Impact of voluntary testing on infectious disease epidemiology: A game theoretic approach.

The World Health Organization recommends test-and-treat interventions to curb and even eliminate epidemics of HIV, viral hepatitis, and sexually transmitted infections (e.g., chlamydia, gonorrhea, syphilis and trichomoniasis). Epidemic models show these goals are achievable, provided the participation of individuals in test-and-treat interventions is sufficiently high. We combine epidemic models and game theoretic models to describe individual's decisions to get tested for infectious diseases within certain epidemiological contexts, and, implicitly, their voluntary participation to test-and-treat interventions. We develop three hybrid models, to discuss interventions against HIV, HCV, and sexually transmitted infections, and the potential behavioral response from the target population. Our findings are similar across diseases. Particularly, individuals use three distinct behavioral patterns relative to testing, based on their perceived costs for testing, besides the payoff for discovering their disease status. Firstly, if the cost of testing is too high, then individuals refrain from voluntary testing and get tested only if they are symptomatic. Secondly, if the cost is moderate, some individuals will test voluntarily, starting treatment if needed. Hence, the spread of the disease declines and the disease epidemiology is mitigated. Thirdly, the most beneficial testing behavior takes place as individuals perceive a per-test payoff that surpasses a certain threshold, every time they get tested. Consequently, individuals achieve high voluntary testing rates, which may result in the elimination of the epidemic, albeit on temporary basis. Trials and studies have attained different levels of participation and testing rates. To increase testing rates, they should provide each eligible individual with a payoff, above a given threshold, each time the individual tests voluntarily.

Can HIV epidemics among MSM be eliminated through participation in preexposure prophylaxis rollouts?

OBJECTIVE: To study the conditions under which preexposure prophylaxis (PrEP) coverage can eliminate HIV among MSM in the Paris region. DESIGN: Mathematical modeling. METHODS: We propose an innovative approach, combining a transmission model with a game-theoretic model, for decision-making about PrEP use. Individuals at high risk of HIV infection decide to use PrEP, depending on their perceived risk of infection and the relative cost of using PrEP versus antiretroviral treatment (ART), which includes monetary and/or nonmonetary aspects, such as price and access model of PrEP, consequences of being infected and lifelong ART. RESULTS: If individuals assessed correctly their infection risk, and the cost of using PrEP were sufficiently low, then the PrEP rollout could lead to elimination. Specifically, assuming 86% PrEP effectiveness, as observed in two clinical trials, a minimum PrEP coverage of 55% [95% confidence interval (CI) 43-64%] among high-risk MSM would achieve elimination in the Paris region. A complete condom drop by MSM using PrEP slightly increases the minimum PrEP coverage required for elimination, by ∼1%, whereas underestimation of their own HIV infection risk would require PrEP programs reduce the cost of using PrEP by a factor ∼2 to achieve elimination. CONCLUSION: Elimination conditions are not yet met in the Paris region, where at most 47% of high-risk MSM were using PrEP as of mid-2019. Further lowering the cost of PrEP and promoting a fair perception of HIV risk are required and should be maintained in the long-run, to maintain elimination status.

Classification of Spatiotemporal Data for Epidemic Alert Systems: Monitoring Influenza-Like Illness in France.

Surveillance data used by epidemic alert systems are typically fully aggregated in space at the national level. However, epidemics may be spatially heterogeneous, undergoing distinct dynamics in distinct regions of the surveillance area. We unveiled this in retrospective analyses by classifying incidence time series. We used Pearson correlation to quantify the similarity between local time series and then classified them using modularity maximization. The surveillance area was thus divided into regions with different incidence patterns. We analyzed 31 years (1985-2016) of data on influenza-like illness from the French Sentinelles system and found spatial heterogeneity in 19 of 31 influenza seasons. However, distinct epidemic regions could be identified only 4-5 weeks after a nationwide alert. The impact of spatial heterogeneity on influenza epidemiology was complex. First, when a nationwide alert was triggered, 32%-41% of the administrative regions of France were experiencing an epidemic, while the others were not. Second, the nationwide alert was timely for the whole surveillance area, but subsequently regions experienced distinct epidemic dynamics. Third, the epidemic dynamics were homogeneous in space. Spatial heterogeneity analyses can provide information on the timing of the peak and end of the epidemic, in various regions, for use in tailoring disease monitoring and control.

Brief Report: Per Sex-Act Risk of HIV Transmission Under Antiretroviral Treatment: A Data-Driven Approach.

BACKGROUND: Before the completion of HPTN 052, PARTNER, and Opposites Attract studies, data were lacking to directly estimate HIV transmission risk under effective combined antiretroviral treatment (cART). Rather, estimates were obtained by extrapolating a dose-response relationship between viral load and risk of HIV transmission, observed among untreated individuals, to treated individuals. Presently, data have accumulated from 9 clinical studies for a direct validation of this extrapolation. METHODS: Using estimates of per sex-act risk of HIV transmission on effective cART obtained by extrapolation, sexual behavior data, and a simple mathematical model, we estimated the number of seroconversions that should have been observed in HIV-serodiscordant couples where the HIV-positive partner was on cART across the 9 studies. We compared this with the number of seroconversions actually observed. Next, we directly estimated the risk of HIV transmission on effective cART, using Bayesian statistics to combine all available data. RESULTS: We found that at least 4.7 (uncertainty bounds: 1.7-12.6) and 35.1 (uncertainty bounds: 13.2-92.0) seroconversions should have been observed among, respectively, heterosexual and men who have sex with men (MSM) serodiscordant couples. This is not validated by observations across the studies, which reported at most 1 seroconversion among heterosexual couples and 0 for MSM. Combining all available data, we found that the maximum per sex-act risk of HIV transmission under effective cART is 3.9:100,000 for heterosexuals and 4.4:100,000 for MSM. CONCLUSIONS: Data have accumulated to render obsolete estimates of the risk of HIV transmission on cART obtained by extrapolation. Direct estimates are substantially lower and should be used in practice.

Prevention of treatable infectious diseases: A game-theoretic approach.

We model outcomes of voluntary prevention using an imperfect vaccine, which confers protection only to a fraction of vaccinees for a limited duration. Our mathematical model combines a single-player game for the individual-level decision to get vaccinated, and a compartmental model for the epidemic dynamics. Mathematical analysis yields a characterization for the effective vaccination coverage, as a function of the relative cost of prevention versus treatment; note that cost may involve monetary as well as non-monetary aspects. Three behaviors are possible. First, the relative cost may be too high, so individuals do not get vaccinated. Second, the relative cost may be moderate, such that some individuals get vaccinated and voluntary vaccination alleviates the epidemic. In this case, the vaccination coverage grows steadily with decreasing relative cost of vaccination versus treatment. Unlike previous studies, we find a third case where relative cost is sufficiently low so epidemics may be averted through the use of prevention, even for an imperfect vaccine. However, we also found that disease elimination is only temporary-as no equilibrium exists for the individual strategy in this third case-and, with increasing perceived cost of vaccination versus treatment, the situation may be reversed toward the epidemic edge, where the effective reproductive number is 1. Thus, maintaining relative cost sufficiently low will be the main challenge to maintain disease elimination. Furthermore, our model offers insight on vaccine parameters, which are otherwise difficult to estimate. We apply our findings to the epidemiology of measles.

Bayesian Monitoring of Emerging Infectious Diseases.

We define data analyses to monitor a change in R, the average number of secondary cases caused by a typical infected individual. The input dataset consists of incident cases partitioned into outbreaks, each initiated from a single index case. We split the input dataset into two successive subsets, to evaluate two successive R values, according to the Bayesian paradigm. We used the Bayes factor between the model with two different R values and that with a single R value to justify that the change in R is statistically significant. We validated our approach using simulated data, generated using known R. In particular, we found that claiming two distinct R values may depend significantly on the number of outbreaks. We then reanalyzed data previously studied by Jansen et al. [Jansen et al. Science 301 (5634), 804], concerning the effective reproduction number for measles in the UK, during 1995-2002. Our analyses showed that the 1995-2002 dataset should be divided into two separate subsets for the periods 1995-1998 and 1999-2002. In contrast, Jansen et al. take this splitting point as input of their analysis. Our estimated effective reproduction numbers R are in good agreement with those found by Jansen et al. In conclusion, our methodology for detecting temporal changes in R using outbreak-size data worked satisfactorily with both simulated and real-world data. The methodology may be used for updating R in real time, as surveillance outbreak data become available.

Role of word-of-mouth for programs of voluntary vaccination: A game-theoretic approach.

We propose a model describing the synergetic feedback between word-of-mouth (WoM) and epidemic dynamics controlled by voluntary vaccination. The key feature consists in combining a game-theoretic model for the spread of WoM and a compartmental model describing VSIR disease dynamics in the presence of a program of voluntary vaccination. We evaluate and compare two scenarios for determinants of behavior, depending on what WoM disseminates: (1) vaccine advertising, which may occur whether or not an epidemic is ongoing and (2) epidemic status, notably disease prevalence. Understanding the synergy between the two strategies could be particularly important for designing voluntary vaccination campaigns. We find that, in the initial phase of an epidemic, vaccination uptake is determined more by vaccine advertising than the epidemic status. As the epidemic progresses, epidemic status becomes increasingly important for vaccination uptake, considerably accelerating vaccination uptake toward a stable vaccination coverage.

Effect of preventive and curative interventions on hepatitis C virus transmission in Egypt (ANRS 1211): a modelling study.

BACKGROUND: Most hepatitis C virus (HCV) transmission in Egypt is related to medical injections and procedures. To control the spread of HCV, the Egyptian Ministry of Health initiated awareness and education campaigns, strengthened infection control in health-care facilities, and subsidised anti-HCV treatment. We aimed to investigate the effect of these interventions on the spread of HCV by mathematical modelling. METHODS: We developed a mathematical model of HCV transmission in Zawyat Razin, a typical rural community. Our model assumes that each individual has two distinct types of medical procedures: injections and more invasive medical procedures. To quantify the severity of the spread of HCV, we used the notion of the basic reproduction number R0, a standard threshold parameter signalling whether transmission of an infectious disease is self-sustained and maintains an epidemic. If R0 is greater than 1, HCV is self-sustained; if R0 is 1 or less, HCV transmission is not self-sustained. We investigated whether heterogeneity in the rate of injection or invasive medical procedures is the determinant factor for HCV transmission and whether most iatrogenic transmission is caused by a small group of individuals who receive health-care interventions frequently. We then assessed whether interventions targeted at this group could reduce the spread of HCV. FINDINGS: The R0 of the spread of HCV without treatment was 3·54 (95% CI 1·28-6·18), suggesting a self-sustained spread. Furthermore, the present national treatment programme only decreased R0 from 3·54 to 3·03 (95% CI 1·10-5·25). Individuals with high rates of medical injections seem to be responsible for the spread of HCV in Egypt; the R0 of the spread of HCV without treatment would be 0·64 (95% CI 0·41-0·93) if everybody followed the average behaviour. The effect of treatment on HCV transmission is greatly enhanced if treatment is provided a mean of 2·5 years (95% CI 0·1-9·2) after chronic infection and with drug regimens with more than 80% efficacy. With these treatment parameters, preventive and curative interventions targeting individuals with high rates of medical injections might decrease R0 below 1 for treatment coverage lower than 5%. INTERPRETATION: Targeting preventive and curative interventions to individuals with high rates of medical injections in Egypt would result in a greater reduction the spread of HCV than would untargeted allocation. Such an approach might prove beneficial in other resource-limited countries with health-care-driven epidemics. FUNDING: Agence Nationale de Recherche sur le SIDA et les Hépatites Virales (ANRS 1211), ANR grant Labex Integrative Biology of Emerging Infectious Diseases.

The niche reduction approach: an opportunity for optimal control of infectious diseases in low-income countries?

BACKGROUND: During the last century, WHO led public health interventions that resulted in spectacular achievements such as the worldwide eradication of smallpox and the elimination of malaria from the Western world. However, besides major successes achieved worldwide in infectious diseases control, most elimination/control programs remain frustrating in many tropical countries where specific biological and socio-economical features prevented implementation of disease control over broad spatial and temporal scales. Emblematic examples include malaria, yellow fever, measles and HIV. There is consequently an urgent need to develop affordable and sustainable disease control strategies that can target the core of infectious diseases transmission in highly endemic areas. DISCUSSION: Meanwhile, although most pathogens appear so difficult to eradicate, it is surprising to realize that human activities are major drivers of the current high rate of extinction among upper organisms through alteration of their ecology and evolution, i.e., their "niche". During the last decades, the accumulation of ecological and evolutionary studies focused on infectious diseases has shown that the niche of a pathogen holds more dimensions than just the immune system targeted by vaccination and treatment. Indeed, it is situated at various intra- and inter- host levels involved on very different spatial and temporal scales. After developing a precise definition of the niche of a pathogen, we detail how major advances in the field of ecology and evolutionary biology of infectious diseases can enlighten the planning and implementation of infectious diseases control in tropical countries with challenging economic constraints. SUMMARY: We develop how the approach could translate into applied cases, explore its expected benefits and constraints, and we conclude on the necessity of such approach for pathogen control in low-income countries.

Heterosexual risk of HIV transmission per sexual act under combined antiretroviral therapy: systematic review and bayesian modeling.

BACKGROUND: Although essential for patient counseling and quality of life of human immunodeficiency virus (HIV)-infected individuals, the risk of HIV transmission during 1 unprotected sex act with an HIV-infected person under combination antiretroviral therapy (cART) remains unknown. METHODS: We reviewed systematically the literature for studies on HIV transmission among heterosexual HIV-serodiscordant couples, where the infected partner was on cART, with regular virological monitoring, reporting on condom use and sexual activity. We used Bayesian statistics to combine data from selected studies, to investigate the per-act risk of HIV transmission through unprotected sex with an HIV-infected person on cART for >6 months. RESULTS: At most, 1 HIV transmission, over an estimated 113 480 sex acts, of which 17% were not condom protected, was reported within 1672 HIV-serodiscordant couples where the index partner had been treated for >6 months. Data were insufficient to determine whether the reported transmission occurred before or after 6 months of cART. We estimated the upper-bound per-act risk of HIV transmission at either 8.7 or 13:100 000, depending on whether the transmission occurred before or after 6 months of cART. These estimates applied whether or not index partners were virally suppressed. Estimating an upper-bound risk <1:100 000 would require observing no HIV transmission while collecting >12 times the available amount of data. CONCLUSIONS: Available data do not support zero risk of HIV transmission under cART. The per-act risk of HIV transmission through unprotected sex with HIV-infected individuals on cART in comprehensive care for >6 months (whether or not virally suppressed) is <13:100 000. Estimating a 10-fold lower upper-bound risk may be unfeasible due to high condom use among HIV-serodiscordant couples in most research studies.

Interhuman transmissibility of Middle East respiratory syndrome coronavirus: estimation of pandemic risk.

BACKGROUND: The new Middle East respiratory syndrome coronavirus (MERS-CoV) infection shares many clinical, epidemiological, and virological similarities with that of severe acute respiratory syndrome (SARS)-CoV. We aimed to estimate virus transmissibility and the epidemic potential of MERS-CoV, and to compare the results with similar findings obtained for prepandemic SARS. METHODS: We retrieved data for MERS-CoV clusters from the WHO summary and subsequent reports, and published descriptions of cases, and took into account 55 of the 64 laboratory-confirmed cases of MERS-CoV reported as of June 21, 2013, excluding cases notified in the previous 2 weeks. To assess the interhuman transmissibility of MERS-CoV, we used Bayesian analysis to estimate the basic reproduction number (R0) and compared it to that of prepandemic SARS. We considered two scenarios, depending on the interpretation of the MERS-CoV cluster-size data. RESULTS: With our most pessimistic scenario (scenario 2), we estimated MERS-CoV R0 to be 0·69 (95% CI 0·50-0·92); by contrast, the R0 for prepandemic SARS-CoV was 0·80 (0·54-1·13). Our optimistic scenario (scenario 1) yielded a MERS-CoV R0 of 0·60 (0·42-0·80). Because of recent implementation of effective contact tracing and isolation procedures, further MERS-CoV transmission data might no longer describe an entire cluster, but only secondary infections directly caused by the index patient. Hence, we calculated that, under scenario 2, eight or more secondary infections caused by the next index patient would translate into a 5% or higher chance that the revised MERS-CoV R0 would exceed 1--ie, that MERS-CoV might have pandemic potential. INTERPRETATION: Our analysis suggests that MERS-CoV does not yet have pandemic potential. We recommend enhanced surveillance, active contact tracing, and vigorous searches for the MERS-CoV animal hosts and transmission routes to human beings. FUNDING: Agence Nationale de la Recherche (Labex Integrative Biology of Emerging Infectious Diseases), and the European Community's Seventh Framework Programme project PREDEMICS.

BCG-mediated bladder cancer immunotherapy: identifying determinants of treatment response using a calibrated mathematical model.

Intravesical Bacillus Calmette Guérin (BCG) immunotherapy is considered the standard of care for treatment of non-muscle invasive bladder cancer; however the treatment parameters were established empirically. In order to evaluate potential optimization of clinical parameters of BCG induction therapy, we constructed and queried a new mathematical model. Specifically, we assessed the impact of (1) duration between resection and the first instillation; (2) BCG dose; (3) indwelling time; and (4) treatment interval of induction therapy - using cure rate as the primary endpoint. Based on available clinical and in vitro experimental data, we constructed and parameterized a stochastic mathematical model describing the interactions between BCG, the immune system, the bladder mucosa and tumor cells. The primary endpoint of the model was the probability of tumor extinction following BCG induction therapy in patients with high risk for tumor recurrence. We theoretically demonstrate that extending the duration between the resection and the first BCG instillation negatively influences treatment outcome. Simulations of higher BCG doses and longer indwelling times both improved the probability of tumor extinction. A remarkable finding was that an inter-instillation interval two times longer than the seven-day interval used in the current standard of care would substantially improve treatment outcome. We provide insight into relevant clinical questions using a novel mathematical model of BCG immunotherapy. Our model predicts an altered regimen that may decrease side effects of treatment while improving response to therapy.

Role of environmental persistence in pathogen transmission: a mathematical modeling approach.

Although diseases such as influenza, tuberculosis and SARS are transmitted through an environmentally mediated mechanism, most modeling work on these topics is based on the concepts of infectious contact and direct transmission. In this paper we use a paradigm model to show that environmental transmission appears like direct transmission in the case where the pathogen persists little time in the environment. Furthermore, we formulate conditions for the validity of this modeling approximation and we illustrate them numerically for the cases of cholera and influenza. According to our results based on recently published parameter estimates, the direct transmission approximation fails for both cholera and influenza. While environmental transmission is typically chosen over direct transmission in modeling cholera, this is not the case for influenza.

Mathematical model of tumor immunotherapy for bladder carcinoma identifies the limitations of the innate immune response.

Treatment for non-muscle invasive carcinoma of the bladder represents one of the few examples of successful tumor immunity. Six weekly intravesical instillations of Bacillus Calmette-Guerin (BCG), often followed by maintenance schedule, result in up to 50-70% clinical response. Current models suggest that the mechanism of action involves the non-specific activation of innate effector cells, which may be capable of acting in the absence of an antigen-specific response. For example, recent evidence suggests that BCG-activated neutrophils possess anti-tumor potential. Moreover, weekly BCG treatment results in a prime-boost pattern with massive influx of innate immune cells (107-108 PMN/ml urine). Calibrating in vivo data, we estimate that the number of neutrophil degranulations per instillation is approximately 106-107, more than sufficient to potentially eliminate ~106 residual tumor cells. Furthermore, neutrophils, as well as other innate effector cells are not selective in their targeting-thus surrounding cells may be influenced by degranulation and / or cytokine production. To establish if these observed conditions could account for clinically effective tumor immunity, we built a mathematical model reflecting the early events and tissue conditioning in patients undergoing BCG therapy. The model incorporates key features of tumor growth, BCG instillations and the observed prime / boost pattern of the innate immune response. Model calibration established that each innate effector cell must kill 90-95 bystander cells for achieving the expected 50-70% clinical response. This prediction was evaluated both empirically and experimentally and found to vastly exceed the capacity of the innate immune system. We therefore conclude that the innate immune system alone is unable to eliminate the tumor cells. We infer that other aspects of the immune response (e.g., antigen-specific lymphocytes) decisively contribute to the success of BCG immunotherapy.

Health newscasts for increasing influenza vaccination coverage: an inductive reasoning game approach.

Both pandemic and seasonal influenza are receiving more attention from mass media than ever before. Topics such as epidemic severity and vaccination are changing the way in which we perceive the utility of disease prevention. Voluntary influenza vaccination has been recently modeled using inductive reasoning games. It has thus been found that severe epidemics may occur because individuals do not vaccinate and, instead, attempt to benefit from the immunity of their peers. Such epidemics could be prevented by voluntary vaccination if incentives were offered. However, a key assumption has been that individuals make vaccination decisions based on whether there was an epidemic each influenza season; no other epidemiological information is available to them. In this work, we relax this assumption and investigate the consequences of making more informed vaccination decisions while no incentives are offered. We obtain three major results. First, individuals will not cooperate enough to constantly prevent influenza epidemics through voluntary vaccination no matter how much they learned about influenza epidemiology. Second, broadcasting epidemiological information richer than whether an epidemic occurred may stabilize the vaccination coverage and suppress severe influenza epidemics. Third, the stable vaccination coverage follows the trend of the perceived benefit of vaccination. However, increasing the amount of epidemiological information released to the public may either increase or decrease the perceived benefit of vaccination. We discuss three scenarios where individuals know, in addition to whether there was an epidemic, (i) the incidence, (ii) the vaccination coverage and (iii) both the incidence and the vaccination coverage, every influenza season. We show that broadcasting both the incidence and the vaccination coverage could yield either better or worse vaccination coverage than broadcasting each piece of information on its own.

A universal long-term flu vaccine may not prevent severe epidemics.

BACKGROUND: Recently, the promise of a new universal long-term flu vaccine has become more tangible than ever before. Such a vaccine would protect against very many seasonal and pandemic flu strains for many years, making annual vaccination unnecessary. However, due to complacency behavior, it remains unclear whether the introduction of such vaccines would maintain high and stable levels of vaccination coverage year after year. FINDINGS: To predict the impact of universal long-term flu vaccines on influenza epidemics we developed a mathematical model that linked human cognition and memory with the transmission dynamics of influenza. Our modeling shows that universal vaccines that provide short-term protection are likely to result in small frequent epidemics, whereas universal vaccines that provide long-term protection are likely to result in severe infrequent epidemics. CONCLUSIONS: Influenza vaccines that provide short-term protection maintain risk awareness regarding influenza in the population and result in stable vaccination coverage. Vaccines that provide long-term protection could lead to substantial drops in vaccination coverage and should therefore include an annual epidemic risk awareness programs in order to minimize the risk of severe epidemics.

A general multi-strain model with environmental transmission: invasion conditions for the disease-free and endemic states.

Although many infectious diseases of humans and wildlife are transmitted via an environmental reservoir, the theory of environmental transmission remains poorly elaborated. Here we introduce an SIR-type multi-strain disease transmission model with perfect cross immunity where environmental transmission is broadly defined by three axioms. We establish the conditions under which a multi-strain endemic state is invaded by another strain which is both directly and environmentally transmitted. We discuss explicit forms for environmental transmission terms and apply our newly derived invasion conditions to a two-strain system. Then, we consider the case of two strains with matching basic reproduction numbers (i.e., R(0)), one directly transmitted only and the other both directly and environmentally transmitted, invading each other's endemic state. We find that the strain which is only directly transmitted can invade the endemic state of the strain with mixed transmission. However, the endemic state of the first strain is neutrally stable to invasion by the second strain. Thus, our results suggest that environmental transmission makes the endemic state less resistant to invasion.