populations). Maintained by natural selection, TIPs may offer a novel therapeutic approach to indefinitely control rapidly evolving viral pandemics.

Characterizing the dynamics of rubella relative to measles: the role of stochasticity

Rubella is a completely immunizing and mild infection in children. Understanding its behaviour is of considerable public health importance because of congenital rubella syndrome, which results from infection with rubella during early pregnancy and may entail a variety of birth defects. The recurrent dynamics of rubella are relatively poorly resolved, and appear to show considerable diversity globally. Here, we investigate the behaviour of a stochastic seasonally forced susceptible-infected-recovered model to characterize the determinants of these dynamics and illustrate patterns by comparison with measles. We perform a systematic analysis of spectra of stochastic fluctuations around stable attractors of the corresponding deterministic model and compare them with spectra from full stochastic simulations in large populations. This approach allows us to quantify the effects of demographic stochasticity and to give a coherent picture of measles and rubella dynamics, explaining essential differences in the recurrent patterns exhibited by these diseases. We discuss the implications of our findings in the context of vaccination and changing birth rates as well as the persistence of these two childhood infections.

Modelling the long-term dynamics of pre-vaccination pertussis

The dynamics of strongly immunizing childhood infections is still not well understood. Although reports of successful modelling of several data records can be found in the previous literature, the key determinants of the observed temporal patterns have not yet been clearly identified. In particular, different models of immunity waning and degree of protection applied to disease- and vaccine-induced immunity have been debated in the previous literature on pertussis. Here, we study the effect of disease-acquired immunity on the long-term patterns of pertussis prevalence. We compare five minimal models, all of which are stochastic, seasonally forced, well-mixed models of infection, based on susceptible-infective-recovered dynamics in a closed population. These models reflect different assumptions about the immune response of naive hosts, namely total permanent immunity, immunity waning, immunity waning together with immunity boosting, reinfection of recovered and repeat infection after partial immunity waning. The power spectra of the output prevalence time series characterize the long-term dynamics of the models. For epidemiological parameters consistent with published data, the power spectra show quantitative and even qualitative differences, which can be used to test their assumptions by comparison with ensembles of several-decades-long pre-vaccination data records. We illustrate this strategy on two publicly available historical datasets.

Phase lag in epidemics on a network of cities

We study the synchronization and phase lag of fluctuations in the number of infected individuals in a network of cities between which individuals commute. The frequency and amplitude of these oscillations is known to be very well captured by the van Kampen system-size expansion, and we use this approximation to compute the complex coherence function that describes their correlation. We find that, if the infection rate differs from city to city and the coupling between them is not too strong, these oscillations are synchronized with a well-defined phase lag between cities. The analytic description of the effect is shown to be in good agreement with the results of stochastic simulations for realistic population sizes.

Stochastic oscillations in models of epidemics on a network of cities

We carry out an analytic investigation of stochastic oscillations in a susceptible-infected-recovered model of disease spread on a network of n cities. In the model a fraction f(jk) of individuals from city k commute to city j, where they may infect, or be infected by, others. Starting from a continuous-time Markov description of the model the deterministic equations, which are valid in the limit when the population of each city is infinite, are recovered. The stochastic fluctuations about the fixed point of these equations are derived by use of the van Kampen system-size expansion. The fixed point structure of the deterministic equations is remarkably simple: A unique nontrivial fixed point always exists and has the feature that the fraction of susceptible, infected, and recovered individuals is the same for each city irrespective of its size. We find that the stochastic fluctuations have an analogously simple dynamics: All oscillations have a single frequency, equal to that found in the one-city case. We interpret this phenomenon in terms of the properties of the spectrum of the matrix of the linear approximation of the deterministic equations at the fixed point.

Stochastic effects in a seasonally forced epidemic model

The interplay of seasonality, the system's nonlinearities and intrinsic stochasticity, is studied for a seasonally forced susceptible-exposed-infective-recovered stochastic model. The model is explored in the parameter region that corresponds to childhood infectious diseases such as measles. The power spectrum of the stochastic fluctuations around the attractors of the deterministic system that describes the model in the thermodynamic limit is computed analytically and validated by stochastic simulations for large system sizes. Size effects are studied through additional simulations. Other effects such as switching between coexisting attractors induced by stochasticity often mentioned in the literature as playing an important role in the dynamics of childhood infectious diseases are also investigated. The main conclusion is that stochastic amplification, rather than these effects, is the key ingredient to understand the observed incidence patterns.

Cluster approximations for infection dynamics on random networks

In this paper, we consider a simple stochastic epidemic model on large regular random graphs and the stochastic process that corresponds to this dynamics in the standard pair approximation. Using the fact that the nodes of a pair are unlikely to share neighbors, we derive the master equation for this process and obtain from the system size expansion the power spectrum of the fluctuations in the quasistationary state. We show that whenever the pair approximation deterministic equations give an accurate description of the behavior of the system in the thermodynamic limit, the power spectrum of the fluctuations measured in long simulations is well approximated by the analytical power spectrum. If this assumption breaks down, then the cluster approximation must be carried out beyond the level of pairs. We construct an uncorrelated triplet approximation that captures the behavior of the system in a region of parameter space where the pair approximation fails to give a good quantitative or even qualitative agreement. For these parameter values, the power spectrum of the fluctuations in finite systems can be computed analytically from the master equation of the corresponding stochastic process.

Fluctuations and oscillations in a simple epidemic model

We show that the simplest stochastic epidemiological models with spatial correlations exhibit two types of oscillatory behavior in the endemic phase. In a large parameter range, the oscillations are due to resonant amplification of stochastic fluctuations, a general mechanism first reported for predator-prey dynamics. In a narrow range of parameters that includes many infectious diseases which confer long lasting immunity the oscillations persist for infinite populations. This effect is apparent in simulations of the stochastic process in systems of variable size and can be understood from the phase diagram of the deterministic pair approximation equations. The two mechanisms combined play a central role in explaining the ubiquity of oscillatory behavior in real data and in simulation results of epidemic and other related models.