Estimating the reproductive number, total outbreak size, and reporting rates for Zika epidemics in South and Central America

A Gaussian-process approximation to a spatial SIR process using moment closures and emulators

The dynamics that govern disease spread are hard to model because infections are functions of both the underlying pathogen as well as human or animal behavior. This challenge is increased when modeling how diseases spread between different spatial locations. Many proposed spatial epidemiological models require trade-offs to fit, either by abstracting away theoretical spread dynamics, fitting a deterministic model, or by requiring large computational resources for many simulations. We propose an approach that approximates the complex spatial spread dynamics with a Gaussian process. We first propose a flexible spatial extension to the well-known SIR stochastic process, and then we derive a moment-closure approximation to this stochastic process. This moment-closure approximation yields ordinary differential equations for the evolution of the means and covariances of the susceptibles and infectious through time. Because these ODEs are a bottleneck to fitting our model by MCMC, we approximate them using a low-rank emulator. This approximation serves as the basis for our hierarchical model for noisy, underreported counts of new infections by spatial location and time. We demonstrate using our model to conduct inference on simulated infections from the underlying, true spatial SIR jump process. We then apply our method to model counts of new Zika infections in Brazil from late 2015 through early 2016.

Three-stage modeling of HIV infection and implications for antiretroviral therapy

We consider a deterministic model of HIV infection that involves macrophages as a long-term active reservoir to describe all three stages of the disease process: the acute stage, chronic infection, and the transition to AIDS. The proposed model is shown to retain crucial properties, such as the positivity of solutions, regardless of variations in model parameters. A dynamical analysis is performed to identify the local stability properties of the viral clearance steady state. This analysis illustrates how chronically infected macrophages can explain the progression to AIDS and provoke viral explosion, while previous models do not. We further demonstrate that the infected T-cell population, even if not responsible for the majority of new infections that lead to viral explosion, may contribute significantly to the transition amongst the three stages of infection. Moreover, we explore the implications of the model for the administration of antiretroviral therapy (ART) and provide quantitative estimates that emphasize the time sensitive nature of treatment initiation and the level of drug efficacy. Finally, we study the effects of treatment interruption on the disease dynamics predicted by the model and elucidate the influence of both interruption time and duration.

Model-Based Projection of Zika Infection Risk with Temperature Effect: A Case Study in Southeast Asia

Zika virus (ZIKV) recently reemerged in the Americas and rapidly expanded in global range. It is posing significant concerns of public health due to its link to birth defects and its complicated transmission routes. Southeast Asia is badly hit by ZIKV, but limited information was found on the transmission potential of ZIKV in the region. In this paper, we develop a new dynamic process-based mathematical model, which incorporates the interactions among humans (sexual transmissibility), and between human and mosquitoes (biting transmissibility), as well as the essential impacts of temperature. The model is first validated by fitting the 2016 ZIKV outbreak in Singapore via Markov chain Monte Carlo method. Based on that, we demonstrate the effects of temperature on mosquito ecology and ZIKV transmission, and further clarify the potential risk of ZIKV outbreak in Southeast Asian countries. The results show that (i) the estimated infection reproduction number [Formula: see text] in Singapore fell from 6.93 (in which the contribution of sexual transmission was 0.89) to 0.24 after the deployment of control strategies; (ii) the optimal temperature for the reproduction of ZIKV infections and adult mosquitoes are estimated to be [Formula: see text]C and [Formula: see text]C, respectively; and (iii) the [Formula: see text] in Southeast Asia could be between 3 and 7, with an inverted-U shape around the year. The large values of [Formula: see text] and the simulative patterns of ZIKV transmission in each country highlights the high risk of ZIKV attack in Southeast Asia.

Inferring the spread of COVID-19: the role of time-varying reporting rate in epidemiological modelling

The role of epidemiological models is crucial for informing public health officials during a public health emergency, such as the COVID-19 pandemic. However, traditional epidemiological models fail to capture the time-varying effects of mitigation strategies and do not account for under-reporting of active cases, thus introducing bias in the estimation of model parameters. To infer more accurate parameter estimates and to reduce the uncertainty of these estimates, we extend the SIR and SEIR epidemiological models with two time-varying parameters that capture the transmission rate and the rate at which active cases are reported to health officials. Using two real data sets of COVID-19 cases, we perform Bayesian inference via our SIR and SEIR models with time-varying transmission and reporting rates and via their standard counterparts with constant rates; our approach provides parameter estimates with more realistic interpretation, and 1-week ahead predictions with reduced uncertainty. Furthermore, we find consistent under-reporting in the number of active cases in the data that we consider, suggesting that the initial phase of the pandemic was more widespread than previously reported.

A modified Susceptible-Infected-Recovered model for observed under-reported incidence data

Fitting Susceptible-Infected-Recovered (SIR) models to incidence data is problematic when not all infected individuals are reported. Assuming an underlying SIR model with general but known distribution for the time to recovery, this paper derives the implied differential-integral equations for observed incidence data when a fixed fraction of newly infected individuals are not observed. The parameters of the resulting system of differential equations are identifiable. Using these differential equations, we develop a stochastic model for the conditional distribution of current disease incidence given the entire past history of reported cases. We estimate the model parameters using Bayesian Markov Chain Monte-Carlo sampling of the posterior distribution. We use our model to estimate the transmission rate and fraction of asymptomatic individuals for the current Coronavirus 2019 outbreak in eight American Countries: the United States of America, Brazil, Mexico, Argentina, Chile, Colombia, Peru, and Panama, from January 2020 to May 2021. Our analysis reveals that the fraction of reported cases varies across all countries. For example, the reported incidence fraction for the United States of America varies from 0.3 to 0.6, while for Brazil it varies from 0.2 to 0.4.

A Zika Endemic Model for the Contribution of Multiple Transmission Routes

Zika virus disease is a viral disease primarily transmitted to humans through the bite of infected female mosquitoes. Recent evidence indicates that the virus can also be sexually transmitted in hosts and vertically transmitted in vectors. In this paper, we propose a Zika model with three transmission routes, that is, vector-borne transmission between humans and mosquitoes, sexual transmission within humans and vertical transmission within mosquitoes. The basic reproduction number [Formula: see text] is computed and shown to be a sharp threshold quantity. Namely, the disease-free equilibrium is globally asymptotically stable as [Formula: see text], whereas there exists a unique endemic equilibrium which is globally asymptotically stable as [Formula: see text]. The relative contributions of each transmission route on the reproduction number, and the short- and long-term host infections are analyzed. Numerical simulations confirm that vectorial transmission contributes the most to the initial and subsequent transmission. The role of sexual transmission in the early phase of a Zika outbreak is greater than the long term, while vertical transmission is the opposite. Reducing mosquito bites is the most effective measure in lowering the risk of Zika virus infection.

Forest Coverage and Socioeconomic Factors Associated with Dengue in El Salvador, 2011-2013

Dengue virus serotypes 1, 2, 3, and 4 are transmitted by Aedes aegypti and Aedes albopictus mosquitoes, which cause illness in an estimated 100 million annually. Although dengue viruses are endemic throughout El Salvador, very little is known about their ecology and epidemiology. The principal methods to prevent and reduce dengue cases are through vector control and by adoption of a vaccine. In addition, understanding the environmental and socioeconomic factors associated with dengue could contribute to case reduction by targeting prevention efforts in dengue hotspots. This study investigated environmental and socioeconomic factors associated with dengue cases in El Salvador. Dengue cases were obtained from 2011 to 2013 for 262 municipalities. The mean incidence was determined for each municipality for the 3 year period. Negative binomial regression models evaluated the relationship between dengue cases and the environmental factors elevation, forest coverage, mean annual temperature, and cumulative precipitation. Twelve socioeconomic and infrastructure variables and their relationship with dengue were also investigated by using negative binomial regression. A total of 29,764 confirmed dengue cases were reported. The mean dengue incidence for 2011-2013 was 135/100,000. The highest number of dengue cases occurred in San Salvador and surrounding municipalities, as well as in two additional cities, Santa Ana and San Miguel; the highest incidence of dengue cases (per 100,000) occurred in cities in the west and at the center of the country. Significant environmental variables associated with dengue included temperature, precipitation, and non-forested area. The socioeconomic variables poverty rate, illiteracy rate, and school attendance, and the infrastructure variables percent of homes with sanitary service, municipal trash service, electricity, and cement brick flooring, as well as population density, were also significant predictors of dengue. Understanding these environmental and socioeconomic factors and their relationship with dengue will help design and implement timely prevention strategies and vector control to reduce dengue in El Salvador.

On the relationship between COVID-19 reported fatalities early in the pandemic and national socio-economic status predating the pandemic

This study investigates the relationship between socio-economic determinants pre-dating the pandemic and the reported number of cases, deaths, and the ratio of deaths/cases in 199 countries/regions during the first months of the COVID-19 pandemic. The analysis is performed by means of machine learning methods. It involves a portfolio/ensemble of 32 interpretable models and considers the case in which the outcome variables (number of cases, deaths, and their ratio) are independent and the case in which their dependence is weighted based on geographical proximity. We build two measures of variable importance, the Absolute Importance Index (AII) and the Signed Importance Index (SII) whose roles are to identify the most contributing socio-economic factors to the variability of the COVID-19 pandemic. Our results suggest that, together with the established influence on cases and deaths of the level of mobility, the specific features of the health care system (smart/poor allocation of resources), the economy of a country (equity/non-equity), and the society (religious/not religious or community-based vs not) might contribute to the number of COVID-19 cases and deaths heterogeneously across countries.

Global Dynamics of a Reaction-Diffusion Model of Zika Virus Transmission with Seasonality

In this paper, we propose a periodic reaction-diffusion model of Zika virus with seasonal and spatial heterogeneous structure in host and vector population. We introduce the basic reproduction ratio [Formula: see text] for this model and show that the disease-free periodic solution is globally asymptotically stable if [Formula: see text], while the system admits a globally asymptotically stable positive periodic solution if [Formula: see text]. Numerically, we study the Zika transmission in Rio de Janeiro Municipality, Brazil, and investigate the effects of some model parameters on [Formula: see text]. We find that the neglect of seasonality underestimates the value of [Formula: see text] and the maximum carrying capacity affects the spread of Zika virus.

Measuring the global burden of chikungunya and Zika viruses: A systematic review

Throughout the last decade, chikungunya virus (CHIKV) and Zika virus (ZIKV) infections have spread globally, causing a spectrum of disease that ranges from self-limited febrile illness to permanent severe disability, congenital anomalies, and early death. Nevertheless, estimates of their aggregate health impact are absent from the literature and are currently omitted from the Global Burden of Disease (GBD) reports. We systematically reviewed published literature and surveillance records to evaluate the global burden caused by CHIKV and ZIKV between 2010 and 2019, to calculate estimates of their disability-adjusted life year (DALY) impact. Extracted data on acute, chronic, and perinatal outcomes were used to create annualized DALY estimates, following techniques outlined in the GBD framework. This study is registered with PROSPERO (CRD42020192502). Of 7,877 studies identified, 916 were screened in detail, and 21 were selected for inclusion. Available data indicate that CHIKV and ZIKV caused the average yearly loss of over 106,000 and 44,000 DALYs, respectively, between 2010 and 2019. Both viruses caused substantially more burden in the Americas than in any other World Health Organization (WHO) region. This unequal distribution is likely due to a combination of limited active surveillance reporting in other regions and the lack of immunity that left the previously unexposed populations of the Americas susceptible to severe outbreaks during the last decade. Long-term rheumatic sequelae provided the largest DALY component for CHIKV, whereas congenital Zika syndrome (CZS) contributed most significantly for ZIKV. Acute symptoms and early mortality accounted for relatively less of the overall burden. Suboptimal reporting and inconsistent diagnostics limit precision when determining arbovirus incidence and frequency of complications. Despite these limitations, it is clear from our assessment that CHIKV and ZIKV represent a significant cause of morbidity that is not included in current disease burden reports. These results suggest that transmission-blocking strategies, including vector control and vaccine development, remain crucial priorities in reducing global disease burden through prevention of potentially devastating arboviral outbreaks.

Chikungunya and Zika are 2 mosquito-borne viral diseases that can cause both acute symptoms and long-term, debilitating complications in infected individuals. Chikungunya is best known as a cause of persistent arthritis in otherwise recovered patients and Zika as a cause of cognitive, motor, and sensory anomalies in newborn children. Both diseases emerged in the Americas within the last decade and have since spread rapidly throughout the region. Despite their widespread transmission there and throughout much of the world, chikungunya and Zika remain neglected diseases. One of the most significant obstacles to address their spread is a lack of data involving their burden. We searched the published literature and surveillance reports to collect information about the incidence, mortality, and morbidity associated with each of these diseases to estimate their regional and global burden during the last decade. Our estimates confirm that chikungunya and Zika caused substantial burden throughout this time frame and place them among the most problematic mosquito-borne viral diseases worldwide. We found that the largest proportion of global burden linked to each disease between 2010 and 2019 occurred in the Americas, although this observation is likely due to limited reporting in other regions.

Leveraging multiple data types to estimate the size of the Zika epidemic in the Americas

Several hundred thousand Zika cases have been reported across the Americas since 2015. Incidence of infection was likely much higher, however, due to a high frequency of asymptomatic infection and other challenges that surveillance systems faced. Using a hierarchical Bayesian model with empirically-informed priors, we leveraged multiple types of Zika case data from 15 countries to estimate subnational reporting probabilities and infection attack rates (IARs). Zika IAR estimates ranged from 0.084 (95% CrI: 0.067–0.096) in Peru to 0.361 (95% CrI: 0.214–0.514) in Ecuador, with significant subnational variability in every country. Totaling infection estimates across these and 33 other countries and territories, our results suggest that 132.3 million (95% CrI: 111.3-170.2 million) people in the Americas had been infected by the end of 2018. These estimates represent the most extensive attempt to determine the size of the Zika epidemic in the Americas, offering a baseline for assessing the risk of future Zika epidemics in this region.

During the recent Zika epidemic in the Americas millions of people were likely infected, but the true size of the epidemic is unknown because of gaps in the surveillance system. The infection attack rate (IAR)—defined as the proportion of the population that was infected over the course of the epidemic—has important implications for the longer-term epidemiology of Zika in the region, such as the timing, location, and likelihood of future outbreaks. To estimate the IAR and the total number of people infected, we leveraged multiple types of Zika case data from 15 countries and territories where subnational data were publicly available. Datasets included confirmed and suspected Zika cases in pregnant women and in the total population, Zika-associated Guillan-Barré syndrome cases, and cases of congenital Zika syndrome. We used a hierarchical Bayesian model with empirically-informed priors that leveraged the different case report types to simultaneously estimate national and subnational reporting probabilities, the fraction of symptomatic infections, and subnational IARs. In these 15 countries and territories, estimates of Zika IAR ranged from 0.084 (95% CrI: 0.067–0.096) in Peru to 0.361 (95% CrI: 0.214–0.514) in Ecuador. Totaling these infection estimates across these and 33 other countries and territories in the region, our results suggest that 132.3 million (95% CrI: 111.3-170.2 million) people in the Americas were infected with ZIKV by the end of 2018.

Reviewing estimates of the basic reproduction number for dengue, Zika and chikungunya across global climate zones

BACKGROUND

Globally, dengue, Zika virus, and chikungunya are important viral mosquito-borne diseases that infect millions of people annually. Their geographic range includes not only tropical areas but also sub-tropical and temperate zones such as Japan and Italy. The relative severity of these arboviral disease outbreaks can vary depending on the setting. In this study we explore variation in the epidemiologic potential of outbreaks amongst these climatic zones and arboviruses in order to elucidate potential reasons behind such differences.

METHODOLOGY

We reviewed the peer-reviewed literature (PubMed) to obtain basic reproduction number (R₀) estimates for dengue, Zika virus, and chikungunya from tropical, sub-tropical and temperate regions. We also computed R₀ estimates for temperate and sub-tropical climate zones, based on the outbreak curves in the initial outbreak phase. Lastly we compared these estimates across climate zones, defined by latitude.

RESULTS

Of 2115 studies, we reviewed the full text of 128 studies and included 65 studies in our analysis. Our results suggest that the R₀ of an arboviral outbreak depends on climate zone, with lower R₀ estimates, on average, in temperate zones (R₀ = 2.03) compared to tropical (R₀ = 3.44) and sub-tropical zones (R₀ = 10.29). The variation in R₀ was considerable, ranging from 0.16 to 65. The largest R₀ was for dengue (65) and was estimated by the Ross-Macdonald model in the tropical zone, whereas the smallest R₀ (0.16) was for Zika virus and was estimated statistically from an outbreak curve in the sub-tropical zone.

CONCLUSIONS

The results indicate climate zone to be an important determinant of the basic reproduction number, R₀, for dengue, Zika virus, and chikungunya. The role of other factors as determinants of R₀, such as methods, environmental and social conditions, and disease control, should be further investigated. The results suggest that R₀ may increase in temperate regions in response to global warming, and highlight the increasing need for strengthening preparedness and control activities.

Modeling Chikungunya control strategies and Mayaro potential outbreak in the city of Rio de Janeiro

Mosquito-borne diseases have become a significant health issue in many regions around the world. For tropical countries, diseases such as Dengue, Zika, and Chikungunya, became epidemic in the last decades. Health surveillance reports during this period were crucial in providing scientific-based information to guide decision making and resources allocation to control outbreaks. In this work, we perform data analysis of the last Chikungunya epidemics in the city of Rio de Janeiro by applying a compartmental mathematical model. Sensitivity analyses were performed in order to describe the contribution of each parameter to the outbreak incidence. We estimate the "basic reproduction number" for those outbreaks and predict the potential epidemic outbreak of the Mayaro virus. We also simulated several scenarios with different public interventions to decrease the number of infected people. Such scenarios should provide insights about possible strategies to control future outbreaks.

Coinfection, Altered Vector Infectivity, and Antibody-Dependent Enhancement: The Dengue-Zika Interplay

Although dengue and Zika cocirculation has increased within the past 5 years, very little is known about its epidemiological consequences. To investigate the effect of dengue and Zika cocirculation on the spread of both pathogens, we create a deterministic dengue and Zika coinfection model, the first to incorporate altered infectivity of mosquitoes (due to coinfection). The model also addresses increased infectivity due to antibody-dependent enhancement (ADE) within the human population. Central to our analysis is the derivation and interpretation of the basic reproductive number and invasion reproductive number of both pathogens. In addition, we investigate how model parameters impact the persistence of each disease. Our results identify threshold conditions under which one disease facilitates the spread of the other and show that ADE has a greater impact on disease persistence than altered vector infectivity. This work highlights the importance of ADE and illustrates that while the endemic presence of dengue facilitates the spread of Zika, it is possible for high Zika prevalence to prevent the establishment of dengue.

Impact of weather seasonality and sexual transmission on the spread of Zika fever

We establish a compartmental model to study the transmission of Zika virus disease including spread through sexual contacts and the role of asymptomatic carriers. To incorporate the impact of the seasonality of weather on the spread of Zika, we apply a nonautonomous model with time-dependent mosquito birth rate and biting rate, which allows us to explain the differing outcome of the epidemic in different countries of South America: using Latin Hypercube Sampling for fitting, we were able to reproduce the different outcomes of the disease in various countries. Sensitivity analysis shows that, although the most important factors in Zika transmission are the birth rate of mosquitoes and the transmission rate from mosquitoes to humans, spread through sexual contacts also highly contributes to the transmission of Zika virus: our study suggests that the practice of safe sex among those who have possibly contracted the disease, can significantly reduce the number of Zika cases.

Heterogeneous local dynamics revealed by classification analysis of spatially disaggregated time series data

Time series data provide a crucial window into infectious disease dynamics, yet their utility is often limited by the spatially aggregated form in which they are presented. When working with time series data, violating the implicit assumption of homogeneous dynamics below the scale of spatial aggregation could bias inferences about underlying processes. We tested this assumption in the context of the 2015-2016 Zika epidemic in Colombia, where time series of weekly case reports were available at national, departmental, and municipal scales. First, we performed a descriptive analysis, which showed that the timing of departmental-level epidemic peaks varied by three months and that departmental-level estimates of the time-varying reproduction number, R(t), showed patterns that were distinct from a national-level estimate. Second, we applied a classification algorithm to six features of proportional cumulative incidence curves, which showed that variability in epidemic duration, the length of the epidemic tail, and consistency with a cumulative normal density curve made the greatest contributions to distinguishing groups. Third, we applied this classification algorithm to data simulated with a stochastic transmission model, which showed that group assignments were consistent with simulated differences in the basic reproduction number, R₀. This result, along with associations between spatial drivers of transmission and group assignments based on observed data, suggests that the classification algorithm is capable of detecting differences in temporal patterns that are associated with differences in underlying drivers of incidence patterns. Overall, this diversity of temporal patterns at local scales underscores the value of spatially disaggregated time series data.

Practical unidentifiability of a simple vector-borne disease model: Implications for parameter estimation and intervention assessment

Mathematical modeling has an extensive history in vector-borne disease epidemiology, and is increasingly used for prediction, intervention design, and understanding mechanisms. Many studies rely on parameter estimation to link models and data, and to tailor predictions and counterfactuals to specific settings. However, few studies have formally evaluated whether vector-borne disease models can properly estimate the parameters of interest given the constraints of a particular dataset. Identifiability analysis allows us to examine whether model parameters can be estimated uniquely-a lack of consideration of such issues can result in misleading or incorrect parameter estimates and model predictions. Here, we evaluate both structural (theoretical) and practical identifiability of a commonly used compartmental model of mosquito-borne disease, using the 2010 dengue epidemic in Taiwan as a case study. We show that while the model is structurally identifiable, it is practically unidentifiable under a range of human and mosquito time series measurement scenarios. In particular, the transmission parameters form a practically identifiable combination and thus cannot be estimated separately, potentially leading to incorrect predictions of the effects of interventions. However, in spite of the unidentifiability of the individual parameters, the basic reproduction number was successfully estimated across the unidentifiable parameter ranges. These identifiability issues can be resolved by directly measuring several additional human and mosquito life-cycle parameters both experimentally and in the field. While we only consider the simplest case for the model, we show that a commonly used model of vector-borne disease is unidentifiable from human and mosquito incidence data, making it difficult or impossible to estimate parameters or assess intervention strategies. This work illustrates the importance of examining identifiability when linking models with data to make predictions and inferences, and particularly highlights the importance of combining laboratory, field, and case data if we are to successfully estimate epidemiological and ecological parameters using models.

Effects of multiple transmission pathways on Zika dynamics

Although the Zika virus is transmitted to humans primarily through the bite of infected female Aedes aegypti mosquitoes, it can also be sexually and vertically transmitted within both populations. In this study, we develop a new mathematical model of the Zika virus which incorporates sexual transmission in humans and mosquitos, vertical transmission in mosquitos, and mosquito to human transmission through bites. Analysis of this deterministic model shows that the secondary transmission routes of Zika increase the basic reproductive number (R0) of the virus by 5%, shift the peak time of an outbreak to occur 10% sooner, increase the initial growth of an epidemic, and have important consequences for control strategies and estimates of R0. Furthermore, sensitivity analysis show that the basic reproductive number is most sensitive to the mosquito biting rate and transmission probability parameters and reveal that the dynamics of juvenile mosquito stages greatly impact the peak time of an outbreak. These discoveries deepen our understanding of the complex transmission routes of ZIKV and the consequences that they may hold for public health officials.

Projecting the end of the Zika virus epidemic in Latin America: a modelling analysis

BACKGROUND

Zika virus (ZIKV) emerged in Latin America and the Caribbean (LAC) region in 2013, with serious implications for population health in the region. In 2016, the World Health Organization declared the ZIKV outbreak a Public Health Emergency of International Concern following a cluster of associated neurological disorders and neonatal malformations. In 2017, Zika cases declined, but future incidence in LAC remains uncertain due to gaps in our understanding, considerable variation in surveillance and the lack of a comprehensive collation of data from affected countries.

METHODS

Our analysis combines information on confirmed and suspected Zika cases across LAC countries and a spatio-temporal dynamic transmission model for ZIKV infection to determine key transmission parameters and projected incidence in 90 major cities within 35 countries. Seasonality was determined by spatio-temporal estimates of Aedes aegypti vectorial capacity. We used country and state-level data from 2015 to mid-2017 to infer key model parameters, country-specific disease reporting rates, and the 2018 projected incidence. A 10-fold cross-validation approach was used to validate parameter estimates to out-of-sample epidemic trajectories.

RESULTS

There was limited transmission in 2015, but in 2016 and 2017 there was sufficient opportunity for wide-spread ZIKV transmission in most cities, resulting in the depletion of susceptible individuals. We predict that the highest number of cases in 2018 would present within some Brazilian States (Sao Paulo and Rio de Janeiro), Colombia and French Guiana, but the estimated number of cases were no more than a few hundred. Model estimates of the timing of the peak in incidence were correlated (p < 0.05) with the reported peak in incidence. The reporting rate varied across countries, with lower reporting rates for those with only confirmed cases compared to those who reported both confirmed and suspected cases.

CONCLUSIONS

The findings suggest that the ZIKV epidemic is by and large over within LAC, with incidence projected to be low in most cities in 2018. Local low levels of transmission are probable, but the estimated rate of infection suggests that most cities have a population with high levels of herd immunity.

Local and regional dynamics of chikungunya virus transmission in Colombia: the role of mismatched spatial heterogeneity

BACKGROUND

Mathematical models of transmission dynamics are routinely fitted to epidemiological time series, which must inevitably be aggregated at some spatial scale. Weekly case reports of chikungunya have been made available nationally for numerous countries in the Western Hemisphere since late 2013, and numerous models have made use of this data set for forecasting and inferential purposes. Motivated by an abundance of literature suggesting that the transmission of this mosquito-borne pathogen is localized at scales much finer than nationally, we fitted models at three different spatial scales to weekly case reports from Colombia to explore limitations of analyses of nationally aggregated time series data.

METHODS

We adapted the recently developed Disease Transmission Kernel (DTK)-Dengue model for modeling chikungunya virus (CHIKV) transmission, given the numerous similarities of these viruses vectored by a common mosquito vector. We fitted versions of this model specified at different spatial scales to weekly case reports aggregated at different spatial scales: (1) single-patch national model fitted to national data; (2) single-patch departmental models fitted to departmental data; and (3) multi-patch departmental models fitted to departmental data, where the multiple patches refer to municipalities within a department. We compared the consistency of simulations from fitted models with empirical data.

RESULTS

We found that model consistency with epidemic dynamics improved with increasing spatial granularity of the model. Specifically, the sum of single-patch departmental model fits better captured national-level temporal patterns than did a single-patch national model. Likewise, multi-patch departmental model fits better captured department-level temporal patterns than did single-patch departmental model fits. Furthermore, inferences about municipal-level incidence based on multi-patch departmental models fitted to department-level data were positively correlated with municipal-level data that were withheld from model fitting.

CONCLUSIONS

Our model performed better when posed at finer spatial scales, due to better matching between human populations with locally relevant risk. Confronting spatially aggregated models with spatially aggregated data imposes a serious structural constraint on model behavior by averaging over epidemiologically meaningful spatial variation in drivers of transmission, impairing the ability of models to reproduce empirical patterns.

Approximate Bayesian algorithm to estimate the basic reproduction number in an influenza pandemic using arrival times of imported cases

BACKGROUND

In an influenza pandemic, arrival times of cases are a proxy of the epidemic size and disease transmissibility. Because of intense surveillance of travelers from infected countries, detection is more rapid and complete than on local surveillance. Travel information can provide a more reliable estimation of transmission parameters.

METHOD

We developed an Approximate Bayesian Computation algorithm to estimate the basic reproduction number (R₀) in addition to the reporting rate and unobserved epidemic start time, utilizing travel, and routine surveillance data in an influenza pandemic. A simulation was conducted to assess the sampling uncertainty. The estimation approach was further applied to the 2009 influenza A/H1N1 pandemic in Mexico as a case study.

RESULTS

In the simulations, we showed that the estimation approach was valid and reliable in different simulation settings. We also found estimates of R₀ and the reporting rate to be 1.37 (95% Credible Interval [CI]: 1.26-1.42) and 4.9% (95% CI: 0.1%-18%), respectively, in the 2009 influenza pandemic in Mexico, which were robust to variations in the fixed parameters. The estimated R₀ was consistent with that in the literature.

CONCLUSIONS

This method is useful for officials to obtain reliable estimates of disease transmissibility for strategic planning. We suggest that improvements to the flow of reporting for confirmed cases among patients arriving at different countries are required.