Can we spend our way out of the AIDS epidemic? A world halting AIDS model

What the reproductive number R0 can and cannot tell us about COVID-19 dynamics

The reproductive number R (or R0, the initial reproductive number in an immune-naïve population) has long been successfully used to predict the likelihood of pathogen invasion, to gauge the potential severity of an epidemic, and to set policy around interventions. However, often ignored complexities have generated confusion around use of the metric. This is particularly apparent with the emergent pandemic virus SARS-CoV-2, the causative agent of COVID-19. We address some misconceptions about the predictive ability of the reproductive number, focusing on how it changes over time, varies over space, and relates to epidemic size by referencing the mathematical definition of R and examples from the current pandemic. We hope that a better appreciation of the uses, nuances, and limitations of R and R0 facilitates a better understanding of epidemic spread, epidemic severity, and the effects of interventions in the context of SARS-CoV-2.

The differential impacts of non-locally acquired infections and treatment interventions on heterosexual HIV transmission in Hong Kong

Introduction

Heterosexual infections have contributed to a high proportion of the HIV burden in Asia and Eastern Europe. Human mobility and non-local infections are important features in some cities/countries. An understanding of the determinants of the sustained growth of the heterosexual HIV epidemics would enable the potential impacts of treatment-based interventions to be assessed.

Methods

We developed a compartmental model for heterosexual HIV transmissions, parameterized by clinical and surveillance data (1984–2014) in Hong Kong. HIV sequence data were included for examining genetic linkages and clustering pattern. We performed sensitivity analyses to evaluate effects of high-risk sexual partnership and proportions of non-locally acquired infections. Four hypothetical interventions (a) immediate treatment, (b) enhancement of retention in care, (c) HIV testing campaigns, and (d) test-and-treat strategy, were examined.

Results

Data of 2174 patients (723 female and 1451 male) diagnosed with HIV between 1984 and 2012 in Hong Kong were collected for model parameterization. Among 1229 sequences of non-MSM (men who have sex with men) patients, 70% were isolates and 17% were either dyads or triads. In base-case scenario, the total estimated number of new infections in 2012–2023 would be 672 for male and 452 for female. Following 100% retention in care intervention, the total proportion of averted new infections in 2012–2023 would be 7% for male and 10% for female. HIV testing campaign in 2012 and 2017 followed by 100% immediate treatment strategy would avert 5% and 9% of male and female new infections, respectively. In the epidemic model, an increase of high-risk sexual partnership from 6% to 9% would increase the epidemic growth (annual number of newly diagnosed and newly infected cases) by about 10%. If no non-locally acquired infection occurred as from 2012, the epidemic growth would slump. To control the heterosexual epidemic, periodic HIV testing at 5-year intervals with immediate treatment would avert 5–13% of annual new infections in 2013–2023.

Conclusions

Enhanced HIV testing with immediate treatment is most effective in controlling the heterosexual epidemic, the impacts of which might however be attenuated by any increase of non-locally acquired infection, assuming little variations of high risk partnership over time.

Effectiveness of combination packages for HIV-1 prevention in sub-Saharan Africa depends on partnership network structure: a mathematical modelling study

OBJECTIVES

Combination packages for HIV prevention can leverage the effectiveness of biomedical and behavioural elements to lower disease incidence with realistic targets for individual and population risk reduction. We investigated how sexual network structures can maximise the effectiveness of a package targeting sexually active adults in sub-Saharan Africa (SSA) with intervention components for medical male circumcision (MMC) and sexual partnership concurrency (having >1 ongoing partner).

METHODS

Network-based mathematical models of HIV type 1 (HIV-1) transmission dynamics among heterosexual couples were used to explore how changes to MMC alone and in combination with changes to concurrency impacted endemic HIV-1 prevalence and incidence. Starting from a base model parameterised from empirical data from West Africa, we simulated the prevalence of circumcision from 10% to 90% and concurrency was modelled at four discrete levels corresponding to values observed across SSA.

RESULTS

MMC and concurrency could contribute to the empirical variation in HIV-1 disease prevalence across SSA. Small reductions in concurrency resulted in large declines in HIV-1 prevalence. Scaling up circumcision in low-concurrency settings yields a greater relative benefit, but the absolute number of infections averted depends on both the circumcision coverage and baseline incidence. Epidemic extinction with this package will require substantial scale-up of MMC in low-concurrency settings.

CONCLUSIONS

Dynamic sexual network structure should be considered in the design and targeting of MMC within combination HIV-1 prevention packages. Realistic levels of coverage for these packages within southern Africa could lead to a reduction of incidence to the low levels observed in western Africa, and possibly, epidemic extinction.

The Impact of Human Mobility on HIV Transmission in Kenya

Disease spreads as a result of people moving and coming in contact with each other. Thus the mobility patterns of individuals are crucial in understanding disease dynamics. Here we study the impact of human mobility on HIV transmission in different parts of Kenya. We build an SIR metapopulation model that incorporates the different regions within the country. We parameterise the model using census data, HIV data and mobile phone data adopted to track human mobility. We found that movement between different regions appears to have a relatively small overall effect on the total increase in HIV cases in Kenya. However, the most important consequence of movement patterns was transmission of the disease from high infection to low prevalence areas. Mobility slightly increases HIV incidence rates in regions with initially low HIV prevalences and slightly decreases incidences in regions with initially high HIV prevalence. We discuss how regional HIV models could be used in public-health planning. This paper is a first attempt to model spread of HIV using mobile phone data, and we also discuss limitations to the approach.

The biological characteristics of predominant strains of HIV-1 genotype: modeling of HIV-1 infection among men who have sex with men

To investigate the molecular subtypes of prevalent HIV-1 strains and characterize the genetics of dominant strains among men who have sex with men. Molecular epidemiology surveys in this study concentrated on the prevalent HIV-1 strains in Liaoning province by year. 229 adult patients infected with HIV-1 and part of a high-risk group of men who have sex with men were recruited. Reverse transcription and nested PCR amplification were performed. Sequencing reactions were conducted and edited, followed by codon-based alignment. NJ phylogenetic tree analyses detected two distinct CRF01_AE phylogenetic clusters, designated clusters 1 and 2. Clusters 1 and 2 accounted for 12.8% and 84.2% of sequences in the pol gene and 17.6% and 73.1% of sequences in the env gene, respectively. Another six samples were distributed on other phylogenetic clusters. Cluster 1 increased significantly from 5.6% to 20.0%, but cluster 2 decreased from 87.5% to 80.0%. Genetic distance analysis indicated that CRF01_AE cluster 1 in Liaoning was homologous to epidemic CRF01_AE strains, but CRF01_AE cluster 2 was different from other scattered strains. Additionally, significant differences were found in tetra-peptide motifs at the tip of V3 loop between cluster 1 and 2; however, differences in coreceptor usage were not detected. This study shows that subtype CRF01_AE strain may be the most prevalent epidemic strain in the men who have sex with men. Genetic characteristics of the subtype CRF01_AE cluster strain in Liaoning showed homology to the prevalent strains of men who have sex with men in other parts of China.

From regional pulse vaccination to global disease eradication: insights from a mathematical model of poliomyelitis

Mass-vaccination campaigns are an important strategy in the global fight against poliomyelitis and measles. The large-scale logistics required for these mass immunisation campaigns magnifies the need for research into the effectiveness and optimal deployment of pulse vaccination. In order to better understand this control strategy, we propose a mathematical model accounting for the disease dynamics in connected regions, incorporating seasonality, environmental reservoirs and independent periodic pulse vaccination schedules in each region. The effective reproduction number, Re, is defined and proved to be a global threshold for persistence of the disease. Analytical and numerical calculations show the importance of synchronising the pulse vaccinations in connected regions and the timing of the pulses with respect to the pathogen circulation seasonality. Our results indicate that it may be crucial for mass-vaccination programs, such as national immunisation days, to be synchronised across different regions. In addition, simulations show that a migration imbalance can increase Re and alter how pulse vaccination should be optimally distributed among the patches, similar to results found with constant-rate vaccination. Furthermore, contrary to the case of constant-rate vaccination, the fraction of environmental transmission affects the value of Re when pulse vaccination is present.

Predicting the HIV/AIDS epidemic and measuring the effect of mobility in mainland China

HIV has spread widely in mainland China, but there is significant geographic variation in the severity of the epidemic. We aimed to assess the HIV/AIDS epidemic in mainland China accurately, and address the effect of population mobility on it. Markov-Chain Monte-Carlo simulations and Latin Hypercube Sampling were used to estimate the basic reproductive ratio and its sensitivity to parameter variations. We estimated a mean reproduction number of 1.708 (95% CI 1.440-1.977). Our analysis using national surveillance data indicates that HIV-positive individuals most likely move from economically developed regions to regions with more numerous HIV cases, while mobility of AIDS patients likely flows in the opposite direction, due to the current policy that AIDS patients must return to their registered residence to receive free antiretroviral therapy. Our results based on a spatially stratified population dynamical model show increasing mobility rates of HIV/AIDS cases can have a significant effect on the number of HIV/AIDS cases per province and has the potential to decrease the overall number of HIV/AIDS cases in the country. We recommend that the community-based HIV/AIDS support and care program should be implemented by some local governments (especially in epidemically severe areas) to mitigate HIV infections in China.

CAN CULLING TO PREVENT MONKEYPOX INFECTION BE COUNTER-PRODUCTIVE? SCENARIOS FROM A THEORETICAL MODEL

In the last two decades, monkeypox outbreaks in human populations in Africa and North America have reminded us that smallpox is not the only poxvirus with potential to cause harm in human populations. Monkeypox transmission is sustained in animal reservoirs, and animal–human contacts are responsible for sporadic outbreaks in humans. Here, we develop and analyze a deterministic epizootic (animal-based) transmission model capturing disease dynamics in an animal population, disease dynamics in an age-structured human population, and their coupling through animal–human contacts. We develop a single-patch model as well as a two-patch meta-population extension. We derive mathematical expressions for the basic reproduction number, which governs the likelihood of a large outbreak. We also investigate the effectiveness of culling strategies and the impact of changes in the animal–human contact rate. Numerical analysis of the model suggests that, for some parameter values, culling can actually have the counter-productive outcome of increasing monkeypox infection in children, if animal reproduction is a density-dependent process. The likelihood of this happening, as well as the prevalence of monkeypox in humans, depends sensitively on the animal–human contact rate. We also find that ignoring age structure in human populations can lead to overestimating the transmissibility of monkeypox in humans. The effectiveness of monkeypox control strategies such as culling can strongly depend on the details of demography and epidemiology in the animal reservoirs that sustain it. Therefore, to better understand how to prevent and control monkeypox outbreaks in humans, better empirical data from wild animal populations where monkeypox is endemic must be collected, and these data must be incorporated into highly structured theoretical models.

The potential impact of immunization campaign budget re-allocation on global eradication of paediatric infectious diseases

BACKGROUND

The potential benefits of coordinating infectious disease eradication programs that use campaigns such as supplementary immunization activities (SIAs) should not be over-looked. One example of a coordinated approach is an adaptive "sequential strategy": first, all annual SIA budget is dedicated to the eradication of a single infectious disease; once that disease is eradicated, the annual SIA budget is re-focussed on eradicating a second disease, etc. Herd immunity suggests that a sequential strategy may eradicate several infectious diseases faster than a non-adaptive "simultaneous strategy" of dividing annual budget equally among eradication programs for those diseases. However, mathematical modeling is required to understand the potential extent of this effect.

METHODS

Our objective was to illustrate how budget allocation strategies can interact with the nonlinear nature of disease transmission to determine time to eradication of several infectious diseases under different budget allocation strategies. Using a mathematical transmission model, we analyzed three hypothetical vaccine-preventable infectious diseases in three different countries. A central decision-maker can distribute funding among SIA programs for these three diseases according to either a sequential strategy or a simultaneous strategy. We explored the time to eradication under these two strategies under a range of scenarios.

RESULTS

For a certain range of annual budgets, all three diseases can be eradicated relatively quickly under the sequential strategy, whereas eradication never occurs under the simultaneous strategy. However, moderate changes to total SIA budget, SIA frequency, order of eradication, or funding disruptions can create disproportionately large differences in the time and budget required for eradication under the sequential strategy. We find that the predicted time to eradication can be very sensitive to small differences in the rate of case importation between the countries. We also find that the time to eradication of all three diseases is not necessarily lowest when the least transmissible disease is targeted first.

CONCLUSIONS

Relatively modest differences in budget allocation strategies in the near-term can result in surprisingly large long-term differences in time required to eradicate, as a result of the amplifying effects of herd immunity and the nonlinearities of disease transmission. More sophisticated versions of such models may be useful to large international donors or other organizations as a planning or portfolio optimization tool, where choices must be made regarding how much funding to dedicate to different infectious disease eradication efforts.

The failure of R0

The basic reproductive ratio, R(0), is one of the fundamental concepts in mathematical biology. It is a threshold parameter, intended to quantify the spread of disease by estimating the average number of secondary infections in a wholly susceptible population, giving an indication of the invasion strength of an epidemic: if R(0) < 1, the disease dies out, whereas if R(0) > 1, the disease persists. R(0) has been widely used as a measure of disease strength to estimate the effectiveness of control measures and to form the backbone of disease-management policy. However, in almost every aspect that matters, R(0) is flawed. Diseases can persist with R(0) < 1, while diseases with R(0) > 1 can die out. We show that the same model of malaria gives many different values of R(0), depending on the method used, with the sole common property that they have a threshold at 1. We also survey estimated values of R(0) for a variety of diseases, and examine some of the alternatives that have been proposed. If R(0) is to be used, it must be accompanied by caveats about the method of calculation, underlying model assumptions and evidence that it is actually a threshold. Otherwise, the concept is meaningless.

The impact of media coverage on the transmission dynamics of human influenza

BACKGROUND

There is an urgent need to understand how the provision of information influences individual risk perception and how this in turn shapes the evolution of epidemics. Individuals are influenced by information in complex and unpredictable ways. Emerging infectious diseases, such as the recent swine flu epidemic, may be particular hotspots for a media-fueled rush to vaccination; conversely, seasonal diseases may receive little media attention, despite their high mortality rate, due to their perceived lack of newness.

METHODS

We formulate a deterministic transmission and vaccination model to investigate the effects of media coverage on the transmission dynamics of influenza. The population is subdivided into different classes according to their disease status. The compartmental model includes the effect of media coverage on reporting the number of infections as well as the number of individuals successfully vaccinated.

RESULTS

A threshold parameter (the basic reproductive ratio) is analytically derived and used to discuss the local stability of the disease-free steady state. The impact of costs that can be incurred, which include vaccination, education, implementation and campaigns on media coverage, are also investigated using optimal control theory. A simplified version of the model with pulse vaccination shows that the media can trigger a vaccinating panic if the vaccine is imperfect and simplified messages result in the vaccinated mixing with the infectives without regard to disease risk.

CONCLUSIONS

The effects of media on an outbreak are complex. Simplified understandings of disease epidemiology, propogated through media soundbites, may make the disease significantly worse.

Halting HIV/AIDS with avatars and havatars: a virtual world approach to modelling epidemics

Background

A major deficit of all approaches to epidemic modelling to date has been the need to approximate or guess at human behaviour in disease-transmission-related contexts. Avatars are generally human-like figures in virtual computer worlds controlled by human individuals.

Methods

We introduce the concept of a "havatar", which is a (human, avatar) pairing. Evidence is mounting that this pairing behaves in virtual contexts much like the human in the pairing might behave in analogous real-world contexts.

Results

We propose that studies of havatars, in a virtual world, may give a realistic approximation of human behaviour in real-world contexts. If the virtual world approximates the real world in relevant details (geography, transportation, etc.), virtual epidemics in that world could accurately simulate real-world epidemics. Havatar modelling of epidemics therefore offers a complementary tool for tackling how best to halt epidemics, including perhaps HIV/AIDS, since sexual behaviour is a significant component of some virtual worlds, such as Second Life.

Conclusion

Havatars place the control parameters of an epidemic in the hands of each individual. By providing tools that everyone can understand and use, we could democratise epidemiology.