Simulating the effect of quarantine on the spread of the 1918-19 flu in central Canada

Metapopulation dynamics of SARS-CoV-2 transmission in a small-scale Amazonian society

The severity of infectious disease outbreaks is governed by patterns of human contact, which vary by geography, social organization, mobility, access to technology and healthcare, economic development, and culture. Whereas globalized societies and urban centers exhibit characteristics that can heighten vulnerability to pandemics, small-scale subsistence societies occupying remote, rural areas may be buffered. Accordingly, voluntary collective isolation has been proposed as one strategy to mitigate the impacts of COVID-19 and other pandemics on small-scale Indigenous populations with minimal access to healthcare infrastructure. To assess the vulnerability of such populations and the viability of interventions such as voluntary collective isolation, we simulate and analyze the dynamics of SARS-CoV-2 infection among Amazonian forager-horticulturalists in Bolivia using a stochastic network metapopulation model parameterized with high-resolution empirical data on population structure, mobility, and contact networks. Our model suggests that relative isolation offers little protection at the population level (expected approximately 80% cumulative incidence), and more remote communities are not conferred protection via greater distance from outside sources of infection, due to common features of small-scale societies that promote rapid disease transmission such as high rates of travel and dense social networks. Neighborhood density, central household location in villages, and household size greatly increase the individual risk of infection. Simulated interventions further demonstrate that without implausibly high levels of centralized control, collective isolation is unlikely to be effective, especially if it is difficult to restrict visitation between communities as well as travel to outside areas. Finally, comparison of model results to empirical COVID-19 outcomes measured via seroassay suggest that our theoretical model is successful at predicting outbreak severity at both the population and community levels. Taken together, these findings suggest that the social organization and relative isolation from urban centers of many rural Indigenous communities offer little protection from pandemics and that standard control measures, including vaccination, are required to counteract effects of tight-knit social structures characteristic of small-scale populations.

Estimating intervention effects on infectious disease control: The effect of community mobility reduction on Coronavirus spread

Understanding the effects of interventions, such as restrictions on community and large group gatherings, is critical to controlling the spread of COVID-19. Susceptible-Infectious-Recovered (SIR) models are traditionally used to forecast the infection rates but do not provide insights into the causal effects of interventions. We propose a spatiotemporal model that estimates the causal effect of changes in community mobility (intervention) on infection rates. Using an approximation to the SIR model and incorporating spatiotemporal dependence, the proposed model estimates a direct and indirect (spillover) effect of intervention. Under an interference and treatment ignorability assumption, this model is able to estimate causal intervention effects, and additionally allows for spatial interference between locations. Reductions in community mobility were measured by cell phone movement data. The results suggest that the reductions in mobility decrease Coronavirus cases 4 to 7 weeks after the intervention.

Modeling the spread of dangerous pandemics with the utilization of a hybrid-statistical–Advanced-Fuzzy-Cognitive-Map algorithm: the example of COVID-19

Purpose

The novel Coronavirus SARS-coV-2 outbreak late in 2019 and early 2020, known today as the COVID-19 pandemic, has spread fast throughout the world. It has considerably affected the lives of all people around the globe while the number of deaths related to the pandemic keeps increasing worldwide. Being able to predict the spread of the pandemic has been very helpful to governments to decide on actions. Statistical prediction models are capable of modeling a single snapshot but have several well-known weaknesses, such as linear assumptions between pandemic variables, while they cannot confirm the actual causality between studied factors. In the present work, the authors propose a state space Advanced Fuzzy Cognitive Maps (AFCM) approach model to predict the spread of the pandemic, using dynamic cause and effect relationships between pre-defined factors.

Methods

State-Space Advanced Fuzzy Cognitive Maps are proposed for modeling the spread of the pandemic, utilizing several social, policy, and healthcare factors. Statistical data from Greece, South Korea, and Germany are gathered to evaluate the performance of the proposed model.

Results

The proposed methodology was able to predict the pandemic trend in the studied countries, in terms of the total number of confirmed patient cases, yielding a coefficient of determination of 0.99, 0.94, and 0.97 respectively. The Pearson’s correlation coefficient was found to be 0.99, 0.97, and 0.98 respectively.

Conclusion

The results demonstrate the effectiveness and the advantages of the proposed methodology when modeling uncertain and dynamic situations, like novel pandemics.

Optimal strategic pandemic control: human mobility and travel restriction

This paper presents a model for finding optimal pandemic control policy considering cross-region human mobility. We extend the baseline susceptible-infectious-recovered (SIR) epidemiology model by including the net human mobility from a severely-impacted region to a mildly-affected region. The strategic optimal mitigation policy combining testing and lockdown in each region is then obtained with the goal of minimizing economic cost under the constraint of limited resources. We parametrize the model using the data of the COVID-19 pandemic and show that the optimal response strategy and mitigation outcome greatly rely on the mitigation duration, available resources, and cross-region human mobility. Furthermore, we discuss the economic impact of travel restriction policies through a quantitative analysis.

A dynamic pandemic model evaluating reopening strategies amid COVID-19

Among over 200 COVID-19 affected countries, some are fighting to "flatten the curve", while some others are considering reopening after lockdown. It remains unclear how different reopening strategies obstruct the local virus containment and impact the economy. We develop a model with travelers across heterogeneous epicenters. A low-risk area attempts to safely reopen utilizing internal policies, such as social distancing and contact tracing, and external policies, including capacity quota, quarantine, and tests. Simulations based on the COVID-19 scenario show that external policies differ in efficacy. They can substitute each other and complement internal policies. Simultaneous relaxation of both channels may lead to a new wave of COVID-19 and large economic costs. This work highlights the importance of quantitative assessment prior to implementing reopening strategies.

Experiences of persons in COVID-19 institutional quarantine in Uganda: a qualitative study

Background

Quarantine has been adopted as a key public health measure to support the control of the Coronavirus disease (COVID-19) pandemic in many countries Uganda adopted institutional quarantine for individuals suspected of exposure to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) to be placed in institutions like hotels and/or hostels of institutions for at least 14 days. This study explored experiences of individuals who underwent institutional quarantine in Uganda to inform measures to increase its effectiveness and reduce its associated negative impact.

Methods

We conducted a qualitative description study using in-depth interviews with 20 purposively selected individuals who had spent time in institutional quarantine facilities. These were mainly phone-based interviews that were audio recorded and transcribed verbatim. Electronic data coding was conducted using Atlas.ti 7 software. Thematic content analysis was used to synthesize the findings with similar codes grouped to form sub-themes and ultimately study themes. The findings are presented thematically with typical participant quotes.

Results

Study participants spent between 14 to 25 days in institutional quarantine. Four themes emerged describing the experiences of study participants during institutional quarantine, which determined whether participants’ experiences were positive or negative. These themes were: quarantine environment including facility related factors and compliance with COVID-19 measures; quarantine management factors of entity paying the costs, communication and days spent in quarantine; individual factors comprising attitude towards quarantine, fears during and post-quarantine and coping mechanisms; and linkage to other services such as health care and post-quarantine follow-up.

Conclusion

The planning, management and implementation of the quarantine process is a key determinant of the experiences of individuals who undergo the measure. To improve the experience of quarantined individuals and reduce its associated negative impact, the pre-quarantine process should be managed to comply with standards, quarantined persons should be provided as much information as possible, their quarantine duration should kept short and costs of the process ought to be minimised. Furthermore, quarantine facilities should be assessed for suitability and monitored to comply with guidelines while avenues for access to healthcare for the quarantined need to be arranged and any potential stigma associated with quarantine thoroughly addressed.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12889-021-10519-z.

The effect of COVID-19 pandemic on domestic tourism: A DEMATEL method analysis on quarantine decisions

Countries' most effective methods to reduce the impact of outbreaks are quarantine the regions during the pandemic periods. Quarantine decisions during a pandemic directly affect the hospitality industry. There is no universal guideline regarding the quarantine decision during a pandemic. There is a gap in the literature on making the right quarantine decisions to decrease the negative effect of a pandemic on the hospitality industry. To fill this gap, this study uses a decision-making trial and evaluation laboratory (DEMATEL) method to help countries for quarantine decisions due to the COVID-19 pandemic. One of the critical hospitality industry indicators is the inter-regional travel flow between regions for local tourism. Data from the household domestic tourism survey obtained from the Turkish Statistical Institute (TurkStat) is used to acquire the number of people entering and exiting among regions. This study's findings indicate that Istanbul has an essential impact on Turkey's rest. The results also demonstrate that the DEMATEL method provides convenient solutions for quarantine decisions during a pandemic. The DEMATEL application results concerning the COVID-19 pandemic effect might shed light on the hospitality industry's prospects and challenges. This study's findings might be adopted to prepare the hospitality industry for the COVID-19 pandemic and similar pandemic.

Crowding and the shape of COVID-19 epidemics

The coronavirus disease 2019 (COVID-19) pandemic is straining public health systems worldwide, and major non-pharmaceutical interventions have been implemented to slow its spread^1-4. During the initial phase of the outbreak, dissemination of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) was primarily determined by human mobility from Wuhan, China^5,6. Yet empirical evidence on the effect of key geographic factors on local epidemic transmission is lacking⁷. In this study, we analyzed highly resolved spatial variables in cities, together with case count data, to investigate the role of climate, urbanization and variation in interventions. We show that the degree to which cases of COVID-19 are compressed into a short period of time (peakedness of the epidemic) is strongly shaped by population aggregation and heterogeneity, such that epidemics in crowded cities are more spread over time, and crowded cities have larger total attack rates than less populated cities. Observed differences in the peakedness of epidemics are consistent with a meta-population model of COVID-19 that explicitly accounts for spatial hierarchies. We paired our estimates with globally comprehensive data on human mobility and predict that crowded cities worldwide could experience more prolonged epidemics.

Crowding and the shape of COVID-19 epidemics

The coronavirus disease 2019 (COVID-19) pandemic is straining public health systems worldwide, and major non-pharmaceutical interventions have been implemented to slow its spread^1-4. During the initial phase of the outbreak, dissemination of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) was primarily determined by human mobility from Wuhan, China^5,6. Yet empirical evidence on the effect of key geographic factors on local epidemic transmission is lacking⁷. In this study, we analyzed highly resolved spatial variables in cities, together with case count data, to investigate the role of climate, urbanization and variation in interventions. We show that the degree to which cases of COVID-19 are compressed into a short period of time (peakedness of the epidemic) is strongly shaped by population aggregation and heterogeneity, such that epidemics in crowded cities are more spread over time, and crowded cities have larger total attack rates than less populated cities. Observed differences in the peakedness of epidemics are consistent with a meta-population model of COVID-19 that explicitly accounts for spatial hierarchies. We paired our estimates with globally comprehensive data on human mobility and predict that crowded cities worldwide could experience more prolonged epidemics.

Evolution of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) as coronavirus disease 2019 (COVID-19) pandemic: A global health emergency

According to data compiled by researchers at Johns Hopkins University in Baltimore, Maryland, more than two and half million cases of coronavirus disease 2019 (COVID-19), caused by a newly discovered virus named severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), have been confirmed on April 20, 2020 (Nature, 2020b). Since the emergence of this infectious disease in Asia (Wuhan, China) late last year, it has been subsequently span to every continent of the world except Antarctica (Rodríguez-Morales et al., 2020). Along with a foothold in every country, the current disease pandemic is disrupting practically every aspect of life all over the world. As the outbreak are continuing to evolve, several research activities have been conducted for better understanding the origin, functions, treatments, and preventions of this novel coronavirus. This review will be a summa of the key features of novel coronavirus (nCoV), the virus causing disease 2019 and the present epidemic situation worldwide up to April 20, 2020. It is expected that this record will play an important role to take more preventive measures for overcoming the challenges faced during this current pandemic.

An SIS model for the epidemic dynamics with two phases of the human day-to-day activity

An SIS model is analyzed to consider the contribution of community structure to the risk of the spread of a transmissible disease. We focus on the human day-to-day activity introduced by commuting to a central place for the social activity. We assume that the community is classified into two subpopulations: commuter and non-commuter, of which the commuter has two phases of the day-to-day activity: private and social. Further we take account of the combination of contact patterns in two phases, making use of mass-action and ratio-dependent types for the infection force. We investigate the dependence of the basic reproduction number on the commuter ratio and the daily expected duration at the social phase as essential factors characterizing the community structure, and show that the dependence is significantly affected by the combination of contact patterns, and that the difference in the commuter ratio could make the risk of the spread of a transmissible disease significantly different.

Estimation of the Excess COVID-19 Cases in Seoul, South Korea by the Students Arriving from China

Background: In March 2020, overall, 37,000 international students from China, a country at risk of the 2019-novel coronavirus (COVID-19) infection has arrived in Seoul, South Korea. Individuals from the country at risk of COVID-19 infection have been included in the Korean home-quarantine program, but the efficacy of the program is uncertain. Methods: To estimate the possible number of infected individuals within the large influx of international students from China, we used a deterministic compartmental model for epidemic and performed a simulation-based search of different rates of compliance with home-quarantine. Results: Under the home-quarantine program, the number of the infected individuals would reach 40-72 from 12 March-24 March with the arrival of 0.2% of pre-infectious individuals. Furthermore, the number of isolated individuals would peak at 40-64 from 13 March-27 March in Seoul, South Korea. Our findings indicated when incoming international students showed strict compliance with quarantine, epidemics by the international student from China were less likely to occur in Seoul, South Korea. Conclusions: To mitigate possible epidemics, additional efforts to improve the compliance of home-quarantine of the individuals from countries with the virus risk are warranted along with other containment policies.

An SIS model for the epidemic dynamics with two phases of the human day-to-day activity

An SIS model is analyzed to consider the contribution of community structure to the risk of the spread of a transmissible disease. We focus on the human day-to-day activity introduced by commuting to a central place for the social activity. We assume that the community is classified into two subpopulations: commuter and non-commuter, of which the commuter has two phases of the day-to-day activity: private and social. Further we take account of the combination of contact patterns in two phases, making use of mass-action and ratio-dependent types for the infection force. We investigate the dependence of the basic reproduction number on the commuter ratio and the daily expected duration at the social phase as essential factors characterizing the community structure, and show that the dependence is significantly affected by the combination of contact patterns, and that the difference in the commuter ratio could make the risk of the spread of a transmissible disease significantly different.

A theoretical single-parameter model for urbanisation to study infectious disease spread and interventions

The world is continuously urbanising, resulting in clusters of densely populated urban areas and more sparsely populated rural areas. We propose a method for generating spatial fields with controllable levels of clustering of the population. We build a synthetic country, and use this method to generate versions of the country with different clustering levels. Combined with a metapopulation model for infectious disease spread, this allows us to in silico explore how urbanisation affects infectious disease spread. In a baseline scenario with no interventions, the underlying population clustering seems to have little effect on the final size and timing of the epidemic. Under within-country restrictions on non-commuting travel, the final size decreases with increased population clustering. The effect of travel restrictions on reducing the final size is larger with higher clustering. The reduction is larger in the more rural areas. Within-country travel restrictions delay the epidemic, and the delay is largest for lower clustering levels. We implemented three different vaccination strategies-uniform vaccination (in space), preferentially vaccinating urban locations and preferentially vaccinating rural locations. The urban and uniform vaccination strategies were most effective in reducing the final size, while the rural vaccination strategy was clearly inferior. Visual inspection of some European countries shows that many countries already have high population clustering. In the future, they will likely become even more clustered. Hence, according to our model, within-country travel restrictions are likely to be less and less effective in delaying epidemics, while they will be more effective in decreasing final sizes. In addition, to minimise final sizes, it is important not to neglect urban locations when distributing vaccines. To our knowledge, this is the first study to systematically investigate the effect of urbanisation on infectious disease spread and in particular, to examine effectiveness of prevention measures as a function of urbanisation.

Quarantine through History

This article reviews in a historical perspective and by means of documented examples the scientific principles relevant to the concept and effectiveness of quarantine, the logistic, economic, and political barriers to its correct implementation through time, and the health impact of local and large-scale quarantine. Quarantine is overall one of the oldest and most disseminated and, despite its limits, most effective health measures elaborated by mankind. The evidence-based history of medicine and evidence-based modern epidemiology indicate that the implementation of correct quarantine procedures is today still feasible and useful provided that a proactive collaboration is operative among those concerned and that the measures are tailored according to geographical, social, and health conditions.

Continuous and discrete SIR-models with spatial distributions

The SIR-model is a basic epidemic model that classifies a population into three subgroups: susceptible S, infected I and removed R. This model does not take into consideration the spatial distribution of each subgroup, but considers the total number of individuals belonging to each subgroup. There are many variants of the SIR-model. For studying the spatial distribution, stochastic processes have often been introduced to describe the dispersion of individuals. Such assumptions do not seem to be applicable to humans, because almost everyone moves within a small fixed radius in practice. Even if individuals do not disperse, the transmission of disease occurs. In this paper, we do not assume the dispersion of individuals, and instead use the infectious radius. Then, we propose simple continuous and discrete SIR-models that show spatial distributions. The results of our simulations show that the propagation speed and size of an epidemic depend on the population density and the infectious radius.

The Impact of Movement on Disease Dynamics in a Multi-city Compartmental Model Including Residency Patch

The impact of population dispersal between two cities on the spread of a disease is investigated analytically. A general SIRS model is presented that tracks the place of residence of individuals, allowing for different movement rates of local residents and visitors in a city. Provided the basic reproduction number is greater than one, we demonstrate in our model that increasing the travel volumes of some infected groups may result in the extinction of a disease, even though the disease cannot be eliminated in each city when the cities are isolated.

An Epidemic Patchy Model with Entry-Exit Screening

A multi-patch SEIQR epidemic model is formulated to investigate the long-term impact of entry-exit screening measures on the spread and control of infectious diseases. A threshold dynamics determined by the basic reproduction number R₀ is established: The disease can be eradicated if R₀ < 1, while the disease persists if R₀ > 1. As an application, six different screening strategies are explored to examine the impacts of screening on the control of the 2009 influenza A (H1N1) pandemic. We find that it is crucial to screen travelers from and to high-risk patches, and it is not necessary to implement screening in all connected patches, and both the dispersal rates and the successful detection rate of screening play an important role on determining an effective and practical screening strategy.

A spatial-temporal transmission model and early intervention policies of 2009 A/H1N1 influenza in South Korea

We developed a spatial-temporal model of the 2009 A/H1N1 influenza pandemic in the Seoul metropolitan area (SMA), which is located in the north-west of South Korea and is the second-most complex metropolitan area worldwide. This multi-patch influenza model consists of a SEIAR influenza transmission model and flow model between two districts. This model is based on the daily confirmed cases of A/H1N1 influenza collected by the Korea Center for Disease Control and Prevention from April 27 to September 15, 2009 and the daily commuting data from 33 districts of SMA reported in the 2010 Population and Housing Census (PHC). We analyzed the spread patterns of 2009 influenza in the SMA by the reproductive numbers and geographic information systems. During the early period of novel influenza pandemics, when pharmaceutical interventions are lacking, non-pharmaceutical public health interventions will be the most critical strategies for impeding the spread of influenza and delaying an epidemic. Using the spatial-temporal model developed herein, we also investigated the impact of non-pharmaceutical public health interventions, isolation and/or commuting restrictions, on the incidence reduction in various scenarios. Our model provides scientific evidence for predicting the spread of disease and preparedness for a future pandemic.

The first wave of the 1918 influenza pandemic among soldiers of the Canadian expeditionary force

OBJECTIVES

This article evaluates the evidence for the presence of the first, mild wave of the 1918 influenza pandemic among soldiers in the Canadian Expeditionary Force (CEF).

METHODS

Death records for soldiers in the CEF who died in Canada in 1917 and 1918 were extracted from the Commonwealth War Graves Commission and record-linked to the Canada War Graves Registers, Circumstances of Casualty database. Monthly mortality rates from pneumonia and influenza (P&I) were compared with mortality rates from all other causes for 1917 and 1918, and by region for 1918.

RESULTS

The herald wave of influenza was present among CEF soldiers in 1918. P&I mortality was significantly higher in March and April 1918 than during the same period in 1917. P&I mortality rates varied across the country and were significantly higher among soldiers who died in the Maritime region of Canada. In March, Maritime P&I mortality was significantly higher than its counterpart in the West; in April it was significantly higher than P&I mortality in both the Central and Western regions.

CONCLUSIONS

The CEF findings suggest that local, geographic heterogeneity characterized the first wave of the 1918 influenza pandemic in Canada and illustrate the ways in which well-established, historical patterns of cross-border social contact with the United States, coupled with the special conditions created by warfare, disproportionately funnelled influenza into particular regions. Identification of the mild first wave among soldiers in the CEF calls for more research on the civilian experience of both waves of influenza in Canada.

Design of non-pharmaceutical intervention strategies for pandemic influenza outbreaks

BACKGROUND

As seen during past pandemic influenza outbreaks, pharmaceutical interventions (PHIs) with vaccines and antivirals are the most effective methods of mitigation. However, availability of PHIs is unlikely to be adequate during the early stages of a pandemic. Hence, for early mitigation and possible containment, non-pharmaceutical interventions (NPIs) offer a viable alternative. Also, NPIs may be the only available interventions for most underdeveloped countries. In this paper we present a comprehensive methodology for design of effective NPI strategies.

METHODS

We develop a statistical ANOVA-based design approach that uses a detailed agent-based simulation as an underlying model. The design approach obtains the marginal effect of the characteristic parameters of NPIs, social behavior, and their interactions on various pandemic outcome measures including total number of contacts, infections, and deaths. We use the marginal effects to establish regression equations for the outcome measures, which are optimized to obtain NPI strategies. Efficacy of the NPI strategies designed using our methodology is demonstrated using simulated pandemic influenza outbreaks with different levels of virus transmissibility.

RESULTS

Our methodology was able to design effective NPI strategies, which were able to contain outbreaks by reducing infection attack rates (IAR) to below 10% in low and medium virus transmissibility scenarios with 33% and 50% IAR, respectively. The level of reduction in the high transmissibility scenario (with 65% IAR) was also significant. As noted in the published literature, we also found school closure to be the single most effective intervention among all NPIs.

CONCLUSIONS

If harnessed effectively, NPIs offer a significant potential for mitigation of pandemic influenza outbreaks. The methodology presented here fills a gap in the literature, which, though replete with models on NPI strategy evaluation, lacks a treatise on optimal strategy design.

The spatial resolution of epidemic peaks

The emergence of novel respiratory pathogens can challenge the capacity of key health care resources, such as intensive care units, that are constrained to serve only specific geographical populations. An ability to predict the magnitude and timing of peak incidence at the scale of a single large population would help to accurately assess the value of interventions designed to reduce that peak. However, current disease-dynamic theory does not provide a clear understanding of the relationship between: epidemic trajectories at the scale of interest (e.g. city); population mobility; and higher resolution spatial effects (e.g. transmission within small neighbourhoods). Here, we used a spatially-explicit stochastic meta-population model of arbitrary spatial resolution to determine the effect of resolution on model-derived epidemic trajectories. We simulated an influenza-like pathogen spreading across theoretical and actual population densities and varied our assumptions about mobility using Latin-Hypercube sampling. Even though, by design, cumulative attack rates were the same for all resolutions and mobilities, peak incidences were different. Clear thresholds existed for all tested populations, such that models with resolutions lower than the threshold substantially overestimated population-wide peak incidence. The effect of resolution was most important in populations which were of lower density and lower mobility. With the expectation of accurate spatial incidence datasets in the near future, our objective was to provide a framework for how to use these data correctly in a spatial meta-population model. Our results suggest that there is a fundamental spatial resolution for any pathogen-population pair. If underlying interactions between pathogens and spatially heterogeneous populations are represented at this resolution or higher, accurate predictions of peak incidence for city-scale epidemics are feasible.

THEORETICAL INVESTIGATION OF THE IMPACT ON EPIDEMIC THRESHOLD OF TRAVEL BETWEEN COMMUNITIES OF RESIDENT POPULATIONS

During the initial phase of an epidemic, individual displacements between different regions modify the contact patterns. Understanding mobility processes and their consequences is necessary to predict the subsequent spread of the disease in order to optimize control policies. The basic reproduction number is commonly used to determine the threshold between extinction and expansion of the disease. Once it is derived for an epidemic model that includes the travel of population between distinct localities, the dependence of the diseases dynamics upon travel rates becomes explicit. In this study, we examine the effects of travel on the epidemic threshold for a model of two communities. The travel rates are treated as varying subject to two scenarios. We show theoretically that if the transmission potentials within communities are moderate, the epidemic threshold can be modified by travel. The conditions for the presence of the threshold induced by travel is determined and the critical values of travel at which the basic reproduction number is equal to one are derived. We show further that these results can also be applied to a model of three communities under specific travel patterns and that the derived basic reproduction number has a form similar to that of the two communities problem.

Renaissance model of an epidemic with quarantine

Quarantine is one possible solution to limit the propagation of an emerging infectious disease. Typically, infected individuals are removed from the population by avoiding physical contact with healthy individuals. A key factor for the success of a quarantine strategy is the carrying capacity of the facility. This is often a known parameter, while other parameters such as those defining the population structure are more difficult to assess. Here we develop a model where we explicitly introduce the carrying capacity of the quarantine facility into a susceptible-infected-recovered (SIR) framework. We show how the model can address the propagation and control of contact and sexually transmitted infections. We illustrate this by a case study of the city of Zurich during the 16th century, when it had to face an epidemic of syphilis. After Swiss mercenaries came back from a war in Naples in 1495, the authorities of the city addressed subsequent epidemics by, among others, placing infected members of the population in quarantine. Our results suggest that a modestly sized quarantine facility can successfully prevent or reduce an epidemic. However, false detection can present a real impediment for this solution. Indiscriminate quarantine of individuals can lead to the overfilling of the facility, and prevent the intake of infected individuals. This results in the failure of the quarantine policy. Hence, improving the rate of true over false detection becomes the key factor for quarantine strategies. Moreover, in the case of sexually transmitted infections, asymmetries in the male to female ratio, and the force of infection pertaining to each sex and class of sexual encounter can alter the effectiveness of quarantine measures. For example, a heterosexually transmitted disease that mainly affects one sex is harder to control in a population with more individuals of the opposite sex. Hence an imbalance in the sex ratios as seen in situations such as mining colonies, or populations at war, can present impediments for the success of quarantine policies.

The effect of public health interventions on the spread of influenza among cities

Infectious disease is no longer a local problem. Modern populations are more mobile than ever before, and with this mobility comes active global mixing of infectious disease. To understand the spread of diseases such as influenza, we use a multi-city epidemic model. We extend the SEIR (susceptible-exposed-infectious-recovered) model to incorporate population migration between cities, and use this model to analyze the geographic spread of influenza. We investigate the effectiveness of travel restrictions as a control against the spread of influenza. First we obtain the basic reproduction number for the single city case, and observe two other control strategies suggested by this case: increasing the number of clinically ill individuals that are treated, and reducing the interval between infection and treatment of such individuals. We evaluate the effectiveness of the three control strategies with numerical simulations. It is shown that travel restrictions are less effective than the other two strategies. In general, travel restriction tends to delay the spread of the disease into new cities. However, it can increase the peak height of infected populations in all cities. An understanding of the epidemiological structures of related cities is strongly recommended in order to effectively apply the travel restriction strategy.

Comparing three basic models for seasonal influenza

In this paper we report the use of the open source Spatiotemporal Epidemiological Modeler (STEM, www.eclipse.org/stem) to compare three basic models for seasonal influenza transmission. The models are designed to test for possible differences between the seasonal transmission of influenza A and B. Model 1 assumes that the seasonality and magnitude of transmission do not vary between influenza A and B. Model 2 assumes that the magnitude of seasonal forcing (i.e., the maximum transmissibility), but not the background transmission or flu season length, differs between influenza A and B. Model 3 assumes that the magnitude of seasonal forcing, the background transmission, and flu season length all differ between strains. The models are all optimized using 10 years of surveillance data from 49 of 50 administrative divisions in Israel. Using a cross-validation technique, we compare the relative accuracy of the models and discuss the potential for prediction. We find that accounting for variation in transmission amplitude increases the predictive ability compared to the base. However, little improvement is obtained by allowing for further variation in the shape of the seasonal forcing function.

Mitigation strategies for pandemic influenza A: balancing conflicting policy objectives

Mitigation of a severe influenza pandemic can be achieved using a range of interventions to reduce transmission. Interventions can reduce the impact of an outbreak and buy time until vaccines are developed, but they may have high social and economic costs. The non-linear effect on the epidemic dynamics means that suitable strategies crucially depend on the precise aim of the intervention. National pandemic influenza plans rarely contain clear statements of policy objectives or prioritization of potentially conflicting aims, such as minimizing mortality (depending on the severity of a pandemic) or peak prevalence or limiting the socio-economic burden of contact-reducing interventions. We use epidemiological models of influenza A to investigate how contact-reducing interventions and availability of antiviral drugs or pre-pandemic vaccines contribute to achieving particular policy objectives. Our analyses show that the ideal strategy depends on the aim of an intervention and that the achievement of one policy objective may preclude success with others, e.g., constraining peak demand for public health resources may lengthen the duration of the epidemic and hence its economic and social impact. Constraining total case numbers can be achieved by a range of strategies, whereas strategies which additionally constrain peak demand for services require a more sophisticated intervention. If, for example, there are multiple objectives which must be achieved prior to the availability of a pandemic vaccine (i.e., a time-limited intervention), our analysis shows that interventions should be implemented several weeks into the epidemic, not at the very start. This observation is shown to be robust across a range of constraints and for uncertainty in estimates of both R₀ and the timing of vaccine availability. These analyses highlight the need for more precise statements of policy objectives and their assumed consequences when planning and implementing strategies to mitigate the impact of an influenza pandemic.

In the event of an influenza pandemic which has high mortality and the potential to spread rapidly, such as the 1918–19 pandemic, there are a number of non-pharmaceutical public health control options available to reduce transmission in the community and mitigate the effects of the pandemic. These include reducing social contacts by closing schools or postponing public events, and encouraging hand washing and the use of masks. These interventions will not only have a non-intuitive impact on the epidemic dynamics, but they will also have direct and indirect social and economic costs, which mean that governments will only want to use them for a limited amount of time. We use simulations to show that limited-time interventions that achieve one aim, e.g., contain the total number of cases below some maximum number of treatments available, are not the same as those that achieve another, e.g., minimize peak demand for health care services. If multiple aims are defined simultaneously, we often see that the optimal intervention need not commence immediately but can begin a few weeks into the epidemic. Our research demonstrates the importance of tailoring pandemic plans to defined policy targets with some flexibility to allow for uncertainty in the characteristics of the pandemic.

Agent-based modeling of the spread of the 1918-1919 flu in three Canadian fur trading communities

OBJECTIVES

Previous attempts to study the 1918-1919 flu in three small communities in central Manitoba have used both three-community population-based and single-community agent-based models. These studies identified critical factors influencing epidemic spread, but they also left important questions unanswered. The objective of this project was to design a more realistic agent-based model that would overcome limitations of earlier models and provide new insights into these outstanding questions.

METHODS

The new model extends the previous agent-based model to three communities so that results can be compared to those from the population-based model. Sensitivity testing was conducted, and the new model was used to investigate the influence of seasonal settlement and mobility patterns, the geographic heterogeneity of the observed 1918-1919 epidemic in Manitoba, and other questions addressed previously.

RESULTS

Results confirm outcomes from the population-based model that suggest that (a) social organization and mobility strongly influence the timing and severity of epidemics and (b) the impact of the epidemic would have been greater if it had arrived in the summer rather than the winter. New insights from the model suggest that the observed heterogeneity among communities in epidemic impact was not unusual and would have been the expected outcome given settlement structure and levels of interaction among communities.

CONCLUSIONS

Application of an agent-based computer simulation has helped to better explain observed patterns of spread of the 1918-1919 flu epidemic in central Manitoba. Contrasts between agent-based and population-based models illustrate the advantages of agent-based models for the study of small populations.

Modelling environmentally-mediated infectious diseases of humans: transmission dynamics of schistosomiasis in China

Macroparasites of humans are sensitive to a variety of environmental variables, including temperature, rainfall and hydrology, yet current comprehension of these relationships is limited. Given the incomplete mechanistic understanding of environment-disease interactions, mathematical models that describe them have seldom included the effects of time-varying environmental processes on transmission dynamics and where they have been included, simple generic, periodic functions are usually used. Few examples exist where seasonal forcing functions describe the actual processes underlying the environmental drivers of disease dynamics. Transmission of human schistosomes, which involves multiple environmental stages, offers a model for applying our understanding of the environmental determinants of the viability, longevity, infectivity and mobility of these stages to controlling disease in diverse environments. Here, a mathematical model of schistosomiasis transmission is presented which incorporates the effects of environmental variables on transmission. Model dynamics are explored and several key extensions to the model are proposed.

A two-scale network dynamic model for human mobility process

The technological changes and educational expansion have created the heterogeneity in the human species. Clearly, this heterogeneity generates a structure in the population dynamics, namely: citizen, permanent resident, visitor, and etc. Furthermore, as the heterogeneity in the population increases, the human mobility between meta-populations patches also increases. Depending on spatial scales, a meta-population patch can be decomposed into sub-patches, for examples: homes, neighborhoods, towns, etc. Members of the population can move between the sub-patches. The dynamics of human mobility in a heterogeneous and scaled structured population is still its infancy level. In this work, an attempt is made to investigate the human mobility dynamics of heterogeneous and scaled structured population. We present a two scaled human mobility model for a meta-population. The sub regions and regions are interlinked via intra-and inter regional transport network systems. Under various types of growth order assumptions on the intra and interregional residence times of the residents of a sub region, different patterns of static behavior of the mobility process is studied. In addition, the results reveal that the system has a natural tendency to quarantine itself without total breaking a link in the transportation network system. Moreover, there is a threshold point for the largest intra regional visiting time of residents of a given sub region that leads to either a total isolation of the residents from other sub regions within the region or a partial isolation of residents from some of the sub regions within the region.

Spatial dynamics of the 1918 influenza pandemic in England, Wales and the United States

There is still limited understanding of key determinants of spatial spread of influenza. The 1918 pandemic provides an opportunity to elucidate spatial determinants of spread on a large scale.

To better characterize the spread of the 1918 major wave, we fitted a range of city-to-city transmission models to mortality data collected for 246 population centres in England and Wales and 47 cities in the US. Using a gravity model for city-to-city contacts, we explored the effect of population size and distance on the spread of disease and tested assumptions regarding density dependence in connectivity between cities. We employed Bayesian Markov Chain Monte Carlo methods to estimate parameters of the model for population, infectivity, distance and density dependence. We inferred the most likely transmission trees for both countries.

For England and Wales, a model that estimated the degree of density dependence in connectivity between cities was preferable by deviance information criterion comparison. Early in the major wave, long distance infective interactions predominated, with local infection events more likely as the epidemic became widespread. For the US, with fewer more widely dispersed cities, statistical power was lacking to estimate population size dependence or the degree of density dependence, with the preferred model depending on distance only. We find that parameters estimated from the England and Wales dataset can be applied to the US data with no likelihood penalty.

Modeling influenza epidemics and pandemics: insights into the future of swine flu (H1N1)

Here we present a review of the literature of influenza modeling studies, and discuss how these models can provide insights into the future of the currently circulating novel strain of influenza A (H1N1), formerly known as swine flu. We discuss how the feasibility of controlling an epidemic critically depends on the value of the Basic Reproduction Number (R0). The R0 for novel influenza A (H1N1) has recently been estimated to be between 1.4 and 1.6. This value is below values of R0 estimated for the 1918-1919 pandemic strain (mean R0 approximately 2: range 1.4 to 2.8) and is comparable to R0 values estimated for seasonal strains of influenza (mean R0 1.3: range 0.9 to 2.1). By reviewing results from previous modeling studies we conclude it is theoretically possible that a pandemic of H1N1 could be contained. However it may not be feasible, even in resource-rich countries, to achieve the necessary levels of vaccination and treatment for control. As a recent modeling study has shown, a global cooperative strategy will be essential in order to control a pandemic. This strategy will require resource-rich countries to share their vaccines and antivirals with resource-constrained and resource-poor countries. We conclude our review by discussing the necessity of developing new biologically complex models. We suggest that these models should simultaneously track the transmission dynamics of multiple strains of influenza in bird, pig and human populations. Such models could be critical for identifying effective new interventions, and informing pandemic preparedness planning. Finally, we show that by modeling cross-species transmission it may be possible to predict the emergence of pandemic strains of influenza.

Connectivity sustains disease transmission in environments with low potential for endemicity: modelling schistosomiasis with hydrologic and social connectivities

Social interaction and physical interconnections between populations can influence the spread of parasites. The role that these pathways play in sustaining the transmission of parasitic diseases is unclear, although increasingly realistic metapopulation models are being used to study how diseases persist in connected environments. We use a mathematical model of schistosomiasis transmission for a distributed set of heterogeneous villages to show that the transport of parasites via social (host movement) and environmental (parasite larvae movement) pathways has consequences for parasite control, spread and persistence. We find that transmission can be sustained regionally throughout a group of connected villages even when individual village conditions appear not to support endemicity. Optimum transmission is determined by an interplay between different transport pathways, and not necessarily by those that are the most dispersive (e.g. disperse social contacts may not be optimal for transmission). We show that the traditional targeting of villages with high infection, without regard to village interconnections, may not lead to optimum control. These findings have major implications for effective disease control, which needs to go beyond considering local variations in disease intensity, to also consider the degree to which populations are interconnected.

A Decentralized Molecular Diagnostic Testing Plan for Pandemic Influenza in the Ontario Public Health Laboratory System

The Ontario Public Health Laboratories system (OPHL) is in the midst of a six-year plan to implement molecular tools for pandemic influenza diagnostics in one central and three regional public health laboratories. This plan has been formulated as a consequence of: 1) experiences gained through severe acute respiratory syndrome (SARS), and comments of the members of the Expert Panel on SARS and Infectious Disease Control (i.e., the Walker report); 2) a review of pandemic preparedness literature; 3) historical and epidemiologic discussions about previous pandemics; and 4) suggestions made by various pandemic working committees. The OPHL plan includes: 1) an aggressive restructuring of the overall molecular microbiology testing capacity of the OPHL; 2) the ability to shift influenza testing of samples between designated OPHL laboratories; and 3) the development of screening tools for pandemic influenza diagnostic tests. The authors believe that investing in increased molecular testing capacity for regional laboratories outside the greater Toronto area will be beneficial to the OPHL system whether or not an influenza pandemic occurs. Well-trained technologists and microbiologists, and the introduction of new technologies, will facilitate the development of a wide variety of molecular tests for other infectious diseases at public health laboratories geographically distant from Toronto, thus enhancing overall laboratory testing capacity in the province of Ontario.

Pandemic planning: non-pharmaceutical interventions

Ongoing concerns about the emergence of an influenza pandemic continue as the number of avian and human infections with the H5N1 virus mount. Adequate amounts of vaccine or anti-virals are unlikely to be available early on in a pandemic, and the latter could become ineffective because of resistance. These factors have focused attention on the use of non-pharmaceutical public health interventions to inhibit human-to-human transmission.

Quantifying the transmission potential of pandemic influenza

This article reviews quantitative methods to estimate the basic reproduction number of pandemic influenza, a key threshold quantity to help determine the intensity of interventions required to control the disease. Although it is difficult to assess the transmission potential of a probable future pandemic, historical epidemiologic data is readily available from previous pandemics, and as a reference quantity for future pandemic planning, mathematical and statistical analyses of historical data are crucial. In particular, because many historical records tend to document only the temporal distribution of cases or deaths (i.e. epidemic curve), our review focuses on methods to maximize the utility of time-evolution data and to clarify the detailed mechanisms of the spread of influenza.

First, we highlight structured epidemic models and their parameter estimation method which can quantify the detailed disease dynamics including those we cannot observe directly. Duration-structured epidemic systems are subsequently presented, offering firm understanding of the definition of the basic and effective reproduction numbers. When the initial growth phase of an epidemic is investigated, the distribution of the generation time is key statistical information to appropriately estimate the transmission potential using the intrinsic growth rate. Applications of stochastic processes are also highlighted to estimate the transmission potential using similar data. Critically important characteristics of influenza data are subsequently summarized, followed by our conclusions to suggest potential future methodological improvements.

Quarantine Through History

This article reviews in a historical perspective and by means of documented examples the scientific principles relevant to the concept and effectiveness of quarantine, the logistic, economic, and political barriers to its correct implementation through time, and the health impact of local and large-scale quarantine. Quarantine is overall one of the oldest and most disseminated and, despite its limits, most effective health measures elaborated by mankind. The evidence-based history of medicine and evidence-based modern epidemiology indicate that the implementation of correct quarantine procedures is today still feasible and useful provided that a proactive collaboration is operative among those concerned and that the measures are tailored according to geographical, social, and health conditions.

Spatial Structure: Patch Models

Discrete spatial heterogenity is introduced into disease transmission models, resulting in large systems of ordinary differential equations. Such metapopulation models describe disease spread on a number of spatial patches. In the first model considered, there is no explicit movement of individuals; rather infectives can pass the disease to susceptibles in other patches. The second type of model explicitly includes rates of travel between patches and also takes account of the resident patch as well as the current patch of individuals. A formula for and useful bounds on the basic reproduction number of the system are determined. Brief descriptions of application of this type of metapopulation model are given to investigate the spread of bovine tuberculosis and the effect of quarantine on the spread of influenza.

Public health interventions and epidemic intensity during the 1918 influenza pandemic

Nonpharmaceutical interventions (NPIs) intended to reduce infectious contacts between persons form an integral part of plans to mitigate the impact of the next influenza pandemic. Although the potential benefits of NPIs are supported by mathematical models, the historical evidence for the impact of such interventions in past pandemics has not been systematically examined. We obtained data on the timing of 19 classes of NPI in 17 U.S. cities during the 1918 pandemic and tested the hypothesis that early implementation of multiple interventions was associated with reduced disease transmission. Consistent with this hypothesis, cities in which multiple interventions were implemented at an early phase of the epidemic had peak death rates approximately 50% lower than those that did not and had less-steep epidemic curves. Cities in which multiple interventions were implemented at an early phase of the epidemic also showed a trend toward lower cumulative excess mortality, but the difference was smaller (approximately 20%) and less statistically significant than that for peak death rates. This finding was not unexpected, given that few cities maintained NPIs longer than 6 weeks in 1918. Early implementation of certain interventions, including closure of schools, churches, and theaters, was associated with lower peak death rates, but no single intervention showed an association with improved aggregate outcomes for the 1918 phase of the pandemic. These findings support the hypothesis that rapid implementation of multiple NPIs can significantly reduce influenza transmission, but that viral spread will be renewed upon relaxation of such measures.

Social contexts, syndemics, and infectious disease in northern Aboriginal populations

Until the last half of the 20th century, infectious diseases dominated the health profile of northern North American Aboriginal communities. Research on the 1918 influenza pandemic exemplifies some of the ways in which the social context of European contact and ensuing economic developments affected the nature of infectious disease ecology as well as the frequency and severity of the problem. To understand these impacts it is necessary to consider the web of interactions among multiple pathogens, the biology of the human host, and the social environment in which people lived. At the very least, an understanding of the history of the impact of infectious diseases on northern North American communities requires attention not only to potential interactions among cocirculating pathogens, but their links to key social, historical, and economic factors that exacerbated their adverse effects and contributed to excess mortality.

An SEIS epidemic model with transport-related infection

In this paper, an SEIS epidemic model is proposed to study the effect of transport-related infection on the spread and control of infectious disease. New result implies that traveling of the exposed (means exposed but not yet infectious) individuals can bring disease from one region to other regions even if the infectious individuals are inhibited from traveling among regions. It is shown that transportation among regions will change the disease dynamics and break infection out even if infectious diseases will go to extinction in each isolated region without transport-related infection. In addition, our analysis shows that transport-related infection intensifies the disease spread if infectious diseases break out to cause an endemic situation in each region, in the sense of that both the absolute and relative size of patients increase. This suggests that it is very essential to strengthen restrictions of passengers once we know infectious diseases appeared.

Impact of travel between patches for spatial spread of disease

A multipatch model is proposed to study the impact of travel on the spatial spread of disease between patches with different level of disease prevalence. The basic reproduction number for the ith patch in isolation is obtained along with the basic reproduction number of the system of patches, Re(0). Inequalities describing the relationship between these numbers are also given. For a two-patch model with one high prevalence patch and one low prevalence patch, results pertaining to the dependence of Re(0) on the travel rates between the two patches are obtained. For parameter values relevant for influenza, these results show that, while banning travel of infectives from the low to the high prevalence patch always contributes to disease control, banning travel of symptomatic travelers only from the high to the low prevalence patch could adversely affect the containment of the outbreak under certain ranges of parameter values. Moreover, banning all travel of infected individuals from the high to the low prevalence patch could result in the low prevalence patch becoming diseasefree, while the high prevalence patch becomes even more disease-prevalent, with the resulting number of infectives in this patch alone exceeding the combined number of infectives in both patches without border control. Under the set of parameter values used, our results demonstrate that if border control is properly implemented, then it could contribute to stopping the spatial spread of disease between patches.

Estimation of potential global pandemic influenza mortality on the basis of vital registry data from the 1918-20 pandemic: a quantitative analysis

BACKGROUND

The threat of an avian influenza pandemic is causing widespread public concern and health policy response, especially in high-income countries. Our aim was to use high-quality vital registration data gathered during the 1918-20 pandemic to estimate global mortality should such a pandemic occur today.

METHODS

We identified all countries with high-quality vital registration data for the 1918-20 pandemic and used these data to calculate excess mortality. We developed ordinary least squares regression models that related excess mortality to per-head income and absolute latitude and used these models to estimate mortality had there been an influenza pandemic in 2004.

FINDINGS

Excess mortality data show that, even in 1918-20, population mortality varied over 30-fold across countries. Per-head income explained a large fraction of this variation in mortality. Extrapolation of 1918-20 mortality rates to the worldwide population of 2004 indicates that an estimated 62 million people (10th-90th percentile range 51 million-81 million) would be killed by a similar influenza pandemic; 96% (95% CI 95-98) of these deaths would occur in the developing world. If this mortality were concentrated in a single year, it would increase global mortality by 114%.

INTERPRETATION

This analysis of the empirical record of the 1918-20 pandemic provides a plausible upper bound on pandemic mortality. Most deaths will occur in poor countries--ie, in societies whose scarce health resources are already stretched by existing health priorities.

Non-pharmaceutical interventions for pandemic influenza, national and community measures

Recommended interventions vary by transmission pattern, pandemic phase, and disease severity.

The World Health Organization's recommended pandemic influenza interventions, based on limited data, vary by transmission pattern, pandemic phase, and illness severity and extent. In the pandemic alert period, recommendations include isolation of patients and quarantine of contacts, accompanied by antiviral therapy. During the pandemic period, the focus shifts to delaying spread and reducing effects through population-based measures. Ill persons should remain home when they first become symptomatic, but forced isolation and quarantine are ineffective and impractical. If the pandemic is severe, social distancing measures such as school closures should be considered. Nonessential domestic travel to affected areas should be deferred. Hand and respiratory hygiene should be routine; mask use should be based on setting and risk, and contaminated household surfaces should be disinfected. Additional research and field assessments during pandemics are essential to update recommendations. Legal authority and procedures for implementing interventions should be understood in advance and should respect cultural differences and human rights.