Chaotic desynchronization of multistrain diseases

Shifting patterns of dengue three years after Zika virus emergence in Brazil

In 2015, the Zika virus (ZIKV) emerged in Brazil, leading to widespread outbreaks in Latin America. Following this, many countries in these regions reported a significant drop in the circulation of dengue virus (DENV), which resurged in 2018-2019. We examine age-specific incidence data to investigate changes in DENV epidemiology before and after the emergence of ZIKV. We observe that incidence of DENV was concentrated in younger individuals during resurgence compared to 2013-2015. This trend was more pronounced in Brazilian states that had experienced larger ZIKV outbreaks. Using a mathematical model, we show that ZIKV-induced cross-protection alone, often invoked to explain DENV decline across Latin America, cannot explain the observed age-shift without also assuming some form of disease enhancement. Our results suggest that a sudden accumulation of population-level immunity to ZIKV could suppress DENV and reduce the mean age of DENV incidence via both protective and disease-enhancing interactions.

Linking mosquito surveillance to dengue fever through Bayesian mechanistic modeling

Our ability to effectively prevent the transmission of the dengue virus through targeted control of its vector, Aedes aegypti, depends critically on our understanding of the link between mosquito abundance and human disease risk. Mosquito and clinical surveillance data are widely collected, but linking them requires a modeling framework that accounts for the complex non-linear mechanisms involved in transmission. Most critical are the bottleneck in transmission imposed by mosquito lifespan relative to the virus' extrinsic incubation period, and the dynamics of human immunity. We developed a differential equation model of dengue transmission and embedded it in a Bayesian hierarchical framework that allowed us to estimate latent time series of mosquito demographic rates from mosquito trap counts and dengue case reports from the city of Vitória, Brazil. We used the fitted model to explore how the timing of a pulse of adult mosquito control influences its effect on the human disease burden in the following year. We found that control was generally more effective when implemented in periods of relatively low mosquito mortality (when mosquito abundance was also generally low). In particular, control implemented in early September (week 34 of the year) produced the largest reduction in predicted human case reports over the following year. This highlights the potential long-term utility of broad, off-peak-season mosquito control in addition to existing, locally targeted within-season efforts. Further, uncertainty in the effectiveness of control interventions was driven largely by posterior variation in the average mosquito mortality rate (closely tied to total mosquito abundance) with lower mosquito mortality generating systems more vulnerable to control. Broadly, these correlations suggest that mosquito control is most effective in situations in which transmission is already limited by mosquito abundance.

A vector-host model to assess the impact of superinfection exclusion on vaccination strategies using dengue and yellow fever as case studies

Superinfection exclusion is a phenomenon whereby the co-infection of a host with a secondary pathogen is prevented due to a current infection by another closely-related pathogenic strain. We construct a novel vector-host mathematical model for two pathogens that exhibit superinfection exclusion and simultaneously account for vaccination strategies against them. We then derive the conditions under which an endemic disease will prevent the establishment of another through the action of superinfection exclusion and show that vaccination against the endemic strain can enable the previously suppressed strain to invade the population. Through appropriate parameterisation of the model for dengue and yellow fever we find that superinfection exclusion alone is unlikely to explain the absence of yellow fever in many regions where dengue is endemic, and that the rollout of the recently licensed dengue vaccine, Dengvaxia, is unlikely to enable the establishment of Yellow Fever in regions where it has previously been absent.

Challenges in dengue research: A computational perspective

The dengue virus is now the most widespread arbovirus affecting human populations, causing significant economic and social impact in South America and South-East Asia. Increasing urbanization and globalization, coupled with insufficient resources for control, misguided policies or lack of political will, and expansion of its mosquito vectors are some of the reasons why interventions have so far failed to curb this major public health problem. Computational approaches have elucidated on dengue's population dynamics with the aim to provide not only a better understanding of the evolution and epidemiology of the virus but also robust intervention strategies. It is clear, however, that these have been insufficient to address key aspects of dengue's biology, many of which will play a crucial role for the success of future control programmes, including vaccination. Within a multiscale perspective on this biological system, with the aim of linking evolutionary, ecological and epidemiological thinking, as well as to expand on classic modelling assumptions, we here propose, discuss and exemplify a few major computational avenues-real-time computational analysis of genetic data, phylodynamic modelling frameworks, within-host model frameworks and GPU-accelerated computing. We argue that these emerging approaches should offer valuable research opportunities over the coming years, as previously applied and demonstrated in the context of other pathogens.

Optimal control problems of mosquito-borne disease subject to changes in feeding behavior of Aedes mosquitoes

Dengue viruses (DENV) are transmitted to humans by the bite of Aedes mosquitoes. It is known that dengue virus infection in Aedes aegypti female mosquitoes makes a change in the feeding behavior of the infected mosquitoes. In this study, using the forces of infection, we incorporated the effect of changes in the feeding behavior of mosquitoes into the standard vector-borne SIR-SI model. It has been proved that both a single-strain model and a two-strain model exhibit forward bifurcations. Moreover, optimal implementations of control with specific prevention measures for dengue transmission are analyzed. As a result we found that more implementation of controls on the secondary infection of humans should be considered for the behavioral changes in feeding of the infected mosquitoes.

The Impact of the Newly Licensed Dengue Vaccine in Endemic Countries

Background

With approximately 3 billion people at risk of acquiring the infection, dengue fever is now considered the most important mosquito-borne viral disease in the world, with 390 million dengue infections occurring every year, of which 96 million manifest symptoms with any level of disease severity. Treatment of uncomplicated dengue cases is only supportive and severe dengue cases require hospital intensive care. A vaccine now licensed in several countries and developed by Sanofi Pasteur (CYD-TDV, named Dengvaxia), was able to protect, in the first 25 months of the two Phase III, 66% of a subset of 9–16 year old participants. However, a significantly lower efficacy (including negative vaccine efficacy) was noted for children younger than 9 years of age.

Methodology/Principal Findings

Analysis of year 3 results of phase III trials of Dengvaxia suggest high rates of protection of vaccinated partial dengue immunes but high rates of hospitalizations during breakthrough dengue infections of persons who were vaccinated when seronegative, with vaccine appearing to induce enhancing antibodies (ADE). An age structured model was developed based on Sanofi’s recommendation to vaccinate persons age 945 years in dengue endemic countries. The model was used to explore the clinical burden of two vaccination strategies: 1) Vaccinate 4 or 20% of individuals, ages 9–45 years, seropositives and seronegatives, and 2) vaccinate 4 or 20% of individuals, ages 9–45 years, who are dengue immune only.

Conclusions/Significance

Our results show that vaccinating dengue monotypic immune individuals prevents dengue hospitalizations, but at the same time dengue infections of vaccine-sensitized persons increases hospitalizations. When the vaccine is given only to partial immune individuals, after immunological screening of the population, disease burden decreases considerably.

Caused by four antigenically related but distinct serotypes a tetravalent vaccine is needed to protect against the huge burden of dengue disease. Dengvaxia is a vaccine candidate now licensed in several countries for individuals 9–45 years of age living in endemic countries with at least 50% (preferably 70%) of seroprevalence. Modelers from Sanofi Pasteur have predicted that this vaccine has the potential to reduce by about 50% the disease burden within 5 years when 20% of an endemic country population is vaccinated, thus achieving a World Health Organization dengue prevention goal. In this paper, mathematical modeling is used to investigate the impact of the newly licensed dengue vaccine using different scenarios. Our results show that to achieve significant reduction in disease burden, the vaccination program is most effective if it includes only individuals that have been already exposed to at least one dengue virus. Immunological screening of the population prior to vaccination is advised and vaccination strategies must be planned based on epidemiological disease dynamics for each specific endemic region.

Dengue Dynamics and Vaccine Cost-Effectiveness Analysis in the Philippines

Dengue is one of the most problematic vector-borne diseases in the Philippines, with an estimated 842,867 cases resulting in medical costs of $345 million U.S. dollars annually. In December 2015, the first dengue vaccine, known as chimeric yellow fever virus-dengue virus tetravalent dengue vaccine, was approved for use in the Philippines and is given to children 9 years of age. To estimate the cost-effectiveness of dengue vaccination in the Philippines, we developed an age-structured model of dengue transmission and vaccination. Using our model, we compared two vaccination scenarios entailing routine vaccination programs both with and without catch-up vaccination. Our results indicate that the higher the cost of vaccination, the less cost-effective the dengue vaccination program. With the current dengue vaccination program that vaccinates children 9 years of age, dengue vaccination is cost-effective for vaccination costs up to $70 from a health-care perspective and up to $75 from a societal perspective. Under a favorable scenario consisting of 1 year of catch-up vaccinations that target children 9-15 years of age, followed by regular vaccination of 9-year-old children, vaccination is cost-effective at costs up to $72 from a health-care perspective and up to $78 from a societal perspective. In general, dengue vaccination is expected to reduce the incidence of both dengue fever and dengue hemorrhagic fever /dengue shock syndrome. Our results demonstrate that even at relatively low vaccine efficacies, age-targeted vaccination may still be cost-effective provided the vaccination cost is sufficiently low.

The Role of Serotype Interactions and Seasonality in Dengue Model Selection and Control: Insights from a Pattern Matching Approach

The epidemiology of dengue fever is characterized by highly seasonal, multi-annual fluctuations, and the irregular circulation of its four serotypes. It is believed that this behaviour arises from the interplay between environmental drivers and serotype interactions. The exact mechanism, however, is uncertain. Constraining mathematical models to patterns characteristic to dengue epidemiology offers a means for detecting such mechanisms. Here, we used a pattern-oriented modelling (POM) strategy to fit and assess a range of dengue models, driven by combinations of temporary cross protective-immunity, cross-enhancement, and seasonal forcing, on their ability to capture the main characteristics of dengue dynamics. We show that all proposed models reproduce the observed dengue patterns across some part of the parameter space. Which model best supports the dengue dynamics is determined by the level of seasonal forcing. Further, when tertiary and quaternary infections are allowed, the inclusion of temporary cross-immunity alone is strongly supported, but the addition of cross-enhancement markedly reduces the parameter range at which dengue dynamics are produced, irrespective of the strength of seasonal forcing. The implication of these structural uncertainties on predicted vulnerability to control is also discussed. With ever expanding spread of dengue, greater understanding of dengue dynamics and control efforts (e.g. a near-future vaccine introduction) has become critically important. This study highlights the capacity of multi-level pattern-matching modelling approaches to offer an analytic tool for deeper insights into dengue epidemiology and control.

The fluctuations of multi-serotype infectious diseases are often highly irregular and hard to predict. Previous theoretical approaches have attempted to disentangle the drivers that may underlie this behaviour in dengue dynamics with variable success. Here, we examine the role of such drivers using a pattern-oriented modelling (POM) approach. In POM, multiple patterns observed at different scales are used to test a model’s proficiency in capturing real-world dynamics. We examined dengue models with combinations of cross-immunity, cross-enhancement, seasonal fluctuations in the transmission rate, and with sensitivity analyses of asymmetric transmission rates between serotypes as well as the possibility for four subsequent heterologous infections. We demonstrate the ability of POM to model dynamical drivers that have gone unnoticed in single pattern or synthetic likelihood approaches. Further, our results present a determining role of seasonality in the selection and operation of these processes in governing dengue dynamics, in particular when full, heterologous immunity is assumed to occur after a secondary infection. We show that this structural model uncertainty can have important practical significance, as demonstrated by the differences in control efforts required to disrupt transmission. These results highlight the importance of localised model selection and calibration using multiple data-matching, as well as taking explicit account of model uncertainty in predicting and planning control efforts for multi-serotype diseases.

A Framework for Inferring Unobserved Multistrain Epidemic Subpopulations Using Synchronization Dynamics

A new method is proposed to infer unobserved epidemic subpopulations by exploiting the synchronization properties of multistrain epidemic models. A model for dengue fever is driven by simulated data from secondary infective populations. Primary infective populations in the driven system synchronize to the correct values from the driver system. Most hospital cases of dengue are secondary infections, so this method provides a way to deduce unobserved primary infection levels. We derive center manifold equations that relate the driven system to the driver system and thus motivate the use of synchronization to predict unobserved primary infectives. Synchronization stability between primary and secondary infections is demonstrated through numerical measurements of conditional Lyapunov exponents and through time series simulations.

Are we modelling the correct dataset? Minimizing false predictions for dengue fever in Thailand

Models describing dengue epidemics are parametrized on disease incidence data and therefore high-quality data are essential. For Thailand, two different sources of long-term dengue data are available, the hard copy data from 1980 to 2005, where hospital admission cases were notified, and the electronic files, from 2003 to the present, where clinically classified forms of disease, i.e. dengue fever, dengue haemorrhagic fever, and dengue shock syndrome, are notified using separate files. The official dengue notification data, provided by the Bureau of Epidemiology, Ministry of Public Health in Thailand, were cross-checked with dengue data used in recent publications, where an inexact continuous time-series was observed to be consistently used since 2003, affecting considerably the model dynamics and its correct application. In this paper, numerical analysis and simulation techniques giving insights on predictability are performed to show the effects of model parametrization by using different datasets.

Partial cross-enhancement in models for dengue epidemiology

Four distinct serotypes of dengue virus co-circulate in many parts of the world. Antibodies to one serotype prevent infection with the homologous serotype, but may enhance infections with heterologous serotypes. Enhanced secondary infections have been implicated in the majority of severe cases, termed dengue hemorrhagic fever. Conventionally, mathematical models assume that all heterologous secondary infections are subject to enhanced susceptibility or transmissibility. However, empirical data show that only a minority of secondary infections lead to severe disease, which suggests that only a minority of secondary infections are subject to enhancement. We present a new modelling framework in which the population susceptible to secondary infection is split into a group prone to enhanced infection and a group with some degree of cross-protection. We use this framework to re-evaluate the role of enhanced infections in several well known dengue models that exhibit multi-annual epidemiological oscillations. We show that enhancement is unlikely to be driving such oscillations but may be modifying the effects of other drivers.

Complex behaviour in a dengue model with a seasonally varying vector population

In recent decades, dengue fever and dengue haemorrhagic fever have become a substantial public health concern in many subtropical and tropical countries throughout the world. Many of these regions have strong seasonal patterns in rainfall and temperature which are directly linked to the transmission of dengue through the mosquito vector population. Our study focuses on the development and analysis of a strongly seasonally forced, multi-subclass dengue model. This model is a compartment-based system of first-order ordinary differential equations with seasonal forcing in the vector population and also includes host population demographics. Our analysis of this model focuses particularly on the existence of deterministic chaos in regions of the parameter space which potentially hinders application of the model to predict and understand future outbreaks. The numerically efficient 0-1 test for deterministic chaos suggested by Gottwald and Melbourne (2004) [18] is used to analyze the long-term behaviour of the model as an alternative to Lyapunov exponents. Various solutions types were found to exist within the studied parameter range. Most notable are the existence of isola n-cycle solutions before the onset of deterministic chaos. Analysis of the seasonal model with the 0-1 test revealed the existence of three disconnected regions in parameter space where deterministic chaos exists in the single subclass model. Knowledge of these regions and how they relate to the parameters of the model gives greater confidence in the predictive power of the seasonal model.

Breaking the symmetry: immune enhancement increases persistence of dengue viruses in the presence of asymmetric transmission rates

The dengue viruses exist as four antigenically distinct serotypes. These four serotypes co-circulate and interact with each other through multiple immune-mediated mechanisms. Though the majority of previous efforts to understand the transmission dynamics of dengue have assumed identical characteristics for these four serotypes, empirical data suggests that they differ from one another in important ways. Here, we examine dynamics and persistence in models that do not assume symmetry between the dengue viruses. We find that for serotype transmission rates that are only slightly asymmetric, increased transmissibility of secondary infections through immune enhancement increases the persistence of all dengue viruses in opposition to findings in symmetric models. We identify an optimal magnitude of immune enhancement that maximizes the probability of persistence of all four serotypes. In contrast to other pathogen systems where heterogeneity between serotypes in transmissibility facilitates competitive exclusion (Bremmermann and Thieme, 1989), here we find that in the presence of Antibody Dependent Enhancement (ADE) heterogeneity can increase the persistence of multiple serotypes of dengue.

Chaos in a seasonally perturbed SIR model: avian influenza in a seabird colony as a paradigm

Seasonality is a complex force in nature that affects multiple processes in wild animal populations. In particular, seasonal variations in demographic processes may considerably affect the persistence of a pathogen in these populations. Furthermore, it has been long observed in computer simulations that under seasonal perturbations, a host-pathogen system can exhibit complex dynamics, including the transition to chaos, as the magnitude of the seasonal perturbation increases. In this paper, we develop a seasonally perturbed Susceptible-Infected-Recovered model of avian influenza in a seabird colony. Numerical simulations of the model give rise to chaotic recurrent epidemics for parameters that reflect the ecology of avian influenza in a seabird population, thereby providing a case study for chaos in a host- pathogen system. We give a computer-assisted exposition of the existence of chaos in the model using methods that are based on the concept of topological hyperbolicity. Our approach elucidates the geometry of the chaos in the phase space of the model, thereby offering a mechanism for the persistence of the infection. Finally, the methods described in this paper may be immediately extended to other infections and hosts, including humans.

Interactions between serotypes of dengue highlight epidemiological impact of cross-immunity

Dengue, a mosquito-borne virus of humans, infects over 50 million people annually. Infection with any of the four dengue serotypes induces protective immunity to that serotype, but does not confer long-term protection against infection by other serotypes. The immunological interactions between serotypes are of central importance in understanding epidemiological dynamics and anticipating the impact of dengue vaccines. We analysed a 38-year time series with 12 197 serotyped dengue infections from a hospital in Bangkok, Thailand. Using novel mechanistic models to represent different hypothesized immune interactions between serotypes, we found strong evidence that infection with dengue provides substantial short-term cross-protection against other serotypes (approx. 1-3 years). This is the first quantitative evidence that short-term cross-protection exists since human experimental infection studies performed in the 1950s. These findings will impact strategies for designing dengue vaccine studies, future multi-strain modelling efforts, and our understanding of evolutionary pressures in multi-strain disease systems.

The effect of antibody-dependent enhancement, cross immunity, and vector population on the dynamics of dengue fever

Dengue is a major international public health concern and impacts one-third of the world's population. No specific vaccine and treatment are available for this vector-borne disease. There are four similar but distinct serotypes of dengue viruses (DENV). Infection with one serotype affords life-long immunity to that serotype but only temporary partial immunity, or cross immunity (CI), to others. This increases the risk of developing lethal complications upon re-infection, mainly because of the effect of antibody-dependent enhancement (ADE). There have been multiple studies of the dynamic behavior created by the interplay of ADE and CI using mathematical models. However, models in the literature seldom capture the vector population, which we consider important because combating the mosquito vector is the only way to contain dengue transmission in the absence of vaccines. We therefore propose two differential-equation models of dengue fever (DF) with different levels of complexity and details. Our results support the need for ADE to explain the complexity of the epidemiological data.

Synchrony of sylvatic dengue isolations: a multi-host, multi-vector SIR model of dengue virus transmission in Senegal

Isolations of sylvatic dengue-2 virus from mosquitoes, humans and non-human primates in Senegal show synchronized multi-annual dynamics over the past 50 years. Host demography has been shown to directly affect the period between epidemics in other pathogen systems, therefore, one might expect unsynchronized multi-annual cycles occurring in hosts with dramatically different birth rates and life spans. However, in Senegal, we observe a single synchronized eight-year cycle across all vector species, suggesting synchronized dynamics in all vertebrate hosts. In the current study, we aim to explore two specific hypotheses: 1) primates with different demographics will experience outbreaks of dengue at different periodicities when observed as isolated systems, and that coupling of these subsystems through mosquito biting will act to synchronize incidence; and 2) the eight-year periodicity of isolations observed across multiple primate species is the result of long-term cycling in population immunity in the host populations. To test these hypotheses, we develop a multi-host, multi-vector Susceptible, Infected, Removed (SIR) model to explore the effects of coupling multiple host-vector systems of dengue virus transmission through cross-species biting rates. We find that under small amounts of coupling, incidence in the host species synchronize. Long-period multi-annual dynamics are observed only when prevalence in troughs reaches vanishingly small levels (), suggesting that these dynamics are inconsistent with sustained transmission in this setting, but are consistent with local dengue virus extinctions followed by reintroductions. Inclusion of a constant introduction of infectious individuals into the system causes the multi-annual periods to shrink, while the effects of coupling remain the same. Inclusion of a stochastic rate of introduction allows for multi-annual periods at a cost of reduced synchrony. Thus, we conclude that the eight-year period separating amplifications of dengue may be explained by cycling in immunity with stochastic introductions.

Dengue virus has been isolated from mosquitoes, non-human primates and humans in Senegalese jungles for the past 50 years. This sylvatic cycle shows unique transmission dynamics that are unexpected given previous theory and observation: First, the isolations appear to be synchronized across several host and vector species each with different natural histories of infection. Second, the periodicity of the isolations (time between outbreaks) is approximately eight years, much longer than the one or two year period observed in human endemic settings (e.g., Thailand, Brazil). In this paper we develop a multi-host, multi-vector differential equation model to test hypotheses that are potentially consistent with these observations. We find that coupling of separate primate-mosquito pairs through mosquito biting induces synchrony that is robust over a wide range of parameters. We also find that the eight year cycle is not robust to the inclusion of a constant introduction of infection, but is to a stochastic rate of introduction, and thus may be due to cycling of immunity among primates with long-period stochastic introductions. An accurate and thorough understanding of the sylvatic cycle of dengue may allow prediction of epidemics and lessen its impact on humans living in surrounding areas. This knowledge is especially important given the potential for these primate species to act as reservoirs for dengue in post-vaccination scenarios.

Dynamic epidemiological models for dengue transmission: a systematic review of structural approaches

Dengue is a vector-borne disease recognized as the major arbovirose with four immunologically distant dengue serotypes coexisting in many endemic areas. Several mathematical models have been developed to understand the transmission dynamics of dengue, including the role of cross-reactive antibodies for the four different dengue serotypes. We aimed to review deterministic models of dengue transmission, in order to summarize the evolution of insights for, and provided by, such models, and to identify important characteristics for future model development. We identified relevant publications using PubMed and ISI Web of Knowledge, focusing on mathematical deterministic models of dengue transmission. Model assumptions were systematically extracted from each reviewed model structure, and were linked with their underlying epidemiological concepts. After defining common terms in vector-borne disease modelling, we generally categorised fourty-two published models of interest into single serotype and multiserotype models. The multi-serotype models assumed either vector-host or direct host-to-host transmission (ignoring the vector component). For each approach, we discussed the underlying structural and parameter assumptions, threshold behaviour and the projected impact of interventions. In view of the expected availability of dengue vaccines, modelling approaches will increasingly focus on the effectiveness and cost-effectiveness of vaccination options. For this purpose, the level of representation of the vector and host populations seems pivotal. Since vector-host transmission models would be required for projections of combined vaccination and vector control interventions, we advocate their use as most relevant to advice health policy in the future. The limited understanding of the factors which influence dengue transmission as well as limited data availability remain important concerns when applying dengue models to real-world decision problems.

The role of seasonality and import in a minimalistic multi-strain dengue model capturing differences between primary and secondary infections: complex dynamics and its implications for data analysis

In many countries in Asia and South-America dengue fever (DF) and dengue hemorrhagic fever (DHF) has become a substantial public health concern leading to serious social-economic costs. Mathematical models describing the transmission of dengue viruses have focussed on the so-called antibody-dependent enhancement (ADE) effect and temporary cross-immunity trying to explain the irregular behavior of dengue epidemics by analyzing available data. However, no systematic investigation of the possible dynamical structures has been performed so far. Our study focuses on a seasonally forced (non-autonomous) model with temporary cross-immunity and possible secondary infection, motivated by dengue fever epidemiology. The notion of at least two different strains is needed in a minimalistic model to describe differences between primary infections, often asymptomatic, and secondary infection, associated with the severe form of the disease. We extend the previously studied non-seasonal (autonomous) model by adding seasonal forcing, mimicking the vectorial dynamics, and a low import of infected individuals, which is realistic in the dynamics of dengue fever epidemics. A comparative study between three different scenarios (non-seasonal, low seasonal and high seasonal with a low import of infected individuals) is performed. The extended models show complex dynamics and qualitatively a good agreement between empirical DHF monitoring data and the obtained model simulation. We discuss the role of seasonal forcing and the import of infected individuals in such systems, the biological relevance and its implications for the analysis of the available dengue data. At the moment only such minimalistic models have a chance to be qualitatively understood well and eventually tested against existing data. The simplicity of the model (low number of parameters and state variables) offer a promising perspective on parameter values inference from the DHF case notifications.

Models of the impact of dengue vaccines: a review of current research and potential approaches

Vaccination reduces transmission of pathogens directly, by preventing individual infections, and indirectly, by reducing the probability of contact between infected individuals and susceptible ones. The potential combined impact of future dengue vaccines can be estimated using mathematical models of transmission. However, there is considerable uncertainty in the structure of models that accurately represent dengue transmission dynamics. Here, we review models that could be used to assess the impact of future dengue immunization programmes. We also review approaches that have been used to validate and parameterize models. A key parameter of all approaches is the basic reproduction number, R(0), which can be used to determine the critical vaccination fraction to eliminate transmission. We review several methods that have been used to estimate this quantity. Finally, we discuss the characteristics of dengue vaccines that must be estimated to accurately assess their potential impact on dengue virus transmission.

The effects of tertiary and quaternary infections on the epidemiology of dengue

The epidemiology of dengue is characterised by irregular epidemic outbreaks and desynchronised dynamics of its four co-circulating virus serotypes. Whilst infection by one serotype appears to convey life-long protection to homologous infection, it is believed to be a risk factor for severe disease manifestations upon secondary, heterologous infection due to the phenomenon of Antibody-Dependent Enhancement (ADE). Subsequent clinical infections are rarely reported and, since the majority of dengue infections are generally asymptomatic, it is not clear if and to what degree tertiary or quaternary infections contribute to dengue epidemiology. Here we investigate the effect of third and subsequent infections on the transmission dynamics of dengue and show that although the qualitative patterns are largely equivalent, the system more readily exhibits the desynchronised serotype oscillations and multi-annual epidemic outbreaks upon their inclusion. More importantly, permitting third and fourth infections significantly increases the force of infection without resorting to high basic reproductive numbers. Realistic age-prevalent patterns and seroconversion rates are therefore easier reconciled with a low value of dengue's transmission potential if allowing for more than two infections; this should have important consequences for dengue control and intervention measures.

Asymmetry in the presence of migration stabilizes multistrain disease outbreaks

We study the effect of migration between coupled populations, or patches, on the stability properties of multistrain disease dynamics. The epidemic model used in this work displays a Hopf bifurcation to oscillations in a single, well-mixed population. It is shown numerically that migration between two non-identical patches stabilizes the endemic steady state, delaying the onset of large amplitude outbreaks and reducing the total number of infections. This result is motivated by analyzing generic Hopf bifurcations with different frequencies and with diffusive coupling between them. Stabilization of the steady state is again seen, indicating that our observation in the full multistrain model is based on qualitative characteristics of the dynamics rather than on details of the disease model.

Epidemics with multistrain interactions: the interplay between cross immunity and antibody-dependent enhancement

This paper examines the interplay of the effect of cross immunity and antibody-dependent enhancement (ADE) in multistrain diseases. Motivated by dengue fever, we study a model for the spreading of epidemics in a population with multistrain interactions mediated by both partial temporary cross immunity and ADE. Although ADE models have previously been observed to cause chaotic outbreaks, we show analytically that weak cross immunity has a stabilizing effect on the system. That is, the onset of disease fluctuations requires a larger value of ADE with small cross immunity than without. However, strong cross immunity is shown numerically to cause oscillations and chaotic outbreaks even for low values of ADE.

Multiyear climate variability and dengue--El Niño southern oscillation, weather, and dengue incidence in Puerto Rico, Mexico, and Thailand: a longitudinal data analysis

BACKGROUND

The mosquito-borne dengue viruses are a major public health problem throughout the tropical and subtropical regions of the world. Changes in temperature and precipitation have well-defined roles in the transmission cycle and may thus play a role in changing incidence levels. The El Niño Southern Oscillation (ENSO) is a multiyear climate driver of local temperature and precipitation worldwide. Previous studies have reported varying degrees of association between ENSO and dengue incidence.

METHODS AND FINDINGS

We analyzed the relationship between ENSO, local weather, and dengue incidence in Puerto Rico, Mexico, and Thailand using wavelet analysis to identify time- and frequency-specific association. In Puerto Rico, ENSO was transiently associated with temperature and dengue incidence on multiyear scales. However, only local precipitation and not temperature was associated with dengue on multiyear scales. In Thailand, ENSO was associated with both temperature and precipitation. Although precipitation was associated with dengue incidence, the association was nonstationary and likely spurious. In Mexico, no association between any of the variables was observed on the multiyear scale.

CONCLUSIONS

The evidence for a relationship between ENSO, climate, and dengue incidence presented here is weak. While multiyear climate variability may play a role in endemic interannual dengue dynamics, we did not find evidence of a strong, consistent relationship in any of the study areas. The role of ENSO may be obscured by local climate heterogeneity, insufficient data, randomly coincident outbreaks, and other, potentially stronger, intrinsic factors regulating transmission dynamics.

Periodic forcing in a three-level cellular automata model for a vector-transmitted disease

A periodically forced two-dimensional cellular automata model is used to reproduce and analyze the complex spatiotemporal patterns observed in the transmission of vector infectious diseases. The system, which comprises three population levels, is introduced to describe complex features of the dynamics of the vector-transmitted dengue epidemics, known to be very sensitive to seasonal variables. The three coupled levels represent the human, the adult, and immature vector populations. The dynamics includes external seasonality forcing, human and mosquito mobility, and vector control effects. The model parameters, even if bounded to well-defined intervals obtained from reported data, can be selected to reproduce specific epidemic outbursts. In the current study, explicit results are obtained by comparison with actual data retrieved from the time series of dengue epidemics in two cities in Brazil. The results show fluctuations that are not captured by mean-field models. It also reveals the qualitative behavior of the spatiotemporal patterns of the epidemics. In the extreme situation of the absence of external periodic drive, the model predicts a completely distinct long-time evolution. The model is robust in the sense that it is able to reproduce the time series of dengue epidemics of different cities, provided that the forcing term takes into account the local rainfall modulation. Finally, an analysis is provided of the effect of the dependence between epidemics threshold and vector control actions, both in the presence and absence of human mobility factor.

Immunological serotype interactions and their effect on the epidemiological pattern of dengue

Long-term epidemiological data reveal multi-annual fluctuations in the incidence of dengue fever and dengue haemorrhagic fever, as well as complex cyclical behaviour in the dynamics of the four serotypes of the dengue virus. It has previously been proposed that these patterns are due to the phenomenon of the so-called antibody-dependent enhancement (ADE) among dengue serotypes, whereby viral replication is increased during secondary infection with a heterologous serotype; however, recent studies have implied that this positive reinforcement cannot account for the temporal patterns of dengue and that some form of cross-immunity or external forcing is necessary. Here, we show that ADE alone can produce the observed periodicities and desynchronized oscillations of individual serotypes if its effects are decomposed into its two possible manifestations: enhancement of susceptibility to secondary infections and increased transmissibility from individuals suffering from secondary infections. This decomposition not only lowers the level of enhancement necessary for realistic disease patterns but also reduces the risk of stochastic extinction. Furthermore, our analyses reveal a time-lagged correlation between serotype dynamics and disease incidence rates, which could have important implications for understanding the irregular pattern of dengue epidemics.

Local and global effects of climate on dengue transmission in Puerto Rico

The four dengue viruses, the agents of dengue fever and dengue hemorrhagic fever in humans, are transmitted predominantly by the mosquito Aedes aegypti. The abundance and the transmission potential of Ae. aegypti are influenced by temperature and precipitation. While there is strong biological evidence for these effects, empirical studies of the relationship between climate and dengue incidence in human populations are potentially confounded by seasonal covariation and spatial heterogeneity. Using 20 years of data and a statistical approach to control for seasonality, we show a positive and statistically significant association between monthly changes in temperature and precipitation and monthly changes in dengue transmission in Puerto Rico. We also found that the strength of this association varies spatially, that this variation is associated with differences in local climate, and that this relationship is consistent with laboratory studies of the impacts of these factors on vector survival and viral replication. These results suggest the importance of temperature and precipitation in the transmission of dengue viruses and suggest a reason for their spatial heterogeneity. Thus, while dengue transmission may have a general system, its manifestation on a local scale may differ from global expectations.

Dengue viruses are a major health problem throughout the tropical and subtropical regions of the world. Because they are transmitted by mosquitoes that are sensitive to changes in rainfall and temperature, transmission intensity may be regulated by weather and climate. Laboratory studies have shown this to be biologically plausible, but studies of transmission in real-life situations have been inconclusive. Here we demonstrate that increased temperature and rainfall are associated with increased dengue transmission in subsequent months across Puerto Rico. We also show that differences in local climate within Puerto Rico can explain local differences observed in the relationship between weather and dengue transmission. This finding is important because it suggests that the determinants of transmission occur on a local level such that although dengue viruses have a basically universal transmission cycle, changes in temperature or rainfall may have diverse local effects.

Dengue

The four dengue viruses are transmitted in tropical countries that circle the globe. All can cause syndromes that are self-limited or severe. The common severe syndrome--dengue haemorrhagic fever/dengue shock syndrome (DHF/DSS)--is characterised by sudden vascular permeability generated by cytokines released when T cells attack dengue-infected cells. Dengue 1 virus became prevalent in Hawaii where it was transmitted by Aedes albopictus, producing a classic virgin soil epidemic, with clinical disease seen largely in adults. In Cuba and Singapore, sequential dengue infections at long intervals produced unusually severe disease in adults. Evidence suggests that enhancing and cross-reactive neutralising antibodies regulate dengue epidemics and disease severity. Classic DHF/DSS arises during initial dengue infections in infants with low circulating amounts of maternal dengue antibodies, an observation that precludes an exclusive causal role for secondary T-cell responses. Here, I review and discuss data on clinical diagnosis and pathophysiology of vascular permeability and coagulopathy, parenteral treatment of DHF/DSS, and new laboratory tests.

Using dimension reduction to improve outbreak predictability of multistrain diseases

Multistrain diseases have multiple distinct coexisting serotypes (strains). For some diseases, such as dengue fever, the serotypes interact by antibody-dependent enhancement (ADE), in which infection with a single serotype is asymptomatic, but contact with a second serotype leads to higher viral load and greater infectivity. We present and analyze a dynamic compartmental model for multiple serotypes exhibiting ADE. Using center manifold techniques, we show how the dynamics rapidly collapses to a lower dimensional system. Using the constructed reduced model, we can explain previously observed synchrony between certain classes of primary and secondary infectives (Schwartz et al. in Phys Rev E 72:066201, 2005). Additionally, we show numerically that the center manifold equations apply even to noisy systems. Both deterministic and stochastic versions of the model enable prediction of asymptomatic individuals that are difficult to track during an epidemic. We also show how this technique may be applicable to other multistrain disease models, such as those with cross-immunity.

Instabilities in multiserotype disease models with antibody-dependent enhancement

This paper investigates the complex dynamics induced by antibody-dependent enhancement (ADE) in multiserotype disease models. ADE is the increase in viral growth rate in the presence of immunity due to a previous infection of a different serotype. The increased viral growth rate is thought to increase the infectivity of the secondary infectious class. In our models, ADE induces the onset of oscillations without external forcing. The oscillations in the infectious classes represent outbreaks of the disease. In this paper, we derive approximations of the ADE parameter needed to induce oscillations and analyze the associated bifurcations that separate the types of oscillations. We then investigate the stability of these dynamics by adding stochastic perturbations to the model. We also present a preliminary analysis of the effect of a single serotype vaccination in the model.

Dynamic effects of antibody-dependent enhancement on the fitness of viruses

Antibody-dependent enhancement (ADE), a phenomenon in which viral replication is increased rather than decreased by immune sera, has been observed in vitro for a large number of viruses of public health importance, including flaviviruses, coronaviruses, and retroviruses. The most striking in vivo example of ADE in humans is dengue hemorrhagic fever, a disease in which ADE is thought to increase the severity of clinical manifestations of dengue virus infection by increasing virus replication. We examine the epidemiological impact of ADE on the prevalence and persistence of viral serotypes. Using a dynamical system model of n cocirculating dengue serotypes, we find that ADE may provide a competitive advantage to those serotypes that undergo enhancement compared with those that do not, and that this advantage increases with increasing numbers of cocirculating serotypes. Paradoxically, there are limits to the selective advantage provided by increasing levels of ADE, because greater levels of enhancement induce large amplitude oscillations in incidence of all dengue virus infections, threatening the persistence of both the enhanced and nonenhanced serotypes. Although the models presented here are specifically designed for dengue, our results are applicable to any epidemiological system in which partial immunity increases pathogen replication rates. Our results suggest that enhancement is most advantageous in settings where multiple serotypes circulate and where a large host population is available to support pathogen persistence during the deep troughs of ADE-induced large amplitude oscillations of virus replication.