Quantifying human mixing patterns in Chinese provinces outside Hubei after the 2020 lockdown was lifted.

BACKGROUND: Contact patterns play a key role in the spread of respiratory infectious diseases in human populations. During the COVID-19 pandemic, the regular contact patterns of the population have been disrupted due to social distancing both imposed by the authorities and individual choices. Many studies have focused on age-mixing patterns before the COVID-19 pandemic, but they provide very little information about the mixing patterns in the COVID-19 era. In this study, we aim at quantifying human heterogeneous mixing patterns immediately after lockdowns implemented to contain COVID-19 spread in China were lifted. We also provide an illustrative example of how the collected mixing patterns can be used in a simulation study of SARS-CoV-2 transmission. METHODS AND RESULTS: In this work, a contact survey was conducted in Chinese provinces outside Hubei in March 2020, right after lockdowns were lifted. We then leveraged the estimated mixing patterns to calibrate a mathematical model of SARS-CoV-2 transmission. Study participants reported 2.3 contacts per day (IQR: 1.0-3.0) and the mean per-contact duration was 7.0 h (IQR: 1.0-10.0). No significant differences in average contact number and contact duration were observed between provinces, the number of recorded contacts did not show a clear trend by age, and most of the recorded contacts occurred with family members (about 78%). The simulation study highlights the importance of considering age-specific contact patterns to estimate the COVID-19 burden. CONCLUSIONS: Our findings suggest that, despite lockdowns were no longer in place at the time of the survey, people were still heavily limiting their contacts as compared to the pre-pandemic situation.

Model-Based Comprehensive Analysis of School Closure Policies for Mitigating Influenza Epidemics and Pandemics.

School closure policies are among the non-pharmaceutical measures taken into consideration to mitigate influenza epidemics and pandemics spread. However, a systematic review of the effectiveness of alternative closure policies has yet to emerge. Here we perform a model-based analysis of four types of school closure, ranging from the nationwide closure of all schools at the same time to reactive gradual closure, starting from class-by-class, then grades and finally the whole school. We consider policies based on triggers that are feasible to monitor, such as school absenteeism and national ILI surveillance system. We found that, under specific constraints on the average number of weeks lost per student, reactive school-by-school, gradual, and county-wide closure give comparable outcomes in terms of optimal infection attack rate reduction, peak incidence reduction or peak delay. Optimal implementations generally require short closures of one week each; this duration is long enough to break the transmission chain without leading to unnecessarily long periods of class interruption. Moreover, we found that gradual and county closures may be slightly more easily applicable in practice as they are less sensitive to the value of the excess absenteeism threshold triggering the start of the intervention. These findings suggest that policy makers could consider school closure policies more diffusely as response strategy to influenza epidemics and pandemics, and the fact that some countries already have some experience of gradual or regional closures for seasonal influenza outbreaks demonstrates that logistic and feasibility challenges of school closure strategies can be to some extent overcome.

Spatiotemporal dynamics of the Ebola epidemic in Guinea and implications for vaccination and disease elimination: a computational modeling analysis.

BACKGROUND: Among the three countries most affected by the Ebola virus disease outbreak in 2014-2015, Guinea presents an unusual spatiotemporal epidemic pattern, with several waves and a long tail in the decay of the epidemic incidence. METHODS: Here, we develop a stochastic agent-based model at the level of a single household that integrates detailed data on Guinean demography, hospitals, Ebola treatment units, contact tracing, and safe burial interventions. The microsimulation-based model is used to assess the effect of each control strategy and the probability of elimination of the epidemic according to different intervention scenarios, including ring vaccination with the recombinant vesicular stomatitis virus-vectored vaccine. RESULTS: The numerical results indicate that the dynamics of the Ebola epidemic in Guinea can be quantitatively explained by the timeline of the implemented interventions. In particular, the early availability of Ebola treatment units and the associated isolation of cases and safe burials helped to limit the number of Ebola cases experienced by Guinea. We provide quantitative evidence of a strong negative correlation between the time series of cases and the number of traced contacts. This result is confirmed by the computational model that suggests that contact tracing effort is a key determinant in the control and elimination of the disease. In data-driven microsimulations, we find that tracing at least 5-10 contacts per case is crucial in preventing epidemic resurgence during the epidemic elimination phase. The computational model is used to provide an analysis of the ring vaccination trial highlighting its potential effect on disease elimination. CONCLUSIONS: We identify contact tracing as one of the key determinants of the epidemic's behavior in Guinea, and we show that the early availability of Ebola treatment unit beds helped to limit the number of Ebola cases in Guinea.

Estimating transmission probability in schools for the 2009 H1N1 influenza pandemic in Italy.

BACKGROUND: Epidemic models are being extensively used to understand the main pathways of spread of infectious diseases, and thus to assess control methods. Schools are well known to represent hot spots for epidemic spread; hence, understanding typical patterns of infection transmission within schools is crucial for designing adequate control strategies. The attention that was given to the 2009 A/H1N1pdm09 flu pandemic has made it possible to collect detailed data on the occurrence of influenza-like illness (ILI) symptoms in two primary schools of Trento, Italy. RESULTS: The data collected in the two schools were used to calibrate a discrete-time SIR model, which was designed to estimate the probabilities of influenza transmission within the classes, grades and schools using Markov Chain Monte Carlo (MCMC) methods. We found that the virus was mainly transmitted within class, with lower levels of transmission between students in the same grade and even lower, though not significantly so, among different grades within the schools. We estimated median values of R 0 from the epidemic curves in the two schools of 1.16 and 1.40; on the other hand, we estimated the average number of students infected by the first school case to be 0.85 and 1.09 in the two schools. CONCLUSIONS: The discrepancy between the values of R 0 estimated from the epidemic curve or from the within-school transmission probabilities suggests that household and community transmission played an important role in sustaining the school epidemics. The high probability of infection between students in the same class confirms that targeting within-class transmission is key to controlling the spread of influenza in school settings and, as a consequence, in the general population.

School closure policies at municipality level for mitigating influenza spread: a model-based evaluation.

BACKGROUND: Nearly every year Influenza affects most countries worldwide and the risk of a new pandemic is always present. Therefore, influenza is a major concern for public health. School-age individuals are often the most affected group, suggesting that the inclusion in preparedness plans of school closure policies may represent an option for influenza mitigation. However, their applicability remains uncertain and their implementation should carefully be weighed on the basis of cost-benefit considerations. METHODS: We developed an individual-based model for influenza transmission integrating data on sociodemography and time use of the Italian population, face-to-face contacts in schools, and influenza natural history. The model was calibrated on the basis of epidemiological data from the 2009 influenza pandemic and was used to evaluate the effectiveness of three reactive school closure strategies, all based on school absenteeism. RESULTS: In the case of a new influenza pandemic sharing similar features with the 2009 H1N1 pandemic, gradual school closure strategies (i.e., strategies closing classes first, then grades or the entire school) could lead to attack rate reduction up to 20-25 % and to peak weekly incidence reduction up to 50-55 %, at the cost of about three school weeks lost per student. Gradual strategies are quite stable to variations in the start of policy application and to the threshold on student absenteeism triggering class (and school) closures. In the case of a new influenza pandemic showing different characteristics with respect to the 2009 H1N1 pandemic, we found that the most critical features determining the effectiveness of school closure policies are the reproduction number and the age-specific susceptibility to infection, suggesting that these two epidemiological quantities should be estimated early on in the spread of a new pandemic for properly informing response planners. CONCLUSIONS: Our results highlight a potential beneficial effect of reactive gradual school closure policies in mitigating influenza spread, conditioned on the effort that decision makers are willing to afford. Moreover, the suggested strategies are solely based on routinely collected and easily accessible data (such as student absenteeism irrespective of the cause and ILI incidence) and thus they appear to be applicable in real world situations.

Containing the accidental laboratory escape of potential pandemic influenza viruses.

BACKGROUND: The recent work on the modified H5N1 has stirred an intense debate on the risk associated with the accidental release from biosafety laboratory of potential pandemic pathogens. Here, we assess the risk that the accidental escape of a novel transmissible influenza strain would not be contained in the local community. METHODS: We develop here a detailed agent-based model that specifically considers laboratory workers and their contacts in microsimulations of the epidemic onset. We consider the following non-pharmaceutical interventions: isolation of the laboratory, laboratory workers' household quarantine, contact tracing of cases and subsequent household quarantine of identified secondary cases, and school and workplace closure both preventive and reactive. RESULTS: Model simulations suggest that there is a non-negligible probability (5% to 15%), strongly dependent on reproduction number and probability of developing clinical symptoms, that the escape event is not detected at all. We find that the containment depends on the timely implementation of non-pharmaceutical interventions and contact tracing and it may be effective (>90% probability per event) only for pathogens with moderate transmissibility (reproductive number no larger than R0 = 1.5). Containment depends on population density and structure as well, with a probability of giving rise to a global event that is three to five times lower in rural areas. CONCLUSIONS: Results suggest that controllability of escape events is not guaranteed and, given the rapid increase of biosafety laboratories worldwide, this poses a serious threat to human health. Our findings may be relevant to policy makers when designing adequate preparedness plans and may have important implications for determining the location of new biosafety laboratories worldwide.

Inferring the structure of social contacts from demographic data in the analysis of infectious diseases spread.

Social contact patterns among individuals encode the transmission route of infectious diseases and are a key ingredient in the realistic characterization and modeling of epidemics. Unfortunately, the gathering of high quality experimental data on contact patterns in human populations is a very difficult task even at the coarse level of mixing patterns among age groups. Here we propose an alternative route to the estimation of mixing patterns that relies on the construction of virtual populations parametrized with highly detailed census and demographic data. We present the modeling of the population of 26 European countries and the generation of the corresponding synthetic contact matrices among the population age groups. The method is validated by a detailed comparison with the matrices obtained in six European countries by the most extensive survey study on mixing patterns. The methodology presented here allows a large scale comparison of mixing patterns in Europe, highlighting general common features as well as country-specific differences. We find clear relations between epidemiologically relevant quantities (reproduction number and attack rate) and socio-demographic characteristics of the populations, such as the average age of the population and the duration of primary school cycle. This study provides a numerical approach for the generation of human mixing patterns that can be used to improve the accuracy of mathematical models in the absence of specific experimental data.

Spatiotemporal dynamics of viral hepatitis A in Italy.

Viral hepatitis A is still common in Italy, especially in Southern regions. In this study, a metapopulation model for hepatitis A virus (HAV) transmission is proposed and analyzed. Analytical results on the asymptotic and transient behaviors of the system are carried out. Based on the available Italian movement data, a national spatial contact matrix at the regional level, which could be used for new studies on the transmission dynamics of other infectious diseases, is derived for modeling fluxes of individuals. Despite the small number of fitted parameters, model simulations are in good agreement with the observed average HAV incidence in all regions. Our results suggest that the mass vaccination program introduced in one Italian region only (Puglia, the one with the highest endemicity level) could have played a role in the decline of HAV incidence in the country as a whole. The only notable exception is represented by Campania, a Southern region showing a high endemicity level, which is not substantially affected by HAV dynamics in Puglia. Finally, our results highlight that the continuation of the vaccination campaign in Puglia would have a relevant impact in decreasing long-term HAV prevalence, especially in Southern Italy.

Mathematical modeling of bacterial virulence and host-pathogen interactions in the Dictyostelium/Pseudomonas system.

We present some studies on the mechanisms of pathogenesis based on experimental work and on its interpretation through a mathematical model. Using a collection of clinical strains of the opportunistic human pathogen Pseudomonas aeruginosa, we performed co-culture experiments with Dictyostelium amoebae, to investigate the two organisms' interaction, characterized by a cross action between amoeba, feeding on bacteria, and bacteria exerting their pathogenic action against amoeba. In order to classify bacteria virulence, independently of this cross interaction, we have also performed killing experiments of bacteria against the nematode Caenorhabditis elegans. A mathematical model was developed to infer how the populations of the amoeba-bacteria system evolve according to a number of parameters, taking into account the specific features underlying the interaction. The model does not fall within the class of traditional prey-predator models because not only does an amoeba feed on bacteria, but also it is in turn attacked by them; thus the model must include a feedback term modeling this further interaction aspect. The model shows the existence of multiple steady states and the resulting behavior of the solutions, showing bi-stability of the system, gives a qualitative explanation of the co-culture experiments.

Inferring high-resolution human mixing patterns for disease modeling.

Mathematical and computational modeling approaches are increasingly used as quantitative tools in the analysis and forecasting of infectious disease epidemics. The growing need for realism in addressing complex public health questions is, however, calling for accurate models of the human contact patterns that govern the disease transmission processes. Here we present a data-driven approach to generate effective population-level contact matrices by using highly detailed macro (census) and micro (survey) data on key socio-demographic features. We produce age-stratified contact matrices for 35 countries, including 277 sub-national administratvie regions of 8 of those countries, covering approximately 3.5 billion people and reflecting the high degree of cultural and societal diversity of the focus countries. We use the derived contact matrices to model the spread of airborne infectious diseases and show that sub-national heterogeneities in human mixing patterns have a marked impact on epidemic indicators such as the reproduction number and overall attack rate of epidemics of the same etiology. The contact patterns derived here are made publicly available as a modeling tool to study the impact of socio-economic differences and demographic heterogeneities across populations on the epidemiology of infectious diseases.

The RAPIDD Ebola forecasting challenge: Model description and synthetic data generation.

The Ebola forecasting challenge organized by the Research and Policy for Infectious Disease Dynamics (RAPIDD) program of the Fogarty International Center relies on synthetic disease datasets generated by numerical simulations of a highly detailed spatially-structured agent-based model. We discuss here the architecture and technical steps of the challenge, leading to datasets that mimic as much as possible the data collection, reporting, and communication process experienced in the 2014-2015 West African Ebola outbreak. We provide a detailed discussion of the model's definition, the epidemiological scenarios' construction, synthetic patient database generation and the data communication platform used during the challenge. Finally we offer a number of considerations and takeaways concerning the extension and scalability of synthetic challenges to other infectious diseases.

The RAPIDD ebola forecasting challenge: Synthesis and lessons learnt.

Infectious disease forecasting is gaining traction in the public health community; however, limited systematic comparisons of model performance exist. Here we present the results of a synthetic forecasting challenge inspired by the West African Ebola crisis in 2014-2015 and involving 16 international academic teams and US government agencies, and compare the predictive performance of 8 independent modeling approaches. Challenge participants were invited to predict 140 epidemiological targets across 5 different time points of 4 synthetic Ebola outbreaks, each involving different levels of interventions and "fog of war" in outbreak data made available for predictions. Prediction targets included 1-4 week-ahead case incidences, outbreak size, peak timing, and several natural history parameters. With respect to weekly case incidence targets, ensemble predictions based on a Bayesian average of the 8 participating models outperformed any individual model and did substantially better than a null auto-regressive model. There was no relationship between model complexity and prediction accuracy; however, the top performing models for short-term weekly incidence were reactive models with few parameters, fitted to a short and recent part of the outbreak. Individual model outputs and ensemble predictions improved with data accuracy and availability; by the second time point, just before the peak of the epidemic, estimates of final size were within 20% of the target. The 4th challenge scenario - mirroring an uncontrolled Ebola outbreak with substantial data reporting noise - was poorly predicted by all modeling teams. Overall, this synthetic forecasting challenge provided a deep understanding of model performance under controlled data and epidemiological conditions. We recommend such "peace time" forecasting challenges as key elements to improve coordination and inspire collaboration between modeling groups ahead of the next pandemic threat, and to assess model forecasting accuracy for a variety of known and hypothetical pathogens.

Containing Ebola at the Source with Ring Vaccination.

Interim results from the Guinea Ebola ring vaccination trial suggest high efficacy of the rVSV-ZEBOV vaccine. These findings open the door to the use of ring vaccination strategies in which the contacts and contacts of contacts of each index case are promptly vaccinated to contain future Ebola virus disease outbreaks. To provide a numerical estimate of the effectiveness of ring vaccination strategies we introduce a spatially explicit agent-based model to simulate Ebola outbreaks in the Pujehun district, Sierra Leone, structurally similar to previous modelling approaches. We find that ring vaccination can successfully contain an outbreak for values of the effective reproduction number up to 1.6. Through an extensive sensitivity analysis of parameters characterising the readiness and capacity of the health care system, we identify interventions that, alongside ring vaccination, could increase the likelihood of containment. In particular, shortening the time from symptoms onset to hospitalisation to 2-3 days on average through improved contact tracing procedures, adding a 2km spatial component to the vaccination ring, and decreasing human mobility by quarantining affected areas might contribute increase our ability to contain outbreaks with effective reproduction number up to 2.6. These results have implications for future control of Ebola and other emerging infectious disease threats.

Spatiotemporal spread of the 2014 outbreak of Ebola virus disease in Liberia and the effectiveness of non-pharmaceutical interventions: a computational modelling analysis.

BACKGROUND: The 2014 epidemic of Ebola virus disease in parts of west Africa defines an unprecedented health threat. We developed a model of Ebola virus transmission that integrates detailed geographical and demographic data from Liberia to overcome the limitations of non-spatial approaches in projecting the disease dynamics and assessing non-pharmaceutical control interventions. METHODS: We modelled the movements of individuals, including patients not infected with Ebola virus, seeking assistance in health-care facilities, the movements of individuals taking care of patients infected with Ebola virus not admitted to hospital, and the attendance of funerals. Individuals were grouped into randomly assigned households (size based on Demographic Health Survey data) that were geographically placed to match population density estimates on a grid of 3157 cells covering the country. The spatial agent-based model was calibrated with a Markov chain Monte Carlo approach. The model was used to estimate Ebola virus transmission parameters and investigate the effectiveness of interventions such as availability of Ebola treatment units, safe burials procedures, and household protection kits. FINDINGS: Up to Aug 16, 2014, we estimated that 38·3% of infections (95% CI 17·4-76·4) were acquired in hospitals, 30·7% (14·1-46·4) in households, and 8·6% (3·2-11·8) while participating in funerals. We noted that the movement and mixing, in hospitals at the early stage of the epidemic, of patients infected with Ebola virus and those not infected was a sufficient driver of the reported pattern of spatial spread. The subsequent decrease of incidence at country and county level is attributable to the increasing availability of Ebola treatment units (which in turn contributed to drastically decreased hospital transmission), safe burials, and distribution of household protection kits. INTERPRETATION: The model allows assessment of intervention options and the understanding of their role in the decrease in incidence reported since Sept 7, 2014. High-quality data (eg, to estimate household secondary attack rate, contact patterns within hospitals, and effects of ongoing interventions) are needed to reduce uncertainty in model estimates. FUNDING: US Defense Threat Reduction Agency, US National Institutes of Health.

Estimating measles transmission potential in Italy over the period 2010-2011.

BACKGROUND: Recent history of measles epidemiology in Italy is characterized by the recurrence of spatially localized epidemics. AIM: In this study we investigate the three major outbreaks occurred in Italy over the period 2010-2011 and estimate the measles transmission potential. The epidemics mainly involved individuals aged 10-28 years and the transmission potential, measured as effective reproduction number - i.e. the number of new infections generated by a primary infector - was estimated to be 1.9-5.9. RESULTS: Despite such high values, we found that, in all investigated outbreaks, the reproduction number has remained above the epidemic threshold for no more than twelve weeks, suggesting that measles may hardly have the potential to give rise to new nationwide epidemics. CONCLUSION: In conclusion, the performed analysis highlights the need of planning additional vaccination programs targeting those age classes currently showing a higher susceptibility to infection, in order not to compromise the elimination goal by 2015.

Qualitative analysis of a model for co-culture of bacteria and amoebae.

In this article we analyze a mathematical model presented in [11]. The model consists of two scalar ordinary differential equations, which describe the interaction between bacteria and amoebae. We first give the sufficient conditions for the uniform persistence of the model, then we prove that the model can undergo Hopf bifurcation and Bogdanov-Takens bifurcation for some parameter values, respectively.