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

Impact of periodic vaccination in SEIRS seasonal model

We study three different strategies of vaccination in an SEIRS (Susceptible-Exposed-Infected-Recovered-Susceptible) seasonal forced model, which are (i) continuous vaccination; (ii) periodic short-time localized vaccination, and (iii) periodic pulsed width campaign. Considering the first strategy, we obtain an expression for the basic reproduction number and infer a minimum vaccination rate necessary to ensure the stability of the disease-free equilibrium (DFE) solution. In the second strategy, short duration pulses are added to a constant baseline vaccination rate. The pulse is applied according to the seasonal forcing phases. The best outcome is obtained by locating intensive immunization at inflection of the transmissivity curve. Therefore, a vaccination rate of 44.4% of susceptible individuals is enough to ensure DFE. For the third vaccination proposal, additionally to the amplitude, the pulses have a prolonged time width. We obtain a non-linear relationship between vaccination rates and the duration of the campaign. Our simulations show that the baseline rates, as well as the pulse duration, can substantially improve the vaccination campaign effectiveness. These findings are in agreement with our analytical expression. We show a relationship between the vaccination parameters and the accumulated number of infected individuals, over the years, and show the relevance of the immunization campaign annual reaching for controlling the infection spreading. Regarding the dynamical behavior of the model, our simulations show that chaotic and periodic solutions as well as bi-stable regions depend on the vaccination parameters range.

Effects of boosting and waning in highly exposed populations on dengue epidemic dynamics

Sequential infection with multiple dengue virus (DENV) serotypes is thought to induce enduring protection against dengue disease. However, long-term antibody waning has been observed after repeated DENV infection. Here, we provide evidence that highly immune Nicaraguan children and adults (n = 4478) experience boosting and waning of antibodies during and after major Zika and dengue epidemics. We develop a susceptible-infected-recovered-susceptible (SIRS-type) model that tracks immunity by titer rather than number of infections to show that boosts in highly immune individuals can contribute to herd immunity, delaying their susceptibility to transmissible infection. In contrast, our model of lifelong immunity in highly immune individuals, as previously assumed, results in complete disease eradication after introduction. Periodic epidemics under this scenario can only be sustained with a constant influx of infected individuals into the population or a high basic reproductive number. We also find that Zika virus infection can boost DENV immunity and produce delays and then surges in dengue epidemics, as observed with real epidemiological data. This work provides insight into factors shaping periodicity in dengue incidence and may inform vaccine efforts to maintain population immunity.

Temporary Cross-Immunity as a Plausible Driver of Asynchronous Cycles of Dengue Serotypes

Many infectious diseases exist as multiple variants, with interactions between variants potentially driving epidemiological dynamics. These diseases include dengue, which infects hundreds of millions of people every year and exhibits complex multi-serotype dynamics. Antibodies produced in response to primary infection by one of the four dengue serotypes can produce a period of temporary cross-immunity (TCI) to infection by other serotypes. After this period, the remaining antibodies can facilitate the entry of heterologous serotypes into target cells, thus enhancing severity of secondary infection by a heterologous serotype. This represents antibody-dependent enhancement (ADE). In this study, we analyze an epidemiological model to provide novel insights into the importance of TCI and ADE in producing cyclic outbreaks of dengue serotypes. Our analyses reveal that without TCI, such cyclic outbreaks are synchronous across serotypes and only occur when ADE produces high transmission rates. In contrast, the presence of TCI allows asynchronous cycles of serotypes by inducing a time lag between recovery from primary infection by one serotype and secondary infection by another, with such cycles able to occur without ADE. Our results suggest that TCI is a fundamental driver of asynchronous cycles of dengue serotypes and possibly other multi-variant diseases.

Fractal and fractional SIS model for syphilis data

This work studies the SIS model extended by fractional and fractal derivatives. We obtain explicit solutions for the standard and fractal formulations; for the fractional case, we study numerical solutions. As a real data example, we consider the Brazilian syphilis data from 2011 to 2021. We fit the data by considering the three variations of the model. Our fit suggests a recovery period of 11.6 days and a reproduction ratio (R0) equal to 6.5. By calculating the correlation coefficient (r) between the real data and the theoretical points, our results suggest that the fractal model presents a higher r compared to the standard or fractional case. The fractal formulation is improved when two different fractal orders with distinguishing weights are considered. This modification in the model provides a better description of the data and improves the correlation coefficient.

Assessing the impact of serostatus-dependent immunization on mitigating the spread of dengue virus

Dengue is the most rapidly spreading mosquito-borne disease that poses great threats to public health. We propose a compartmental model with primary and secondary infection and targeted vaccination to assess the impact of serostatus-dependent immunization on mitigating the spread of dengue virus. We derive the basic reproduction number and investigate the stability and bifurcations of the disease-free equilibrium and endemic equilibria. The existence of a backward bifurcation is proved and is used to explain the threshold dynamics of the transmission. We also carry out numerical simulations and present bifurcation diagrams to reveal rich dynamics of the model such as bi-stability of the equilibria, limit cycles, and chaos. We prove the uniform persistence and global stability of the model. Sensitivity analysis suggests that mosquito control and protection from mosquito bites are still the key measures of controlling the spread of dengue virus, though serostatus-dependent immunization is implemented. Our findings provide insightful information for public health in mitigating dengue epidemics through vaccination.

Using compartmental models and Particle Swarm Optimization to assess Dengue basic reproduction number R 0 for the Republic of Panama in the 1999-2022 period

Nowadays, the ability to make data-driven decisions in public health is of utmost importance. To achieve this, it is necessary for modelers to comprehend the impact of models on the future state of healthcare systems. Compartmental models are a valuable tool for making informed epidemiological decisions, and the proper parameterization of these models is crucial for analyzing epidemiological events. This work evaluated the use of compartmental models in conjunction with Particle Swarm Optimization (PSO) to determine optimal solutions and understand the dynamics of Dengue epidemics. The focus was on calculating and evaluating the rate of case reproduction, R 0 , for the Republic of Panama. Three compartmental models were compared: Susceptible-Infected-Recovered (SIR), Susceptible-Exposed-Infected-Recovered (SEIR), and Susceptible-Infected-Recovered Human-Susceptible-Infected Vector (SIR Human-SI Vector, SIR-SI). The models were informed by demographic data and Dengue incidence in the Republic of Panama between 1999 and 2022, and the susceptible population was analyzed. The SIR, SEIR, and SIR-SI models successfully provided R 0 estimates ranging from 1.09 to 1.74. This study provides, to the best of our understanding, the first calculation of R 0 for Dengue outbreaks in the Republic of Panama.

Comparing Short-Term Univariate and Multivariate Time-Series Forecasting Models in Infectious Disease Outbreak

Predicting infectious disease outbreak impacts on population, healthcare resources and economics and has received a special academic focus during coronavirus (COVID-19) pandemic. Focus on human disease outbreak prediction techniques in current literature, Marques et al. (Predictive models for decision support in the COVID-19 crisis. Springer, Switzerland, 2021) state that there are four main methods to address forecasting problem: compartmental models, classic statistical models, space-state models and machine learning models. We adopt their framework to compare our research with previous works. Besides being divided by methods, forecasting problems can also be divided by the number of variables that are considered to make predictions. Considering this number of variables, forecasting problems can be classified as univariate, causal and multivariate models. Multivariate approaches have been applied in less than 10% of research found. This research is the first attempt to evaluate, over real time-series data of 3 different countries with univariate and multivariate methods to provide a short-term prediction. In literature we found no research with that scope and aim. A comparison of univariate and multivariate methods has been conducted and we concluded that besides the strong potential of multivariate methods, in our research univariate models presented best results in almost all regions' predictions.

Ecological and evolutionary dynamics of multi-strain RNA viruses

Potential interactions among co-circulating viral strains in host populations are often overlooked in the study of virus transmission. However, these interactions probably shape transmission dynamics by influencing host immune responses or altering the relative fitness among co-circulating strains. In this Review, we describe multi-strain dynamics from ecological and evolutionary perspectives, outline scales in which multi-strain dynamics occur and summarize important immunological, phylogenetic and mathematical modelling approaches used to quantify interactions among strains. We also discuss how host-pathogen interactions influence the co-circulation of pathogens. Finally, we highlight outstanding questions and knowledge gaps in the current theory and study of ecological and evolutionary dynamics of multi-strain viruses.

Mathematical models for dengue fever epidemiology: A 10-year systematic review

Mathematical models have a long history in epidemiological research, and as the COVID-19 pandemic progressed, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease spreading. Mathematical models describing dengue fever epidemiological dynamics are found back from 1970. Dengue fever is a viral mosquito-borne infection caused by four antigenically related but distinct serotypes (DENV-1 to DENV-4). With 2.5 billion people at risk of acquiring the infection, it is a major international public health concern. Although most of the cases are asymptomatic or mild, the disease immunological response is complex, with severe disease linked to the antibody-dependent enhancement (ADE) - a disease augmentation phenomenon where pre-existing antibodies to previous dengue infection do not neutralize but rather enhance the new infection. Here, we present a 10-year systematic review on mathematical models for dengue fever epidemiology. Specifically, we review multi-strain frameworks describing host-to-host and vector-host transmission models and within-host models describing viral replication and the respective immune response. Following a detailed literature search in standard scientific databases, different mathematical models in terms of their scope, analytical approach and structural form, including model validation and parameter estimation using empirical data, are described and analyzed. Aiming to identify a consensus on infectious diseases modeling aspects that can contribute to public health authorities for disease control, we revise the current understanding of epidemiological and immunological factors influencing the transmission dynamics of dengue. This review provide insights on general features to be considered to model aspects of real-world public health problems, such as the current epidemiological scenario we are living in.

Complexity of host-vector dynamics in a two-strain dengue model

We introduce a compartmental host-vector model for dengue with two viral strains, temporary cross-immunity for the hosts, and possible secondary infections. We study the conditions on existence of endemic equilibria where one strain displaces the other or the two virus strains co-exist. Since the host and vector epidemiology follow different time scales, the model is described as a slow-fast system. We use the geometric singular perturbation technique to reduce the model dimension. We compare the behaviour of the full model with that of the model with a quasi-steady approximation for the vector dynamics. We also perform numerical bifurcation analysis with parameter values from the literature and compare the bifurcation structure to that of previous two-strain host-only models.

Modeling Dengue Immune Responses Mediated by Antibodies: A Qualitative Study

Simple Summary

With more than one-third of the world population at risk of acquiring the disease, dengue fever is a major public health problem. Caused by four antigenically distinct but related serotypes, disease severity is associated with the immunological status of the individual, seronegative or seropositive, prior to a natural dengue infection. While a primary natural dengue infection is often asymptomatic or mild, individuals experiencing a secondary dengue infection with a heterologous serotype have higher risk of developing the severe form of the disease, linked to the antibody-dependent enhancement (ADE) process. We develop a modeling framework to describe the dengue immune responses mediated by antibodies. Our model framework can describe qualitatively the dynamic of the viral load and antibodies production for scenarios of primary and secondary infections, as found in the empirical immunology literature. Studies such as the one described here serve as a baseline to further model extensions. Future refinements of our framework will be of use to evaluate the impact of imperfect dengue vaccines.

Abstract

Dengue fever is a viral mosquito-borne infection and a major international public health concern. With 2.5 billion people at risk of acquiring the infection around the world, disease severity is influenced by the immunological status of the individual, seronegative or seropositive, prior to natural infection. Caused by four antigenically related but distinct serotypes, DENV-1 to DENV-4, infection by one serotype confers life-long immunity to that serotype and a period of temporary cross-immunity (TCI) to other serotypes. The clinical response on exposure to a second serotype is complex with the so-called antibody-dependent enhancement (ADE) process, a disease augmentation phenomenon when pre-existing antibodies to previous dengue infection do not neutralize but rather enhance the new infection, used to explain the etiology of severe disease. In this paper, we present a minimalistic mathematical model framework developed to describe qualitatively the dengue immunological response mediated by antibodies. Three models are analyzed and compared: (i) primary dengue infection, (ii) secondary dengue infection with the same (homologous) dengue virus and (iii) secondary dengue infection with a different (heterologous) dengue virus. We explore the features of viral replication, antibody production and infection clearance over time. The model is developed based on body cells and free virus interactions resulting in infected cells activating antibody production. Our mathematical results are qualitatively similar to the ones described in the empiric immunology literature, providing insights into the immunopathogenesis of severe disease. Results presented here are of use for future research directions to evaluate the impact of dengue vaccines.

Migration rate estimation in an epidemic network

Most of the recent epidemic outbreaks in the world have as a trigger, a strong migratory component as has been evident in the recent Covid-19 pandemic. In this work we address the problem of migration of human populations and its effect on pathogen reinfections in the case of Dengue, using a Markov-chain susceptible-infected-susceptible (SIS) metapopulation model over a network. Our model postulates a general contact rate that represents a local measure of several factors: the population size of infected hosts that arrive at a given location as a function of total population size, the current incidence at neighboring locations, and the connectivity of the network where the disease spreads. This parameter can be interpreted as an indicator of outbreak risk at a given location. This parameter is tied to the fraction of individuals that move across boundaries (migration). To illustrate our model capabilities, we estimate from epidemic Dengue data in Mexico the dynamics of migration at a regional scale incorporating climate variability represented by an index based on precipitation data.

The effect of demographic and environmental variability on disease outbreak for a dengue model with a seasonally varying vector population

Seasonal changes in temperature, humidity, and rainfall affect vector survival and emergence of mosquitoes and thus impact the dynamics of vector-borne disease outbreaks. Recent studies of deterministic and stochastic epidemic models with periodic environments have shown that the average basic reproduction number is not sufficient to predict an outbreak. We extend these studies to time-nonhomogeneous stochastic dengue models with demographic variability wherein the adult vectors emerge from the larval stage vary periodically. The combined effects of variability and periodicity provide a better understanding of the risk of dengue outbreaks. A multitype branching process approximation of the stochastic dengue model near the disease-free periodic solution is used to calculate the probability of a disease outbreak. The approximation follows from the solution of a system of differential equations derived from the backward Kolmogorov differential equation. This approximation shows that the risk of a disease outbreak is also periodic and depends on the particular time and the number of the initial infected individuals. Numerical examples are explored to demonstrate that the estimates of the probability of an outbreak from that of branching process approximations agree well with that of the continuous-time Markov chain. In addition, we propose a simple stochastic model to account for the effects of environmental variability on the emergence of adult vectors from the larval stage.

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.

Modelling COVID 19 in the Basque Country from introduction to control measure response

In March 2020, a multidisciplinary task force (so-called Basque Modelling Task Force, BMTF) was created to assist the Basque health managers and Government during the COVID-19 responses. BMTF is a modelling team, working on different approaches, including stochastic processes, statistical methods and artificial intelligence. Here we describe the efforts and challenges to develop a flexible modeling framework able to describe the dynamics observed for the tested positive cases, including the modelling development steps. The results obtained by a new stochastic SHARUCD model framework are presented. Our models differentiate mild and asymptomatic from severe infections prone to be hospitalized and were able to predict the course of the epidemic, providing important projections on the national health system's necessities during the increased population demand on hospital admissions. Short and longer-term predictions were tested with good results adjusted to the available epidemiological data. We have shown that the partial lockdown measures were effective and enough to slow down disease transmission in the Basque Country. The growth rate [Formula: see text] was calculated from the model and from the data and the implications for the reproduction ratio r are shown. The analysis of the growth rates from the data led to improved model versions describing after the exponential phase also the new information obtained during the phase of response to the control measures. This framework is now being used to monitor disease transmission while the country lockdown was gradually lifted, with insights to specific programs for a general policy of "social distancing" and home quarantining.

Reproduction ratio and growth rates: Measures for an unfolding pandemic

The initial exponential growth rate of an epidemic is an important measure that follows directly from data at hand, commonly used to infer the basic reproduction number. As the growth rates λ(t) of tested positive COVID-19 cases have crossed the threshold in many countries, with negative numbers as surrogate for disease transmission deceleration, lockdowns lifting are linked to the behavior of the momentary reproduction numbers r(t), often called R₀. Important to note that this concept alone can be easily misinterpreted as it is bound to many internal assumptions of the underlying model and significantly affected by the assumed recovery period. Here we present our experience, as part of the Basque Country Modeling Task Force (BMTF), in monitoring the development of the COVID-19 epidemic, by considering not only the behaviour of r(t) estimated for the new tested positive cases—significantly affected by the increased testing capacities, but also the momentary growth rates for hospitalizations, ICU admissions, deceased and recovered cases, in assisting the Basque Health Managers and the Basque Government during the lockdown lifting measures. Two different data sets, collected and then refined during the COVID-19 responses, are used as an exercise to estimate the momentary growth rates and reproduction numbers over time in the Basque Country, and the implications of using those concepts to make decisions about easing lockdown and relaxing social distancing measures are discussed. These results are potentially helpful for task forces around the globe which are now struggling to provide real scientific advice for health managers and governments while the lockdown measures are relaxed.

Climatological, virological and sociological drivers of current and projected dengue fever outbreak dynamics in Sri Lanka

The largest ever Sri Lankan dengue outbreak of 2017 provides an opportunity for investigating the relative contributions of climatological, epidemiological and sociological drivers on the epidemic patterns of this clinically important vector-borne disease. To do so, we develop a climatologically driven disease transmission framework for dengue virus using spatially resolved temperature and precipitation data as well as the time-series susceptible-infected-recovered (SIR) model. From this framework, we first demonstrate that the distinct climatological patterns encountered across the island play an important role in establishing the typical yearly temporal dynamics of dengue, but alone are unable to account for the epidemic case numbers observed in Sri Lanka during 2017. Using a simplified two-strain SIR model, we demonstrate that the re-introduction of a dengue virus serotype that had been largely absent from the island in previous years may have played an important role in driving the epidemic, and provide a discussion of the possible roles for extreme weather events and human mobility patterns on the outbreak dynamics. Lastly, we provide estimates for the future burden of dengue across Sri Lanka using the Coupled Model Intercomparison Phase 5 climate projections. Critically, we demonstrate that climatological and serological factors can act synergistically to yield greater projected case numbers than would be expected from the presence of a single driver alone. Altogether, this work provides a holistic framework for teasing apart and analysing the various complex drivers of vector-borne disease outbreak dynamics.

Forecasting dengue and influenza incidences using a sparse representation of Google trends, electronic health records, and time series data

Dengue and influenza-like illness (ILI) are two of the leading causes of viral infection in the world and it is estimated that more than half the world’s population is at risk for developing these infections. It is therefore important to develop accurate methods for forecasting dengue and ILI incidences. Since data from multiple sources (such as dengue and ILI case counts, electronic health records and frequency of multiple internet search terms from Google Trends) can improve forecasts, standard time series analysis methods are inadequate to estimate all the parameter values from the limited amount of data available if we use multiple sources. In this paper, we use a computationally efficient implementation of the known variable selection method that we call the Autoregressive Likelihood Ratio (ARLR) method. This method combines sparse representation of time series data, electronic health records data (for ILI) and Google Trends data to forecast dengue and ILI incidences. This sparse representation method uses an algorithm that maximizes an appropriate likelihood ratio at every step. Using numerical experiments, we demonstrate that our method recovers the underlying sparse model much more accurately than the lasso method. We apply our method to dengue case count data from five countries/states: Brazil, Mexico, Singapore, Taiwan, and Thailand and to ILI case count data from the United States. Numerical experiments show that our method outperforms existing time series forecasting methods in forecasting the dengue and ILI case counts. In particular, our method gives a 18 percent forecast error reduction over a leading method that also uses data from multiple sources. It also performs better than other methods in predicting the peak value of the case count and the peak time.

Dengue and influenza-like illness (ILI) are leading causes of viral infection in the world and hence it is important to develop accurate methods for forecasting their incidence. We use Autoregressive Likelihood Ratio method, which is a computationally efficient implementation of the variable selection method, in order to obtain a sparse (non-lasso) representation of time series, Google Trends and electronic health records (for ILI) data. This method is used to forecast dengue incidence in five countries/states and ILI incidence in USA. We show that this method outperforms existing time series methods in forecasting these diseases. The method is general and can also be used to forecast other diseases.

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.

Optimal control of a multi-patch Dengue model under the influence of Wolbachia bacterium

In this work, a multi-patch model for dengue transmission dynamics including the bacterium Wolbachia is studied and by that the control efforts to minimize the disease spread by host and vector control are investigated. The multi-patch system models the host movement within the patches which coupled via a residence-time budgeting matrix P. Numerical results confirm that the control mechanism embedded in incidence rates of the disease transmission, effectively reduce the spread of the disease.

Comparison of stochastic and deterministic frameworks in dengue modelling

We perform estimations of compartment models for dengue transmission in rural Cambodia with increasing complexity regarding both model structure and the account for stochasticity. On the one hand, we successively account for three embedded sources of stochasticity: observation noise, demographic variability and environmental hazard. On the other hand, complexity in the model structure is increased by introducing vector-borne transmission, explicit asymptomatic infections and interacting virus serotypes. Using two sources of case data from dengue epidemics in Kampong Cham (Cambodia), models are estimated in the bayesian framework, with Markov Chain Monte Carlo and Particle Markov Chain Monte Carlo. We highlight the advantages and drawbacks of the different formulations in a practical setting. Although in this case the deterministic models provide a good approximation of the mean trajectory for a low computational cost, the stochastic frameworks better reflect and account for parameter and simulation uncertainty.

Non-linear Dynamics of Two-Patch Model Incorporating Secondary Dengue Infection

In this paper, the impact of human migration on the dynamics of dengue epidemic has been discussed. The vector-host model considers two patches with different dengue serotype in each patch. The model considers the constant rate of migration in susceptible and recovered class from one patch to other. Recovered migrants from prior infection are exposed to secondary infection in the patch where different serotype is present. The basic reproduction number is computed and analyzed in terms of migration parameters. The model is analyzed for the existence and local stability of various equilibrium states in terms of migration parameters. The numerical simulations for the choice of relevant data from literature have been performed to verify analytical results and to further explore the dynamics of the system. The sensitivity analysis of basic reproduction number with respect to migration parameters is carried out. It is found that immigration in a patch increases the basic reproduction in respective patch and vice-versa. The basic reproduction number has been estimated for the two states of Brazil which verifies the occurrence of severe epidemic in one of the states of Brazil.

Advances in using Internet searches to track dengue

Dengue is a mosquito-borne disease that threatens over half of the world’s population. Despite being endemic to more than 100 countries, government-led efforts and tools for timely identification and tracking of new infections are still lacking in many affected areas. Multiple methodologies that leverage the use of Internet-based data sources have been proposed as a way to complement dengue surveillance efforts. Among these, dengue-related Google search trends have been shown to correlate with dengue activity. We extend a methodological framework, initially proposed and validated for flu surveillance, to produce near real-time estimates of dengue cases in five countries/states: Mexico, Brazil, Thailand, Singapore and Taiwan. Our result shows that our modeling framework can be used to improve the tracking of dengue activity in multiple locations around the world.

As communicable diseases spread in our societies, people frequently turn to the Internet to search for medical information. In recent years, multiple research teams have investigated how to utilize Internet users’ search activity to track infectious diseases around our planet. In this article, we show that a methodology, originally developed to track flu in the US, can be extended to improve dengue surveillance in multiple countries/states where dengue has been observed in the last several years. Our result suggests that our methodology performs best in dengue-endemic areas with high number of yearly cases and with sustained seasonal incidence.

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.

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.

Exploring the dynamics of respiratory syncytial virus (RSV) transmission in children

Respiratory syncytial virus (RSV) is the main cause of lower respiratory tract infections in children. Whilst highly seasonal, RSV dynamics can have either one-year (annual) or two-year (biennial) cycles. Furthermore, some countries show a 'delayed biennial' pattern, where the epidemic peak in low incidence years is delayed. We develop a compartmental model for RSV infection, driven by a seasonal forcing function, and conduct parameter space and bifurcation analyses to document parameter ranges that give rise to these different seasonal patterns. The model is sensitive to the birth rate, transmission rate, and seasonality parameters, and can replicate RSV dynamics observed in different countries. The seasonality parameter must exceed a threshold for the model to produce biennial cycles. Intermediate values of the birth rate produce the greatest delay in these biennial cycles, while the model reverts to annual cycles if the duration of immunity is too short. Finally, the existence of period doubling and period halving bifurcations suggests robust model dynamics, in agreement with the known regularity of RSV outbreaks. These findings help explain observed RSV data, such as regular biennial dynamics in Western Australia, and delayed biennial dynamics in Finland. From a public health perspective, our findings provide insight into the drivers of RSV transmission, and a foundation for exploring RSV interventions.

Carnival or football, is there a real risk for acquiring dengue fever in Brazil during holidays seasons?

More than 600,000 football fans, coming from all over the world, were expected to visit Brazil during the FIFA World Cup 2014. International travel can become a public health problem when the visitors start to become sick, needing medical intervention and eventually hospitalization. The occurrence of dengue fever infections in Brazil is persistent and has been increasing since the 1980s, and the health authorities were expected to take preventive measures and to warn the visitors about the risks during the tournament period. Before the World Cup started, studies have been published stating that dengue could be a significant problem in some of the Brazilian cities hosting the games. These conclusions were taken after a brief observation of the available data, analyzing its mean and standard deviation only, or based on seasonal climate forecasts, causing alarm for the world cup in Brazil. Here, with a more careful data analysis, we show that the seasonality of the disease plays a major role in dengue transmission. The density of dengue cases in Brazil is residual during winter in the Southern hemisphere (mid June to mid September) and the fans of football were not likely to get dengue during the tournament period.

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.

Dynamical crises, multistability and the influence of the duration of immunity in a seasonally-forced model of disease transmission

BACKGROUND

Highly successful strategies to make populations more resilient to infectious diseases, such as childhood vaccinations programs, may nonetheless lead to unpredictable outcomes due to the interplay between seasonal variations in transmission and a population's immune status.

METHODS

Motivated by the study of diseases such as pertussis we introduce a seasonally-forced susceptible-infectious-recovered model of disease transmission with waning and boosting of immunity. We study the system's dynamical properties using a combination of numerical simulations and bifurcation techniques, paying particular attention to the properties of the initial condition space.

RESULTS

We find that highly unpredictable behaviour can be triggered by changes in biologically relevant model parameters such as the duration of immunity. In the particular system we analyse--used in the literature to study pertussis dynamics--we identify the presence of an initial-condition landscape containing three coexisting attractors. The system's response to interventions which perturb population immunity (e.g. vaccination "catch-up" campaigns) is therefore difficult to predict.

CONCLUSION

Given the increasing use of models to inform policy decisions regarding vaccine introduction and scheduling and infectious diseases intervention policy more generally, our findings highlight the importance of thoroughly investigating the dynamical properties of those models to identify key areas of uncertainty. Our findings suggest that the often stated tension between capturing biological complexity and utilising mathematically simple models is perhaps more nuanced than generally suggested. Simple dynamical models, particularly those which include forcing terms, can give rise to incredibly complex behaviour.

The dynamical consequences of seasonal forcing, immune boosting and demographic change in a model of disease transmission

The impact of seasonal effects on the time course of an infectious disease can be dramatic. Seasonal fluctuations in the transmission rate for an infectious disease are known mathematically to induce cyclical behaviour and drive the onset of multistable and chaotic dynamics. These properties of forced dynamical systems have previously been used to explain observed changes in the period of outbreaks of infections such as measles, varicella (chickenpox), rubella and pertussis (whooping cough). Here, we examine in detail the dynamical properties of a seasonally forced extension of a model of infection previously used to study pertussis. The model is novel in that it includes a non-linear feedback term capturing the interaction between exposure and the duration of protection against re-infection. We show that the presence of limit cycles and multistability in the unforced system give rise to complex and intricate behaviour as seasonal forcing is introduced. Through a mixture of numerical simulation and bifurcation analysis, we identify and explain the origins of chaotic regions of parameter space. Furthermore, we identify regions where saddle node lines and period-doubling cascades of different orbital periods overlap, suggesting that the system is particularly sensitive to small perturbations in its parameters and prone to multistable behaviour. From a public health point of view - framed through the 'demographic transition' whereby a population׳s birth rate drops over time (and life-expectancy commensurately increases) - we argue that even weak levels of seasonal-forcing and immune boosting may contribute to the myriad of complex and unexpected epidemiological behaviours observed for diseases such as pertussis. Our approach helps to contextualise these epidemiological observations and provides guidance on how to consider the potential impact of vaccination programs.

Prediction of high incidence of dengue in the Philippines

Background

Accurate prediction of dengue incidence levels weeks in advance of an outbreak may reduce the morbidity and mortality associated with this neglected disease. Therefore, models were developed to predict high and low dengue incidence in order to provide timely forewarnings in the Philippines.

Methods

Model inputs were chosen based on studies indicating variables that may impact dengue incidence. The method first uses Fuzzy Association Rule Mining techniques to extract association rules from these historical epidemiological, environmental, and socio-economic data, as well as climate data indicating future weather patterns. Selection criteria were used to choose a subset of these rules for a classifier, thereby generating a Prediction Model. The models predicted high or low incidence of dengue in a Philippines province four weeks in advance. The threshold between high and low was determined relative to historical incidence data.

Principal Findings

Model accuracy is described by Positive Predictive Value (PPV), Negative Predictive Value (NPV), Sensitivity, and Specificity computed on test data not previously used to develop the model. Selecting a model using the F_0.5 measure, which gives PPV more importance than Sensitivity, gave these results: PPV = 0.780, NPV = 0.938, Sensitivity = 0.547, Specificity = 0.978. Using the F₃ measure, which gives Sensitivity more importance than PPV, the selected model had PPV = 0.778, NPV = 0.948, Sensitivity = 0.627, Specificity = 0.974. The decision as to which model has greater utility depends on how the predictions will be used in a particular situation.

Conclusions

This method builds prediction models for future dengue incidence in the Philippines and is capable of being modified for use in different situations; for diseases other than dengue; and for regions beyond the Philippines. The Philippines dengue prediction models predicted high or low incidence of dengue four weeks in advance of an outbreak with high accuracy, as measured by PPV, NPV, Sensitivity, and Specificity.

A largely automated methodology is described for creating models that use past and recent data to predict dengue incidence levels several weeks in advance for a specific time period and a geographic region that can be sub-national. The input data include historical and recent dengue incidence, socioeconomic factors, and remotely sensed variables related to weather, climate, and the environment. Among the climate variables are those known to indicate future weather patterns that may or may not be seasonal. The final prediction models adhere to these principles: 1) the data used must be available at the time the prediction is made (avoiding pitfalls made by studies that use recent data that, in actual practice, would not be available until after the date the prediction was made); and 2) the models are tested on data not used in their development (thereby avoiding overly optimistic measures of accuracy of the prediction). Local public health preferences for low numbers of false positives and negatives are taken into account. These models appear to be robust even when applied to nearby geographic regions that were not used in model development. The method may be applied to other vector borne and environmentally affected diseases.

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.

Seasonal and nonseasonal dynamics of Aedes aegypti in Rio de Janeiro, Brazil: fitting mathematical models to trap data

Mathematical models suggest that seasonal transmission and temporary cross-immunity between serotypes can determine the characteristic multi-year dynamics of dengue fever. Seasonal transmission is attributed to the effect of climate on mosquito abundance and within host virus dynamics. In this study, we validate a set of temperature and density dependent entomological models that are built-in components of most dengue models by fitting them to time series of ovitrap data from three distinct neighborhoods in Rio de Janeiro, Brazil. The results indicate that neighborhoods differ in the strength of the seasonal component and that commonly used models tend to assume more seasonal structure than found in data. Future dengue models should investigate the impact of heterogeneous levels of seasonality on dengue dynamics as it may affect virus maintenance from year to year, as well as the risk of disease outbreaks.

Impact of combined vector-control and vaccination strategies on transmission dynamics of dengue fever: a model-based analysis

Dengue fever is a vector-borne disease prevalent in tropical and subtropical regions. It is an important public health problem with a considerable and often under-valued disease burden in terms of frequency, cost and quality-of-life. Recent literature reviews have documented the development of mathematical models of dengue fever both to identify important characteristics for future model development as well as to assess the impact of dengue control interventions. Such reviews highlight the importance of short-term cross-protection; antibody-dependent enhancement; and seasonality (in terms of both favourable and unfavourable conditions for mosquitoes). The compartmental model extends work by Bartley (2002) and combines the following factors: seasonality, age-structure, consecutive infection by all four serotypes, cross-protection and immune enhancement, as well as combined vector-host transmission. The model is used to represent dengue transmission dynamics using parameters appropriate for Thailand and to assess the potential impact of combined vector-control and vaccination strategies including routine and catch-up vaccination strategies on disease dynamics. When seasonality and temporary cross-protection between serotypes are included, the model is able to approximate the observed incidence of dengue fever in Thailand. We find vaccination to be the most effective single intervention, albeit with imperfect efficacy (30.2 %) and limited duration of protection. However, in combination, control interventions and vaccination exhibit a marked impact on dengue fever transmission. This study shows that an imperfect vaccine can be a useful weapon in reducing disease spread within the community, although it will be most effective when promoted as one of several strategies for combating dengue fever transmission.

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.

A simple periodic-forced model for dengue fitted to incidence data in Singapore

Dengue is the world's major arbovirosis and therefore an important public health concern in endemic areas. The availability of weekly reports of dengue cases in Singapore offers the opportunity to analyze the transmission dynamics and the impact of vector control strategies. Based on a previous model studying the impact of vector control strategies in Singapore during the 2005 outbreak, a simple vector-host model accounting for seasonal fluctuation in vector density was developed to estimate the parameters governing the vector population dynamics using dengue fever incidence data from August 2003 to December 2007. The impact of vector control, which consisted principally of a systematic removal of actual and potential breeding sites during a six-week period in 2005, was also investigated. Although our approach does not account for the complex life cycle of the vector, the good fit between data and model outputs showed that the impact of seasonality on the transmission dynamics is highly important. Moreover, the periodic fluctuations of the vector population were found in phase with temperature variations, suggesting a strong climate effect on the vector density and, in turn, on the transmission dynamics.

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.

Dynamic noise, chaos and parameter estimation in population biology

We revisit the parameter estimation framework for population biological dynamical systems, and apply it to calibrate various models in epidemiology with empirical time series, namely influenza and dengue fever. When it comes to more complex models such as multi-strain dynamics to describe the virus-host interaction in dengue fever, even the most recently developed parameter estimation techniques, such as maximum likelihood iterated filtering, reach their computational limits. However, the first results of parameter estimation with data on dengue fever from Thailand indicate a subtle interplay between stochasticity and the deterministic skeleton. The deterministic system on its own already displays complex dynamics up to deterministic chaos and coexistence of multiple attractors.