Resource allocation for epidemic control in metapopulations

Model-informed health and socio-economic benefits of enhancing global equity and access to Covid-19 vaccines

We take a model-informed approach to the view that a global equitable access (GEA) to Covid-19 vaccines is the key to bring this pandemic to an end. We show that the equitable redistribution (proportional to population size) of the currently available vaccines is not sufficient to stop the pandemic, whereas a 60% increase in vaccine access (the global share of vaccinated people) would have allowed the current distribution to stop the pandemic in about a year of vaccination, saving millions of people in poor countries. We then investigate the interplay between access to vaccines and their distribution among rich and poor countries, showing that the access increase to stop the pandemic gets minimized at + 32% by the equitable distribution (- 36% in rich countries and + 60% in poor ones). To estimate the socio-economic benefits of a vaccination campaign with enhanced global equity and access (eGEA), we compare calibrated simulations of the current scenario with a hypothetical, vaccination-intensive scenario that assumes high rollouts (shown however by many rich and poor countries during the 2021-2022 vaccination campaign) and an improved equity from the current 2.5:1 to a 2:1 rich/poor-ratio of the population fractions vaccinated per day. Assuming that the corresponding + 130% of vaccine production is made possible by an Intellectual Property waiver, we show that the money saved on vaccines globally by the selected eGEA scenario overcomes the 5-year profit of the rights holders in the current situation. This justifies compensation mechanisms in exchange for the necessary licensing agreements. The good news is that the benefits of this eGEA scenario are still relevant, were we ready to implement it now.

Optimal spatial evaluation of a pro rata vaccine distribution rule for COVID-19

The COVID-19 Vaccines Global Access (COVAX) is a World Health Organization (WHO) initiative that aims for an equitable access of COVID-19 vaccines. Despite potential heterogeneous infection levels across a country, countries receiving allotments of vaccines may follow WHO's allocation guidelines and distribute vaccines based on a jurisdictions' relative population size. Utilizing economic-epidemiological modeling, we benchmark the performance of this pro rata allocation rule by comparing it to an optimal one that minimizes the economic damages and expenditures over time, including a penalty representing the social costs of deviating from the pro rata strategy. The pro rata rule performs better when the duration of naturally- and vaccine-acquired immunity is short, when there is population mixing, when the supply of vaccine is high, and when there is minimal heterogeneity in demographics. Despite behavioral and epidemiological uncertainty diminishing the performance of the optimal allocation, it generally outperforms the pro rata vaccine distribution rule.

Delays in Epidemic Outbreak Control Cost Disproportionately Large Treatment Footprints to Offset

Epidemic outbreak control often involves a spatially explicit treatment area (quarantine, inoculation, ring cull) that covers the outbreak area and adjacent regions where hosts are thought to be latently infected. Emphasis on space however neglects the influence of treatment timing on outbreak control. We conducted field and in silico experiments with wheat stripe rust (WSR), a long-distance dispersed plant disease, to understand interactions between treatment timing and area interact to suppress an outbreak. Full-factorial field experiments with three different ring culls (outbreak area only to a 25-fold increase in treatment area) at three different disease control timings (1.125, 1.25, and 1.5 latent periods after initial disease expression) indicated that earlier treatment timing had a conspicuously greater suppressive effect than the area treated. Disease spread computer simulations over a broad range of influential epidemic parameter values (R0, outbreak disease prevalence, epidemic duration) suggested that potentially unrealistically large increases in treatment area would be required to compensate for even small delays in treatment timing. Although disease surveillance programs are costly, our results suggest that treatments early in an epidemic disease outbreak require smaller areas to be effective, which may ultimately compensate for the upfront costs of proactive disease surveillance programs.

Dynamic resource allocation for controlling pathogen spread on a large metapopulation network

To control the spread of an infectious disease over a large network, the optimal allocation by a social planner of a limited resource is a fundamental and difficult problem. We address this problem for a livestock disease that propagates on an animal trade network according to an epidemiological–demographic model based on animal demographics and trade data. We assume that the resource is dynamically allocated following a certain score, up to the limit of resource availability. We adapt a greedy approach to the metapopulation framework, obtaining new scores that minimize approximations of two different objective functions, for two control measures: vaccination and treatment. Through intensive simulations, we compare the greedy scores with several heuristics. Although topology-based scores can limit the spread of the disease, information on herd health status seems crucial to eradicating the disease. In particular, greedy scores are among the most effective in reducing disease prevalence, even though they do not always perform the best. However, some scores may be preferred in real life because they are easier to calculate or because they use a smaller amount of resources. The developed approach could be adapted to other epidemiological models or to other control measures in the metapopulation setting.

Hierarchical Epidemic Model on Structured Population: Diffusion Patterns and Control Policies

In the current study, we define a hierarchical epidemic model that helps to describe the propagation of a pathogen in a clustered human population. The estimation of a novel coronavirus spreading worldwide leads to the idea of the hierarchical structure of the epidemic process. Thus, the propagation process is divided into three possible levels: a city, a country, and a worldwide. On each level, the pathogen propagation process is based on the susceptible-exposed-infected-recovered (SEIR) model. We thus formulate a modified transmission model of infected individuals between levels. The control of the pathogen’s spread can be seen as an optimal control problem. A trade-off exists between the cost of active virus propagation and the design of appropriate quarantine measures. Each level of the hierarchy is defined by its network. A series of numerical experiments was conducted to corroborate the obtained results.

Optimal strategies to protect a sub-population at risk due to an established epidemic

Epidemics can particularly threaten certain sub-populations. For example, for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the elderly are often preferentially protected. For diseases of plants and animals, certain sub-populations can drive mitigation because they are intrinsically more valuable for ecological, economic, socio-cultural or political reasons. Here, we use optimal control theory to identify strategies to optimally protect a ‘high-value’ sub-population when there is a limited budget and epidemiological uncertainty. We use protection of the Redwood National Park in California in the face of the large ongoing state-wide epidemic of sudden oak death (caused by Phytophthora ramorum) as a case study. We concentrate on whether control should be focused entirely within the National Park itself, or whether treatment of the growing epidemic in the surrounding ‘buffer region’ can instead be more profitable. We find that, depending on rates of infection and the size of the ongoing epidemic, focusing control on the high-value region is often optimal. However, priority should sometimes switch from the buffer region to the high-value region only as the local outbreak grows. We characterize how the timing of any switch depends on epidemiological and logistic parameters, and test robustness to systematic misspecification of these factors due to imperfect prior knowledge.

A multi-stage stochastic programming approach to epidemic resource allocation with equity considerations

Existing compartmental models in epidemiology are limited in terms of optimizing the resource allocation to control an epidemic outbreak under disease growth uncertainty. In this study, we address this core limitation by presenting a multi-stage stochastic programming compartmental model, which integrates the uncertain disease progression and resource allocation to control an infectious disease outbreak. The proposed multi-stage stochastic program involves various disease growth scenarios and optimizes the distribution of treatment centers and resources while minimizing the total expected number of new infections and funerals. We define two new equity metrics, namely infection and capacity equity, and explicitly consider equity for allocating treatment funds and facilities over multiple time stages. We also study the multi-stage value of the stochastic solution (VSS), which demonstrates the superiority of the proposed stochastic programming model over its deterministic counterpart. We apply the proposed formulation to control the Ebola Virus Disease (EVD) in Guinea, Sierra Leone, and Liberia of West Africa to determine the optimal and fair resource-allocation strategies. Our model balances the proportion of infections over all regions, even without including the infection equity or prevalence equity constraints. Model results also show that allocating treatment resources proportional to population is sub-optimal, and enforcing such a resource allocation policy might adversely impact the total number of infections and deaths, and thus resulting in a high cost that we have to pay for the fairness. Our multi-stage stochastic epidemic-logistics model is practical and can be adapted to control other infectious diseases in meta-populations and dynamically evolving situations.

Allocating epidemic response teams and vaccine deliveries by drone in generic network structures, according to expected prevented exposures

The tumultuous inception of an epidemic is usually accompanied by difficulty in determining how to respond best. In developing nations, this can be compounded by logistical challenges, such as vaccine shortages and poor road infrastructure. To provide guidance towards improved epidemic response, various resource allocation models, in conjunction with a network-based SEIRVD epidemic model, are proposed in this article. Further, the feasibility of using drones for vaccine delivery is evaluated, and assorted relevant parameters are discussed. For the sake of generality, these results are presented for multiple network structures, representing interconnected populations-upon which repeated epidemic simulations are performed. The resource allocation models formulated maximise expected prevented exposures on each day of a simulated epidemic, by allocating response teams and vaccine deliveries according to the solutions of two respective integer programming problems-thereby influencing the simulated epidemic through the SEIRVD model. These models, when compared with a range of alternative resource allocation strategies, were found to reduce both the number of cases per epidemic, and the number of vaccines required. Consequently, the recommendation is made that such models be used as decision support tools in epidemic response. In the absence thereof, prioritizing locations for vaccinations according to susceptible population, rather than total population or number of infections, is most effective for the majority of network types. In other results, fixed-wing drones are demonstrated to be a viable delivery method for vaccines in the context of an epidemic, if sufficient drones can be promptly procured; the detrimental effect of intervention delay was discovered to be significant. In addition, the importance of well-documented routine vaccination activities is highlighted, due to the benefits of increased pre-epidemic immunity rates, and targeted vaccination.

The Current State of Infectious Disasters Preparedness Around the World: A Qualitative Systematic Review (2007-2019)

Infectious disasters have specific features which require special approaches and facilities. The main challenge is the rate of spread, and their ability to traverse the Earth in a short time. The preparedness of hospitals to face these events is therefore of the utmost importance. This study was designed to assess the preparedness of countries facing biological events worldwide. A qualitative systematic review was done from PubMed (National Library of Medicine, Bethesda, MD), Scopus (Elsevier, Amsterdam, Netherlands), Web of Science (Thomson Reuters, New York, NY), ProQuest (Ann Arbor, MI), and Google Scholar (Google Inc, Mountain View, CA). Two journals were searched as key journals. The search period was from January 1, 2007 to December 30, 2018. Twenty-one (21) documents were selected including 7 (33%) from Asia, 7 (33%) from Europe, 4 (19%) from USA, 2 (10%) from Africa, and 1 (5%) multi-continental. Forty-six (46) common sub-themes were obtained and categorized into 13 themes (infection prevention control, risk perception, planning, essential support services, surveillance, laboratory, vulnerable groups, education and exercise and evaluation, human resource, clinical management of patients, risk communication, budget, and coordination). Not all articles discussed all the identified categories. There is an extended process required to reach complete preparedness for confronting biological events, including adequate and well-managed budget. Medical centers may have trouble dealing with such events, at least in some respects, but most developed countries seem to be more prepared in this regard.

Strategies for the efficient use of diagnostic resource under constraints: a model-based study on overflow of patients and insufficient diagnostic kits

This article addresses an optimisation problem of distributing rapid diagnostic kits among patients when the demands far surpass the supplies. This problem has not been given much attention in the field, and therefore, this article aims to provide a preliminary result in this problem domain. First, we describe the problem and define the goal of the optimisation by introducing an evaluation metric that measures the efficiency of the distribution strategies. Then, we propose two simple strategies, and a strategy that incorporates a prediction of patients' visits utilising a standard epidemic model. The strategies were evaluated using the metric, with past statistics in Kitami City, Hokkaido, Japan, and the prediction-based strategy outperformed the other distribution strategies. We discuss the properties of the strategies and the limitations of the proposed approach. Although the problem must be generalised before the actual deployment of the suggested strategy, the preliminary result is promising in its ability to address the shortage of diagnostic capacity currently observed worldwide because of the ongoing coronavirus disease pandemic.

Applying optimal control theory to complex epidemiological models to inform real-world disease management

Mathematical models provide a rational basis to inform how, where and when to control disease. Assuming an accurate spatially explicit simulation model can be fitted to spread data, it is straightforward to use it to test the performance of a range of management strategies. However, the typical complexity of simulation models and the vast set of possible controls mean that only a small subset of all possible strategies can ever be tested. An alternative approach-optimal control theory-allows the best control to be identified unambiguously. However, the complexity of the underpinning mathematics means that disease models used to identify this optimum must be very simple. We highlight two frameworks for bridging the gap between detailed epidemic simulations and optimal control theory: open-loop and model predictive control. Both these frameworks approximate a simulation model with a simpler model more amenable to mathematical analysis. Using an illustrative example model, we show the benefits of using feedback control, in which the approximation and control are updated as the epidemic progresses. Our work illustrates a new methodology to allow the insights of optimal control theory to inform practical disease management strategies, with the potential for application to diseases of humans, animals and plants. This article is part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'. This theme issue is linked with the earlier issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'.

Coevolution spreading in complex networks

The propagations of diseases, behaviors and information in real systems are rarely independent of each other, but they are coevolving with strong interactions. To uncover the dynamical mechanisms, the evolving spatiotemporal patterns and critical phenomena of networked coevolution spreading are extremely important, which provide theoretical foundations for us to control epidemic spreading, predict collective behaviors in social systems, and so on. The coevolution spreading dynamics in complex networks has thus attracted much attention in many disciplines. In this review, we introduce recent progress in the study of coevolution spreading dynamics, emphasizing the contributions from the perspectives of statistical mechanics and network science. The theoretical methods, critical phenomena, phase transitions, interacting mechanisms, and effects of network topology for four representative types of coevolution spreading mechanisms, including the coevolution of biological contagions, social contagions, epidemic-awareness, and epidemic-resources, are presented in detail, and the challenges in this field as well as open issues for future studies are also discussed.

Applying optimal control theory to complex epidemiological models to inform real-world disease management

Mathematical models provide a rational basis to inform how, where and when to control disease. Assuming an accurate spatially explicit simulation model can be fitted to spread data, it is straightforward to use it to test the performance of a range of management strategies. However, the typical complexity of simulation models and the vast set of possible controls mean that only a small subset of all possible strategies can ever be tested. An alternative approach-optimal control theory-allows the best control to be identified unambiguously. However, the complexity of the underpinning mathematics means that disease models used to identify this optimum must be very simple. We highlight two frameworks for bridging the gap between detailed epidemic simulations and optimal control theory: open-loop and model predictive control. Both these frameworks approximate a simulation model with a simpler model more amenable to mathematical analysis. Using an illustrative example model, we show the benefits of using feedback control, in which the approximation and control are updated as the epidemic progresses. Our work illustrates a new methodology to allow the insights of optimal control theory to inform practical disease management strategies, with the potential for application to diseases of humans, animals and plants. This article is part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'. This theme issue is linked with the earlier issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'.

How should HIV resources be allocated? Lessons learnt from applying Optima HIV in 23 countries

Introduction

With limited funds available, meeting global health targets requires countries to both mobilize and prioritize their health spending. Within this context, countries have recognized the importance of allocating funds for HIV as efficiently as possible to maximize impact. Over the past six years, the governments of 23 countries in Africa, Asia, Eastern Europe and Latin America have used the Optima HIV tool to estimate the optimal allocation of HIV resources.

Methods

Each study commenced with a request by the national government for technical assistance in conducting an HIV allocative efficiency study using Optima HIV. Each study team validated the required data, calibrated the Optima HIV epidemic model to produce HIV epidemic projections, agreed on cost functions for interventions, and used the model to calculate the optimal allocation of available funds to best address national strategic plan targets. From a review and analysis of these 23 country studies, we extract common themes around the optimal allocation of HIV funding in different epidemiological contexts.

Results and discussion

The optimal distribution of HIV resources depends on the amount of funding available and the characteristics of each country's epidemic, response and targets. Universally, the modelling results indicated that scaling up treatment coverage is an efficient use of resources. There is scope for efficiency gains by targeting the HIV response towards the populations and geographical regions where HIV incidence is highest. Across a range of countries, the model results indicate that a more efficient allocation of HIV resources could reduce cumulative new HIV infections by an average of 18% over the years to 2020 and 25% over the years to 2030, along with an approximately 25% reduction in deaths for both timelines. However, in most countries this would still not be sufficient to meet the targets of the national strategic plan, with modelling results indicating that budget increases of up to 185% would be required.

Conclusions

Greater epidemiological impact would be possible through better targeting of existing resources, but additional resources would still be required to meet targets. Allocative efficiency models have proven valuable in improving the HIV planning and budgeting process.

Resource Allocation for Epidemic Control Across Multiple Sub-populations

The number of pathogenic threats to plant, animal and human health is increasing. Controlling the spread of such threats is costly and often resources are limited. A key challenge facing decision makers is how to allocate resources to control the different threats in order to achieve the least amount of damage from the collective impact. In this paper we consider the allocation of limited resources across n independent target populations to treat pathogens whose spread is modelled using the susceptible–infected–susceptible model. Using mathematical analysis of the systems dynamics, we show that for effective disease control, with a limited budget, treatment should be focused on a subset of populations, rather than attempting to treat all populations less intensively. The choice of populations to treat can be approximated by a knapsack-type problem. We show that the knapsack closely approximates the exact optimum and greatly outperforms a number of simpler strategies. A key advantage of the knapsack approximation is that it provides insight into the way in which the economic and epidemiological dynamics affect the optimal allocation of resources. In particular using the knapsack approximation to apportion control takes into account two important aspects of the dynamics: the indirect interaction between the populations due to the shared pool of limited resources and the dependence on the initial conditions.

The effects of invasive pests and pathogens on strategies for forest diversification

Diversification of the tree species composition of production forests is a frequently advocated strategy to increase resilience to pests and pathogens; however, there is a lack of a general framework to analyse the impact of economic and biological conditions on the optimal planting strategy in the presence of tree disease. To meet this need we use a novel bioeconomic model to quantitatively assess the effect of tree disease on the optimal planting proportion of two tree species. We find that diversifying the species composition can reduce the economic loss from disease even when the benefit from the resistant species is small. However, this key result is sensitive to a pathogen's characteristics (probability of arrival, time of arrival, rate of spread of infection) and the losses (damage of the disease to the susceptible species and reduced benefit of planting the resistant species). This study provides an exemplar framework which can be used to help understand the effect of a pathogen on forest management strategies.

Controlling infectious disease outbreaks: A deterministic allocation-scheduling model with multiple discrete resources

Infectious disease outbreaks occurred many times in the past and are more likely to happen in the future. In this paper the problem of allocating and scheduling limited multiple, identical or non-identical, resources employed in parallel, when there are several infected areas, is considered. A heuristic algorithm, based on Shih's (1974) and Pappis and Rachaniotis' (2010) algorithms, is proposed as the solution methodology. A numerical example implementing the proposed methodology in the context of a specific disease outbreak, namely influenza, is presented. The proposed methodology could be of significant value to those drafting contingency plans and healthcare policy agendas.

Complex Dynamical Behaviour in an Epidemic Model with Control

We analyse the dynamical behaviour of a simple, widely used model that integrates epidemiological dynamics with disease control and economic constraint on the control resources. We consider both the deterministic model and its stochastic counterpart. Despite its simplicity, the model exhibits mathematically rich dynamics, including multiple stable fixed points and stable limit cycles arising from global bifurcations. We show that the existence of the limit cycles in the deterministic model has important consequences in modelling the range of potential effects the control can have. The stochastic effects further interact with the deterministic dynamical structure by facilitating transitions between different attractors of the system. The interaction is important for the predictive power of the model and in using the model to optimize allocation when resources for control are limited. We conclude that when studying models with constrained control, special care should be given to the dynamical behaviour of the system and its interplay with stochastic effects.

Efficient Vaccine Distribution Based on a Hybrid Compartmental Model

To effectively and efficiently reduce the morbidity and mortality that may be caused by outbreaks of emerging infectious diseases, it is very important for public health agencies to make informed decisions for controlling the spread of the disease. Such decisions must incorporate various kinds of intervention strategies, such as vaccinations, school closures and border restrictions. Recently, researchers have paid increased attention to searching for effective vaccine distribution strategies for reducing the effects of pandemic outbreaks when resources are limited. Most of the existing research work has been focused on how to design an effective age-structured epidemic model and to select a suitable vaccine distribution strategy to prevent the propagation of an infectious virus. Models that evaluate age structure effects are common, but models that additionally evaluate geographical effects are less common. In this paper, we propose a new SEIR (susceptible-exposed-infectious šC recovered) model, named the hybrid SEIR-V model (HSEIR-V), which considers not only the dynamics of infection prevalence in several age-specific host populations, but also seeks to characterize the dynamics by which a virus spreads in various geographic districts. Several vaccination strategies such as different kinds of vaccine coverage, different vaccine releasing times and different vaccine deployment methods are incorporated into the HSEIR-V compartmental model. We also design four hybrid vaccination distribution strategies (based on population size, contact pattern matrix, infection rate and infectious risk) for controlling the spread of viral infections. Based on data from the 2009-2010 H1N1 influenza epidemic, we evaluate the effectiveness of our proposed HSEIR-V model and study the effects of different types of human behaviour in responding to epidemics.

Limiting the spread of disease through altered migration patterns

We consider a model for an epidemic in a population that occupies geographically distinct locations. The disease is spread within subpopulations by contacts between infective and susceptible individuals, and is spread between subpopulations by the migration of infected individuals. We show how susceptible individuals can act collectively to limit the spread of disease during the initial phase of an epidemic by specifying the distribution that minimises the growth rate of the epidemic when the infectives are migrating so as to maximise the growth rate. We also give an explicit strategy that minimises the basic reproduction number, which is also shown be optimal in terms of the probability of extinction and total size of the epidemic.

A Framework for Training Public Health Practitioners in Crisis Decision-Making

Three sets of issues tend to be overlooked in public health emergency preparedness and response, which can be addressed with new training protocols. The first issue is procedural and concerns the often intuitive (as opposed to deliberative) nature of effective crisis decision-making. The second issue is substantive and pertains to the incorporation and prioritization of ethical, political, and logistical concerns in public health emergency guidelines. The third issue is affective and concerns human feelings and human frailty, which can derail the most well designed and best practiced procedural and substantive approaches to emergency response. This article offers an outline for a decision-making framework for public health emergencies that addresses and incorporates these issues within relevant guidelines and training.

Inferring disease transmission networks at a metapopulation level

Background

To investigate transmission patterns of an infectious disease, e.g., malaria, it is desirable to use the observed surveillance data to discover the underlying (often hidden) disease transmission networks. Previous studies have provided methods for inferring information diffusion networks in which each node corresponds to an individual person. However, in the case of disease transmission, to effectively propose and implement intervention strategies, it is more realistic and reasonable for policy makers to study the diffusion patterns at a metapopulation level when the disease transmission is affected by mobile population, that is, to consider disease transmission networks in which nodes represent subpopulations, and links indicate their interrelationships.

Results

A network inference method called NetEpi (Network Epidemic) is developed and evaluated using both synthetic and real-world datasets. The experimental results show that NetEpi can not only recover most of the ground-truth disease transmission networks using only surveillance data, but also find a malaria transmission network based on a real-world dataset. The inferred malaria network can characterize the real-world observations to a certain extent. In addition, it also discloses some hidden phenomenon.

Conclusions

This research addresses the problem of inferring disease transmission networks at a metapopulation level. Such networks can be useful in several ways: (i) to investigate hidden impact factors that influence epidemic dynamics, (ii) to reveal possible sources of epidemic outbreaks, and (iii) to practically develop and/or improve strategies for controlling the spread of infectious diseases.

Thirteen challenges in modelling plant diseases

The underlying structure of epidemiological models, and the questions that models can be used to address, do not necessarily depend on the host organism in question. This means that certain preoccupations of plant disease modellers are similar to those of modellers of diseases in human, livestock and wild animal populations. However, a number of aspects of plant epidemiology are very distinctive, and this leads to specific challenges in modelling plant diseases, which in turn sets a certain agenda for modellers. Here we outline a selection of 13 challenges, specific to plant disease epidemiology, that we feel are important targets for future work.

Simulation models for socioeconomic inequalities in health: a systematic review

Background: The emergence and evolution of socioeconomic inequalities in health involves multiple factors interacting with each other at different levels. Simulation models are suitable for studying such complex and dynamic systems and have the ability to test the impact of policy interventions in silico. Objective: To explore how simulation models were used in the field of socioeconomic inequalities in health. Methods: An electronic search of studies assessing socioeconomic inequalities in health using a simulation model was conducted. Characteristics of the simulation models were extracted and distinct simulation approaches were identified. As an illustration, a simple agent-based model of the emergence of socioeconomic differences in alcohol abuse was developed. Results: We found 61 studies published between 1989 and 2013. Ten different simulation approaches were identified. The agent-based model illustration showed that multilevel, reciprocal and indirect effects of social determinants on health can be modeled flexibly. Discussion and Conclusions: Based on the review, we discuss the utility of using simulation models for studying health inequalities, and refer to good modeling practices for developing such models. The review and the simulation model example suggest that the use of simulation models may enhance the understanding and debate about existing and new socioeconomic inequalities of health frameworks.

Country- and age-specific optimal allocation of dengue vaccines

Several dengue vaccines are under development, and some are expected to become available imminently. Concomitant with the anticipated release of these vaccines, vaccine allocation strategies for dengue-endemic countries in Southeast Asia and Latin America are currently under development. We developed a model of dengue transmission that incorporates the age-specific distributions of dengue burden corresponding to those in Thailand and Brazil, respectively, to determine vaccine allocations that minimize the incidence of dengue hemorrhagic fever, taking into account limited availability of vaccine doses in the initial phase of production. We showed that optimal vaccine allocation strategies vary significantly with the demographic burden of dengue hemorrhagic fever. Consequently, the strategy that is optimal for one country may be sub-optimal for another country. More specifically, we showed that, during the first years following introduction of a dengue vaccine, it is optimal to target children for dengue mass vaccination in Thailand, whereas young adults should be targeted in Brazil.

Mitigation of epidemics in contact networks through optimal contact adaptation

This paper presents an optimal control problem formulation to minimize the total number of infection cases during the spread of susceptible-infected-recovered SIR epidemics in contact networks. In the new approach, contact weighted are reduced among nodes and a global minimum contact level is preserved in the network. In addition, the infection cost and the cost associated with the contact reduction are linearly combined in a single objective function. Hence, the optimal control formulation addresses the tradeoff between minimization of total infection cases and minimization of contact weights reduction. Using Pontryagin theorem, the obtained solution is a unique candidate representing the dynamical weighted contact network. To find the near-optimal solution in a decentralized way, we propose two heuristics based on Bang-Bang control function and on a piecewise nonlinear control function, respectively. We perform extensive simulations to evaluate the two heuristics on different networks. Our results show that the piecewise nonlinear control function outperforms the well-known Bang-Bang control function in minimizing both the total number of infection cases and the reduction of contact weights. Finally, our results show awareness of the infection level at which the mitigation strategies are effectively applied to the contact weights.

Development of a resource modelling tool to support decision makers in pandemic influenza preparedness: The AsiaFluCap Simulator

BACKGROUND

Health care planning for pandemic influenza is a challenging task which requires predictive models by which the impact of different response strategies can be evaluated. However, current preparedness plans and simulations exercises, as well as freely available simulation models previously made for policy makers, do not explicitly address the availability of health care resources or determine the impact of shortages on public health. Nevertheless, the feasibility of health systems to implement response measures or interventions described in plans and trained in exercises depends on the available resource capacity. As part of the AsiaFluCap project, we developed a comprehensive and flexible resource modelling tool to support public health officials in understanding and preparing for surges in resource demand during future pandemics.

RESULTS

The AsiaFluCap Simulator is a combination of a resource model containing 28 health care resources and an epidemiological model. The tool was built in MS Excel© and contains a user-friendly interface which allows users to select mild or severe pandemic scenarios, change resource parameters and run simulations for one or multiple regions. Besides epidemiological estimations, the simulator provides indications on resource gaps or surpluses, and the impact of shortages on public health for each selected region. It allows for a comparative analysis of the effects of resource availability and consequences of different strategies of resource use, which can provide guidance on resource prioritising and/or mobilisation. Simulation results are displayed in various tables and graphs, and can also be easily exported to GIS software to create maps for geographical analysis of the distribution of resources.

CONCLUSIONS

The AsiaFluCap Simulator is freely available software (http://www.cdprg.org) which can be used by policy makers, policy advisors, donors and other stakeholders involved in preparedness for providing evidence based and illustrative information on health care resource capacities during future pandemics. The tool can inform both preparedness plans and simulation exercises and can help increase the general understanding of dynamics in resource capacities during a pandemic. The combination of a mathematical model with multiple resources and the linkage to GIS for creating maps makes the tool unique compared to other available software.

Canine parvovirus in Australia: the role of socio-economic factors in disease clusters

To identify clusters of canine parvoviral related disease occurring in Australia during 2010 and investigate the role of socio-economic factors contributing to these clusters, reported cases of canine parvovirus were extracted from an on-line disease surveillance system. Reported residential postcode was used to locate cases, and clusters were identified using a scan statistic. Cases included in clusters were compared to those not included in such clusters with respect to human socioeconomic factors (postcode area relative socioeconomic disadvantage, economic resources, education and occupation) and dog factors (neuter status, breed, age, gender, vaccination status). During 2010, there were 1187 cases of canine parvovirus reported. Nineteen significant (P<0.05) disease clusters were identified, most commonly located in New South Wales. Eleven (58%) clusters occurred between April and July, and the average cluster length was 5.7 days. All clusters occurred in postcodes with a significantly (P<0.05) greater level of relative socioeconomic disadvantage and a lower rank in education and occupation, and it was noted that clustered cases were less likely to have been neutered (P=0.004). No significant difference (P>0.05) was found between cases reported from cluster postcodes and those not within clusters for dog age, gender, breed or vaccination status (although the latter needs to be interpreted with caution, since vaccination was absent in most of the cases). Further research is required to investigate the apparent association between indicators of poor socioeconomic status and clusters of reported canine parvovirus diseases; however these initial findings may be useful for developing geographically- and temporally-targeted prevention and disease control programs.