A dengue model with a dynamic Aedes albopictus vector population

Mathematical modeling in perspective of vector-borne viral infections: a review

Background

Viral diseases are highly widespread infections caused by viruses. These viruses are passing from one human to other humans through a certain medium. The medium might be mosquito, animal, reservoir and food, etc. Here, the population of both human and mosquito vectors are important.

Main body of the abstract

The main objectives are here to introduce the historical perspective of mathematical modeling, enable the mathematical modeler to understand the basic mathematical theory behind this and present a systematic review on mathematical modeling for four vector-borne viral diseases using the deterministic approach. Furthermore, we also introduced other mathematical techniques to deal with vector-borne diseases. Mathematical models could help forecast the infectious population of humans and vectors during the outbreak.

Short conclusion

This study will be helpful for mathematical modelers in vector-borne diseases and ready-made material in the review for future advancement in the subject. This study will not only benefit vector-borne conditions but will enable ideas for other illnesses.

A dynamically structured matrix population model for insect life histories observed under variable environmental conditions

Various environmental drivers influence life processes of insect vectors that transmit human disease. Life histories observed under experimental conditions can reveal such complex links; however, designing informative experiments for insects is challenging. Furthermore, inferences obtained under controlled conditions often extrapolate poorly to field conditions. Here, we introduce a pseudo-stage-structured population dynamics model to describe insect development as a renewal process with variable rates. The model permits representing realistic life stage durations under constant and variable environmental conditions. Using the model, we demonstrate how random environmental variations result in fluctuating development rates and affect stage duration. We apply the model to infer environmental dependencies from the life history observations of two common disease vectors, the southern (Culex quinquefasciatus) and northern (Culex pipiens) house mosquito. We identify photoperiod, in addition to temperature, as pivotal in regulating larva stage duration, and find that carefully timed life history observations under semi-field conditions accurately predict insect development throughout the year. The approach we describe augments existing methods of life table design and analysis, and contributes to the development of large-scale climate- and environment-driven population dynamics models for important disease vectors.

Assessing the Spatio-temporal Spread of COVID-19 via Compartmental Models with Diffusion in Italy, USA, and Brazil

The outbreak of COVID-19 in 2020 has led to a surge in interest in the mathematical modeling of infectious diseases. Such models are usually defined as compartmental models, in which the population under study is divided into compartments based on qualitative characteristics, with different assumptions about the nature and rate of transfer across compartments. Though most commonly formulated as ordinary differential equation models, in which the compartments depend only on time, recent works have also focused on partial differential equation (PDE) models, incorporating the variation of an epidemic in space. Such research on PDE models within a Susceptible, Infected, Exposed, Recovered, and Deceased framework has led to promising results in reproducing COVID-19 contagion dynamics. In this paper, we assess the robustness of this modeling framework by considering different geometries over more extended periods than in other similar studies. We first validate our code by reproducing previously shown results for Lombardy, Italy. We then focus on the U.S. state of Georgia and on the Brazilian state of Rio de Janeiro, one of the most impacted areas in the world. Our results show good agreement with real-world epidemiological data in both time and space for all regions across major areas and across three different continents, suggesting that the modeling approach is both valid and robust.

Adaptive mesh refinement and coarsening for diffusion-reaction epidemiological models

The outbreak of COVID-19 in 2020 has led to a surge in the interest in the mathematical modeling of infectious diseases. Disease transmission may be modeled as compartmental models, in which the population under study is divided into compartments and has assumptions about the nature and time rate of transfer from one compartment to another. Usually, they are composed of a system of ordinary differential equations in time. A class of such models considers the Susceptible, Exposed, Infected, Recovered, and Deceased populations, the SEIRD model. However, these models do not always account for the movement of individuals from one region to another. In this work, we extend the formulation of SEIRD compartmental models to diffusion-reaction systems of partial differential equations to capture the continuous spatio-temporal dynamics of COVID-19. Since the virus spread is not only through diffusion, we introduce a source term to the equation system, representing exposed people who return from travel. We also add the possibility of anisotropic non-homogeneous diffusion. We implement the whole model in libMesh, an open finite element library that provides a framework for multiphysics, considering adaptive mesh refinement and coarsening. Therefore, the model can represent several spatial scales, adapting the resolution to the disease dynamics. We verify our model with standard SEIRD models and show several examples highlighting the present model's new capabilities.

Simulation models of dengue transmission in Funchal, Madeira Island: Influence of seasonality

The recent emergence and established presence of Aedes aegypti in the Autonomous Region of Madeira, Portugal, was responsible for the first autochthonous outbreak of dengue in Europe. The island has not reported any dengue cases since the outbreak in 2012. However, there is a high risk that an introduction of the virus would result in another autochthonous outbreak given the presence of the vector and permissive environmental conditions. Understanding the dynamics of a potential epidemic is critical for targeted local control strategies. Here, we adopt a deterministic model for the transmission of dengue in Aedes aegypti mosquitoes. The model integrates empirical and mechanistic parameters for virus transmission, under seasonally varying temperatures for Funchal, Madeira Island. We examine the epidemic dynamics as triggered by the arrival date of an infectious individual; the influence of seasonal temperature mean and variation on the epidemic dynamics; and performed a sensitivity analysis on the following quantities of interest: the epidemic peak size, time to peak, and the final epidemic size. Our results demonstrate the potential for summer and autumn season transmission of dengue, with the arrival date significantly affecting the distribution of the timing and peak size of the epidemic. Late-summer arrivals were more likely to produce large epidemics within a short peak time. Epidemics within this favorable period had an average of 11% of the susceptible population infected at the peak, at an average peak time of 95 days. We also demonstrated that seasonal temperature variation dramatically affects the epidemic dynamics, with warmer starting temperatures producing large epidemics with a short peak time and vice versa. Overall, our quantities of interest were most sensitive to variance in the date of arrival, seasonal temperature, transmission rates, mortality rate, and the mosquito population; the magnitude of sensitivity differs across quantities. Our model could serve as a useful guide in the development of effective local control and mitigation strategies for dengue fever in Madeira Island.

Multi-cluster and environmental dependant vector born disease models

Vector-born disease models are extensively used for surveillance and control processes. The most simple and generally use model (SEIR-SEI model) cannot explain a variety of phenomena involved in these diseases spread and development. In order to obtain a wider insight of the vector-born disease models (and the dynamics involved in them), this work focuses into analyse the classical model, a modified versions of it, and 8 their parameters. The modified version includes host mobility, 9 environmental, re-susceptibility, and mosquito life cycle considerations. As results it is observed that there are a limiting number of parameters that play the most important roles in the dynamics (those related to mortality rates, recovery rate from infectious, and pathogen transmission probabilities). Therefore, parameters determination should focus primarily into estimate these values. Stronger effects of the environmental variables are observed and expected by using different parameters and/or the use of multiple environmental variable at the same time.

Dengue transmission: mathematical model with discrete time delays and estimation of the reproduction number

In this paper, we establish a mathematical model with two delays to reflect the intrinsic and extrinsic incubation periods of virus in dengue transmission. The basic reproduction number [Formula: see text] of the model is defined. It is proved that the disease-free equilibrium is stable when [Formula: see text] and the positive equilibrium is stable when [Formula: see text]. Next, we derive an estimation formula for the reproduction number [Formula: see text] when the human population is partially susceptible to dengue. As an application, the [Formula: see text] values of dengue transmission in Singapore in the years 2013-2015 are estimated. Our estimation method can be applied to estimating [Formula: see text] of other infectious diseases, especially when the human population is not completely susceptible to the disease.

Evaluating the effects of control interventions and estimating the inapparent infections for dengue outbreak in Hangzhou, China

Background

The number of dengue fever (DF) cases and the number of dengue outbreaks have increased in recent years in Zhejiang Province, China. An unexpected dengue outbreak was reported in Hangzhou in 2017 and caused more than one thousand dengue cases. This study was undertaken to evaluate the effectiveness of the actual control measures, estimate the proportion of inapparent infections during this outbreak and simulate epidemic development based on different levels of control measures taking inapparent infections into consideration.

Methods

The epidemic data of dengue cases in Hangzhou, Zhejiang Province, in 2017 and the number of the people exposed to the outbreaks were obtained from the China Information Network System of Disease Prevention and Control. The epidemic without intervention measures was used to estimate the unknown parameters. A susceptible-exposed-infectious/inapparent-recovered (SEIAR) model was used to estimate the effectiveness of the control interventions. The inapparent infections were also evaluated at the same time.

Results

In total, 1137 indigenous dengue cases were reported in Hangzhou in 2017. The number of indigenous dengue cases was estimated by the SEIAR model. This number was predicted to reach 6090 by the end of November 2, 2017, if no control measures were implemented. The total number of reported cases was reduced by 81.33% in contrast to the estimated incidence without intervention. The number of average daily inapparent cases was 10.18 times higher than the number of symptomatic cases. The earlier and more rigorously the vector control interventions were implemented, the more effective they were. The results showed that implementing vector control continuously for more than twenty days was more effective than every few days of implementation. Case isolation is not sufficient enough for epidemic control and only reduced the incidence by 38.10% in contrast to the estimated incidence without intervention, even if case isolation began seven days after the onset of the first case.

Conclusions

The practical control interventions in the outbreaks that occurred in Hangzhou City were highly effective. The proportion of inapparent infections was large, and it played an important role in transmitting the disease during this epidemic. Early, continuous and high efficacy vector control interventions are necessary to limit the development of a dengue epidemic. Timely diagnosis and case reporting are important in the intervention at an early stage of the epidemic.

Fine-scale modelling finds that breeding site fragmentation can reduce mosquito population persistence

Fine-scale geographic variation in the transmission intensity of mosquito-borne diseases is primarily caused by variation in the density of female adult mosquitoes. Therefore, an understanding of fine-scale mosquito population dynamics is critical to understanding spatial heterogeneity in disease transmission and persistence at those scales. However, mathematical models of dengue and malaria transmission, which consider the dynamics of mosquito larvae, generally do not account for the fragmented structure of larval breeding sites. Here, we develop a stochastic metapopulation model of mosquito population dynamics and explore the impact of accounting for breeding site fragmentation when modelling fine-scale mosquito population dynamics. We find that, when mosquito population densities are low, fragmentation can lead to a reduction in population size, with population persistence dependent on mosquito dispersal and features of the underlying landscape. We conclude that using non-spatial models to represent fine-scale mosquito population dynamics may substantially underestimate the stochastic volatility of those populations.

Estimating Past, Present, and Future Trends in the Global Distribution and Abundance of the Arbovirus Vector Aedes aegypti Under Climate Change Scenarios

Background:Aedes aegypti is the principal vector for several important arbovirus diseases, including dengue, chikungunya, yellow fever, and Zika. While recent empirical research has attempted to identify the current global distribution of the vector, the seasonal, and longer-term dynamics of the mosquito in response to trends in climate, population, and economic development over the twentieth and the twenty-first century remains to be elucidated.

Methods: In this study, we use a process-based mathematical model to estimate global vector distribution and abundance. The model is based on the lifecycle of the vector and its dependence on climate, and the model sensitivity to socio-economic development is tested. Model parameters were generally empirically based, and the model was calibrated to global databases and time series of occurrence and abundance records. Climate data on temperature and rainfall were taken from CRU TS3.25 (1901–2015) and five global circulation models (CMIP5; 2006–2099) forced by a high-end (RCP8.5) and a low-end (RCP2.6) emission scenario. Socio-economic data on global GDP and human population density were from ISIMIP (1950–2099).

Findings: The change in the potential of global abundance in A. aegypti over the last century up to today is estimated to be an increase of 9.5% globally and a further increase of 20 or 30% by the end of this century under a low compared to a high carbon emission future, respectively. The largest increase has occurred in the last two decades, indicating a tipping point in climate-driven global abundance which will be stabilized at the earliest in the mid-twenty-first century. The realized abundance is estimated to be sensitive to socioeconomic development.

Interpretation: Our data indicate that climate change mitigation, i.e., following the Paris Agreement, could considerably help in suppressing risks of increased abundance and emergence of A. aegypti globally in the second half of the twenty-first century.

Predicting aquatic development and mortality rates of Aedes aegypti

Mosquito-borne pathogens continue to be a significant burden within human populations, with Aedes aegypti continuing to spread dengue, chikungunya, and Zika virus throughout the world. Using data from a previously conducted study, a linear regression model was constructed to predict the aquatic development rates based on the average temperature, temperature fluctuation range, and larval density. Additional experiments were conducted with different parameters of average temperature and larval density to validate the model. Using a paired t-test, the model predictions were compared to experimental data and showed that the prediction models were not significantly different for average pupation rate, adult emergence rate, and juvenile mortality rate. The models developed will be useful for modeling and estimating the upper limit of the number of Aedes aegypti in the environment under different temperature, diurnal temperature variations, and larval densities.

Climate change may enable Aedes aegypti infestation in major European cities by 2100

BACKGROUND

Climate change allows Aedes aegypti to infest new areas. Consequently, it enables the arboviruses the mosquito transmits -- e.g., dengue, chikungunya, Zika and yellow fever - to emerge in previously uninfected areas. An example is the Portuguese island of Madeira during 2012-13.

OBJECTIVE

We aim to understand how climate change will affect the future spread of this potent vector, as an aid in assessing the risk of disease outbreaks and effectively allocating resources for vector control.

METHODS

We used an empirically-informed, process-based mathematical model to study the feasibility of Aedes aegypti infestation into continental Europe. Based on established global climate-change scenario data, we assess the potential of Aedes aegypti to establish in Europe over the 21st century by estimating the vector population growth rate for five climate models (GCM5).

RESULTS

In a low carbon emission future (RCP2.6), we find minimal change to the current situation throughout the whole of the 21st century. In a high carbon future (RCP8.5), a large parts of southern Europe risks being invaded by Aedes aegypti.

CONCLUSION

Our results show that successfully enforcing the Paris Agreement by limiting global warming to below 2 °C significantly lowers the risk for infestation of Aedes aegypti and consequently of potential large-scale arboviral disease outbreaks in Europe within the 21st century.

(Meta)population dynamics determine effective spatial distributions of mosquito-borne disease control

Recent epidemics of mosquito-borne dengue and Zika viruses demonstrate the urgent need for effective measures to control these diseases. The best method currently available to prevent or reduce the size of outbreaks is to reduce the abundance of their mosquito vectors, but there is little consensus on which mechanisms of control are most effective, or when and where they should be implemented. Although the optimal methods are likely context dependent, broadly applicable strategies for mosquito control, such as how to distribute limited resources across a landscape in times of high epidemic risk, can mitigate (re)emerging outbreaks. We used mathematical simulations to examine how the spatial distribution of larval mosquito control affects the size of disease outbreaks, and how mosquito metapopulation dynamics and demography might impact the efficacy of different spatial distributions of control. We found that the birth rate and mechanism of density-dependent regulation of mosquito populations affected the average outbreak size across all control distributions. These factors also determined whether control distributions favoring the interior or the edges of the landscape most effectively reduced human infections. Thus, understanding local mosquito population regulation and dispersion can lead to more effective control strategies.

Uncovering mechanisms behind mosquito seasonality by integrating mathematical models and daily empirical population data: Culex pipiens in the UK

BACKGROUND

Many mosquito-borne diseases exhibit substantial seasonality, due to strong links between environmental variables and vector and pathogen life-cycles. Further, a range of density-dependent and density-independent biotic and abiotic processes affect the phenology of mosquito populations, with potentially large knock-on effects for vector dynamics and disease transmission. Whilst it is understood that density-independent and density-dependent processes affect seasonal population levels, it is not clear how these interact temporally to shape the population peaks and troughs. Due to this, the paucity of high-resolution data for validation, and the difficulty of parameterizing density-dependent processes, models of vector dynamics may poorly estimate abundances, which has knock-on effects for our ability predict vector-borne disease outbreaks.

RESULTS

We present a rich dataset describing seasonal abundance patterns of each life stage of Culex pipiens, a widespread vector of West Nile virus, at a field site in southern England in 2015. Abundance of immature stages was measured three times per week, whilst adult traps were run four nights each week. This dataset is integrated with an existing delay-differential equation model predicting Cx. pipiens seasonal abundance to improve understanding of observed seasonal abundance patterns. At our field site, the outcome of our model fitting suggests interspecific predation on mosquito larvae and temperature-dependent larval mortality combine to act as the main sources of population regulation throughout the active season, whilst competition for resources is a relatively small source of larval mortality.

CONCLUSIONS

The model suggests that density-independent mortality and interspecific predation interact to shape patterns of mosquito seasonal abundance in a permanent aquatic habitat and we propose that competition for resources is likely to be important where periods of high rainfall create transient habitats. Further, we highlight the importance of challenging population abundance models with data from across all life stages of the species of interest if reliable inferences are to be drawn from these models, particularly when considering mosquito control and vector-borne disease transmission.

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.

Modeling the Heterogeneity of Dengue Transmission in a City

Dengue fever is one of the most important vector-borne diseases in the world, and modeling its transmission dynamics allows for determining the key influence factors and helps to perform interventions. The heterogeneity of mosquito bites of humans during the spread of dengue virus is an important factor that should be considered when modeling the dynamics. However, traditional models generally assumed homogeneous mixing between humans and vectors, which is inconsistent with reality. In this study, we proposed a compartmental model with negative binomial distribution transmission terms to model this heterogeneity at the population level. By including the aquatic stage of mosquitoes and incorporating the impacts of the environment and climate factors, an extended model was used to simulate the 2014 dengue outbreak in Guangzhou, China, and to simulate the spread of dengue in different scenarios. The results showed that a high level of heterogeneity can result in a small peak size in an outbreak. As the level of heterogeneity decreases, the transmission dynamics approximate the dynamics predicted by the corresponding homogeneous mixing model. The simulation results from different scenarios showed that performing interventions early and decreasing the carrying capacity for mosquitoes are necessary for preventing and controlling dengue epidemics. This study contributes to a better understanding of the impact of heterogeneity during the spread of dengue virus.

Assessing the effects of daily commuting in two-patch dengue dynamics: A case study of Cali, Colombia

There are many infectious diseases that can be spread by daily commuting of people and dengue fever is one of them. The absence of vaccine and irregularities in ongoing vector control programs make this disease the most frequent and persistent in many tropical and subtropical regions of the world. This paper targets to access the effects of daily commuting on dengue transmission dynamics by using a deterministic two-patch model fitted to observed data gathered in Cali, Colombia where dengue fever is highly persistent and exhibits endemo-epidemic patterns. The two-patch dengue transmission model with daily communing of human residents between patches (that is, between the city and its suburban areas) is presented using the concept of residence times, which certainly affect the disease transmission rates by inducing variability in human population sizes and vectorial densities at each patch. The same modeling framework is applied to two primary scenarios (epidemic outbreaks and endemic persistence of the disease) and for each scenario two coupling cases (one-way and asymmetric commuting) with different inflow and outflow intensities are analyzed. The concept of effective vectorial density, introduced in this paper, allows to explain in very simple terms why the daily commuting affects quite differently the dengue morbidity among human residents in both patches. In particular, residents of the patch with a greater share of incoming than outgoing commuters may actually "benefit" from inflow of daily commuter by avoiding a considerable number of infections. However, residents of the patch with a greater share of outgoing than incoming commuters, especially those who stay at home patch, incur more risk of getting infected. Additionally, the model shows that daily commuting enhance the total number of human infections acquired in both patches and may even provoke an epidemic outbreak in one patch while moderately lowering the level of the disease persistence in another patch.

Impacts of diurnal temperature and larval density on aquatic development of Aedes aegypti

The increasing range of Aedes aegypti, vector for Zika, dengue, chikungunya, and other viruses, has brought attention to the need to understand the population and transmission dynamics of this mosquito. It is well understood that environmental factors and breeding site characteristics play a role in organismal development and the potential to transmit pathogens. In this study, we observe the impact of larval density in combination with diurnal temperature on the time to pupation, emergence, and mortality of Aedes aegypti. Experiments were conducted at two diurnal temperature ranges based on 10 years of historical temperatures of Houston, Texas (21–32°C and 26.5–37.5°C). Experiments at constant temperatures (26.5°C, 32°C) were also conducted for comparison. At each temperature setting, five larval densities were observed (0.2, 1, 2, 4, 5 larvae per mL of water). Data collected shows significant differences in time to first pupation, time of first emergence, maximum rate of pupation, time of maximum rate of pupation, maximum rate of emergence, time of maximum rate of emergence, final average proportion of adult emergence, and average proportion of larval mortality. Further, data indicates a significant interactive effect between temperature fluctuation and larval density on these measures. Thus, wild population estimates should account for temperature fluctuations, larval density, and their interaction in low-volume containers.

Simulation Study of the Effects of Host Availability on Bite Rate of Aedes albopictus (Skuse) (Diptera: Culicidae) and Risk of Dengue Outbreaks in Non-Endemic Areas

Aedes albopictus is an important vector of dengue fever and tends to live in specific area, where it may ambush blood host that it encounters. Thus, host contact frequency may affect the bite rate and risk of disease outbreak, although no studies have examined these parameters. The present study used a simple model to clarify the fundamental relationship between host availability, bite rate, and risk of dengue outbreaks in non-endemic areas. A hypothetical isolated mosquito population was divided into "ambush" and "resting" subpopulations, and human hosts were modeled as visiting the mosquito population at constant intervals. A single infectious human who visited the mosquito population only on a single occasion was responsible for mosquito infections and consequently, secondary infections among humans who subsequently visit the area after the incubation period. The results confirmed that the bite rate per host increased with decreasing host availability. The number of secondary infections among hosts exhibited a unimodal relationship with the frequency of host visits, with a maximum value at host visits every 24 h. Furthermore, when host availability was not very low, the bite rate was a good indicator of the potential risk of dengue outbreaks. Therefore, human-bait-sweep collection data may be useful for monitoring the risk of dengue outbreaks.

Framework for Infectious Disease Analysis: A comprehensive and integrative multi-modeling approach to disease prediction and management

The impact of infectious disease on human populations is a function of many factors including environmental conditions, vector dynamics, transmission mechanics, social and cultural behaviors, and public policy. A comprehensive framework for disease management must fully connect the complete disease lifecycle, including emergence from reservoir populations, zoonotic vector transmission, and impact on human societies. The Framework for Infectious Disease Analysis is a software environment and conceptual architecture for data integration, situational awareness, visualization, prediction, and intervention assessment. Framework for Infectious Disease Analysis automatically collects biosurveillance data using natural language processing, integrates structured and unstructured data from multiple sources, applies advanced machine learning, and uses multi-modeling for analyzing disease dynamics and testing interventions in complex, heterogeneous populations. In the illustrative case studies, natural language processing from social media, news feeds, and websites was used for information extraction, biosurveillance, and situation awareness. Classification machine learning algorithms (support vector machines, random forests, and boosting) were used for disease predictions.

The importance of being urgent: The impact of surveillance target and scale on mosquito-borne disease control

With the emergence or re-emergence of numerous mosquito-borne diseases in recent years, effective methods for emergency vector control responses are necessary to reduce human infections. Current vector control practices often vary significantly between different jurisdictions, and are executed independently and at different spatial scales. Various types of surveillance information (e.g. number of human infections or adult mosquitoes) trigger the implementation of control measures, though the target and scale of surveillance vary locally. This patchy implementation of control measures likely alters the efficacy of control. We modeled six different scenarios, with larval mosquito control occurring in response to surveillance data of different types and at different scales (e.g. across the landscape or in each patch). Our results indicate that: earlier application of larvicide after an escalation of disease risk achieves much greater reductions in human infections than later control implementation; uniform control across the landscape provides better outbreak mitigation than patchy control application; and different types of surveillance data require different levels of sensitivity in their collection to effectively inform control measures. Our simulations also demonstrate a potential logical fallacy of reactive, surveillance-driven vector control: measures stop being implemented as soon as they are deemed effective. This false sense of security leads to patchier control efforts that will do little to curb the size of future vector-borne disease outbreaks. More investment should be placed in collecting high quality information that can trigger early and uniform implementation, while researchers work to discover more informative metrics of human risk to trigger more effective control.

The Influence of Spatial Configuration of Residential Area and Vector Populations on Dengue Incidence Patterns in an Individual-Level Transmission Model

Dengue is a mosquito-borne infectious disease that is endemic in tropical and subtropical countries. Many individual-level simulation models have been developed to test hypotheses about dengue virus transmission. Often these efforts assume that human host and mosquito vector populations are randomly or uniformly distributed in the environment. Although, the movement of mosquitoes is affected by spatial configuration of buildings and mosquito populations are highly clustered in key buildings, little research has focused on the influence of the local built environment in dengue transmission models. We developed an agent-based model of dengue transmission in a village setting to test the importance of using realistic environments in individual-level models of dengue transmission. The results from one-way ANOVA analysis of simulations indicated that the differences between scenarios in terms of infection rates as well as serotype-specific dominance are statistically significant. Specifically, the infection rates in scenarios of a realistic environment are more variable than those of a synthetic spatial configuration. With respect to dengue serotype-specific cases, we found that a single dengue serotype is more often dominant in realistic environments than in synthetic environments. An agent-based approach allows a fine-scaled analysis of simulated dengue incidence patterns. The results provide a better understanding of the influence of spatial heterogeneity on dengue transmission at a local scale.

A large-scale stochastic spatiotemporal model for Aedes albopictus-borne chikungunya epidemiology

Chikungunya is a viral disease transmitted to humans primarily via the bites of infected Aedes mosquitoes. The virus caused a major epidemic in the Indian Ocean in 2004, affecting millions of inhabitants, while cases have also been observed in Europe since 2007. We developed a stochastic spatiotemporal model of Aedes albopictus-borne chikungunya transmission based on our recently developed environmentally-driven vector population dynamics model. We designed an integrated modelling framework incorporating large-scale gridded climate datasets to investigate disease outbreaks on Reunion Island and in Italy. We performed Bayesian parameter inference on the surveillance data, and investigated the validity and applicability of the underlying biological assumptions. The model successfully represents the outbreak and measures of containment in Italy, suggesting wider applicability in Europe. In its current configuration, the model implies two different viral strains, thus two different outbreaks, for the two-stage Reunion Island epidemic. Characterisation of the posterior distributions indicates a possible relationship between the second larger outbreak on Reunion Island and the Italian outbreak. The model suggests that vector control measures, with different modes of operation, are most effective when applied in combination: adult vector intervention has a high impact but is short-lived, larval intervention has a low impact but is long-lasting, and quarantining infected territories, if applied strictly, is effective in preventing large epidemics. We present a novel approach in analysing chikungunya outbreaks globally using a single environmentally-driven mathematical model. Our study represents a significant step towards developing a globally applicable Ae. albopictus-borne chikungunya transmission model, and introduces a guideline for extending such models to other vector-borne diseases.

DengueME: A Tool for the Modeling and Simulation of Dengue Spatiotemporal Dynamics

The prevention and control of dengue are great public health challenges for many countries, particularly since 2015, as other arboviruses have been observed to interact significantly with dengue virus. Different approaches and methodologies have been proposed and discussed by the research community. An important tool widely used is modeling and simulation, which help us to understand epidemic dynamics and create scenarios to support planning and decision making processes. With this aim, we proposed and developed DengueME, a collaborative open source platform to simulate dengue disease and its vector's dynamics. It supports compartmental and individual-based models, implemented over a GIS database, that represent Aedes aegypti population dynamics, human demography, human mobility, urban landscape and dengue transmission mediated by human and mosquito encounters. A user-friendly graphical interface was developed to facilitate model configuration and data input, and a library of models was developed to support teaching-learning activities. DengueME was applied in study cases and evaluated by specialists. Other improvements will be made in future work, to enhance its extensibility and usability.

A climate-driven mechanistic population model of Aedes albopictus with diapause

Background

The mosquito Aedes albopitus is a competent vector for the transmission of many blood-borne pathogens. An important factor that affects the mosquitoes’ development and spreading is climate, such as temperature, precipitation and photoperiod. Existing climate-driven mechanistic models overlook the seasonal pattern of diapause, referred to as the survival strategy of mosquito eggs being dormant and unable to hatch under extreme weather. With respect to diapause, several issues remain unaddressed, including identifying the time when diapause eggs are laid and hatched under different climatic conditions, demarcating the thresholds of diapause and non-diapause periods, and considering the mortality rate of diapause eggs.

Methods

Here we propose a generic climate-driven mechanistic population model of Ae. albopitus applicable to most Ae. albopictus-colonized areas. The new model is an improvement over the previous work by incorporating the diapause behaviors with many modifications to the stage-specific mechanism of the mosquitoes’ life-cycle. monthly Container Index (CI) of Ae. albopitus collected in two Chinese cities, Guangzhou and Shanghai is used for model validation.

Results

The simulation results by the proposed model is validated with entomological field data by the Pearson correlation coefficient r² in Guangzhou (r² = 0.84) and in Shanghai (r² = 0.90). In addition, by consolidating the effect of diapause-related adjustments and temperature-related parameters in the model, the improvement is significant over the basic model.

Conclusions

The model highlights the importance of considering diapause in simulating Ae. albopitus population. It also corroborates that temperature and photoperiod are significant in affecting the population dynamics of the mosquito. By refining the relationship between Ae. albopitus population and climatic factors, the model serves to establish a mechanistic relation to the growth and decline of the species. Understanding this relationship in a better way will benefit studying the transmission and the spatiotemporal distribution of mosquito-borne epidemics and eventually facilitating the early warning and control of the diseases.

Large-Scale Modelling of the Environmentally-Driven Population Dynamics of Temperate Aedes albopictus (Skuse)

The Asian tiger mosquito, Aedes albopictus, is a highly invasive vector species. It is a proven vector of dengue and chikungunya viruses, with the potential to host a further 24 arboviruses. It has recently expanded its geographical range, threatening many countries in the Middle East, Mediterranean, Europe and North America. Here, we investigate the theoretical limitations of its range expansion by developing an environmentally-driven mathematical model of its population dynamics. We focus on the temperate strain of Ae. albopictus and compile a comprehensive literature-based database of physiological parameters. As a novel approach, we link its population dynamics to globally-available environmental datasets by performing inference on all parameters. We adopt a Bayesian approach using experimental data as prior knowledge and the surveillance dataset of Emilia-Romagna, Italy, as evidence. The model accounts for temperature, precipitation, human population density and photoperiod as the main environmental drivers, and, in addition, incorporates the mechanism of diapause and a simple breeding site model. The model demonstrates high predictive skill over the reference region and beyond, confirming most of the current reports of vector presence in Europe. One of the main hypotheses derived from the model is the survival of Ae. albopictus populations through harsh winter conditions. The model, constrained by the environmental datasets, requires that either diapausing eggs or adult vectors have increased cold resistance. The model also suggests that temperature and photoperiod control diapause initiation and termination differentially. We demonstrate that it is possible to account for unobserved properties and constraints, such as differences between laboratory and field conditions, to derive reliable inferences on the environmental dependence of Ae. albopictus populations.

Climate and the Timing of Imported Cases as Determinants of the Dengue Outbreak in Guangzhou, 2014: Evidence from a Mathematical Model

As the world’s fastest spreading vector-borne disease, dengue was estimated to infect more than 390 million people in 2010, a 30-fold increase in the past half century. Although considered to be a non-endemic country, mainland China had 55,114 reported dengue cases from 2005 to 2014, of which 47,056 occurred in 2014. Furthermore, 94% of the indigenous cases in this time period were reported in Guangdong Province, 83% of which were in Guangzhou City. In order to determine the possible determinants of the unprecedented outbreak in 2014, a population-based deterministic model was developed to describe dengue transmission dynamics in Guangzhou. Regional sensitivity analysis (RSA) was adopted to calibrate the model and entomological surveillance data was used to validate the mosquito submodel. Different scenarios were created to investigate the roles of the timing of an imported case, climate, vertical transmission from mosquitoes to their offspring, and intervention. The results suggested that an early imported case was the most important factor in determining the 2014 outbreak characteristics. Precipitation and temperature can also change the transmission dynamics. Extraordinary high precipitation in May and August, 2014 appears to have increased vector abundance. Considering the relatively small number of cases in 2013, the effect of vertical transmission was less important. The earlier and more frequent intervention in 2014 also appeared to be effective. If the intervention in 2014 was the same as that in 2013, the outbreak size may have been over an order of magnitude higher than the observed number of new cases in 2014.The early date of the first imported and locally transmitted case was largely responsible for the outbreak in 2014, but it was influenced by intervention, climate and vertical transmission. Early detection and response to imported cases in the spring and early summer is crucial to avoid large outbreaks in the future.

Dengue has not been considered to be a major problem in China since it is recognized as an imported disease and only 8,058 cases were reported from 2005 to 2013. However, in 2014 alone, 47,056 new cases were reported. In this study, a mathematical model was developed to determine the possible cause of this outbreak. The most important parameters found to underlie the pattern of a small outbreak in 2013 and a much larger one in 2014 was the timing of the first imported and locally transmitted case. The importance of precipitation and temperature was also confirmed by the simulation results under different climate scenarios. The model also suggests that the earlier and more frequent control interventions in 2014 targeting immature mosquitoes, such as emptying water containers, and adult control, were effective in preventing larger outbreaks. Furthermore, more attention should be paid to imported cases occurring between March 1^st and July 1^st to prevent early and prolonged transmission. Without early detection and response, the final outbreak size might otherwise be an order of magnitude or more the size when the imported case occurred outside this time period.

The many projected futures of dengue

Dengue is a vector-borne disease that causes a substantial public health burden within its expanding range. Several modelling studies have attempted to predict the future global distribution of dengue. However, the resulting projections are difficult to compare and are sometimes contradictory because the models differ in their approach, in the quality of the disease data that they use and in the choice of variables that drive disease distribution. In this Review, we compare the main approaches that have been used to model the future global distribution of dengue and propose a set of minimum criteria for future projections that, by analogy, are applicable to other vector-borne diseases.

Aedes aegypti and Aedes albopictus Habitat Preferences in South Texas, USA

The South Texas region has a historical record of occasional dengue outbreaks. The recent introduction of chikungunya virus to the Caribbean suggests that this disease may be a concern as well. Six different cities and three field habitat types (residential, tire shops, and cemeteries) were examined for evidence of habitat and longitudinal preference of two vector species, Aedes aegypti and Aedes albopictus. A. aegypti was more prevalent in tire shop sites, while A. albopictus was more prevalent in cemetery sites. In residential sites, the relative abundance of the two species varied with longitude, with A. albopictus being more abundant near the coast, and A. aegypti being more abundant inland. There was also a temporal variation, with A. aegypti declining in frequency over time in residential sites. These results have implications for control strategies and disease risk and suggest a greater need for increased surveillance and research in the region.

Dengue outbreaks in Divinopolis, south-eastern Brazil and the geographic and climatic distribution of Aedes albopictus and Aedes aegypti in 2011-2012

OBJECTIVE

To entomologically monitor Aedes spp. and correlate the presence of these vectors with the recent epidemic of dengue in Divinopolis, Minas Gerais State, Brazil.

METHODS

Ovitraps were installed at 44 points in the city, covering six urban areas, from May 2011 to May 2012. After collection, the eggs were incubated until hatching. In the 4th stage of development, the larvae were classified as Ae. aegypti or Ae. albopictus.

RESULTS

In total, 25 633 Aedes spp. eggs were collected. February was the month with the highest incidence, with 5635 eggs collected and a hatching rate of 46.7%. Ae. aegypti eggs had the highest hatching rate, at 72.3%, whereas Ae. albopictus eggs had 27.7%. Climate and population density influenced the number of eggs found. Indicators of vector presence were positively correlated with the occurrence of dengue cases.

CONCLUSION

These data reinforce the need for entomological studies, highlight the relevance of Ae. albopictus as a possible disease vector and demonstrate its adaptation. Ae. albopictus, most commonly found in forested areas, comprised a substantial proportion of the urban mosquito population.

A comparative analysis of the relative efficacy of vector-control strategies against dengue fever

Dengue is considered one of the most important vector-borne infection, affecting almost half of the world population with 50 to 100 million cases every year. In this paper, we present one of the simplest models that can encapsulate all the important variables related to vector control of dengue fever. The model considers the human population, the adult mosquito population and the population of immature stages, which includes eggs, larvae and pupae. The model also considers the vertical transmission of dengue in the mosquitoes and the seasonal variation in the mosquito population. From this basic model describing the dynamics of dengue infection, we deduce thresholds for avoiding the introduction of the disease and for the elimination of the disease. In particular, we deduce a Basic Reproduction Number for dengue that includes parameters related to the immature stages of the mosquito. By neglecting seasonal variation, we calculate the equilibrium values of the model's variables. We also present a sensitivity analysis of the impact of four vector-control strategies on the Basic Reproduction Number, on the Force of Infection and on the human prevalence of dengue. Each of the strategies was studied separately from the others. The analysis presented allows us to conclude that of the available vector control strategies, adulticide application is the most effective, followed by the reduction of the exposure to mosquito bites, locating and destroying breeding places and, finally, larvicides. Current vector-control methods are concentrated on mechanical destruction of mosquitoes' breeding places. Our results suggest that reducing the contact between vector and hosts (biting rates) is as efficient as the logistically difficult but very efficient adult mosquito's control.

Maximum equilibrium prevalence of mosquito-borne microparasite infections in humans

To determine the maximum equilibrium prevalence of mosquito-borne microparasitic infections, this paper proposes a general model for vector-borne infections which is flexible enough to comprise the dynamics of a great number of the known diseases transmitted by arthropods. From equilibrium analysis, we determined the number of infected vectors as an explicit function of the model's parameters and the prevalence of infection in the hosts. From the analysis, it is also possible to derive the basic reproduction number and the equilibrium force of infection as a function of those parameters and variables. From the force of infection, we were able to conclude that, depending on the disease's structure and the model's parameters, there is a maximum value of equilibrium prevalence for each of the mosquito-borne microparasitic infections. The analysis is exemplified by the cases of malaria and dengue fever. With the values of the parameters chosen to illustrate those calculations, the maximum equilibrium prevalence found was 31% and 0.02% for malaria and dengue, respectively. The equilibrium analysis demonstrated that there is a maximum prevalence for the mosquito-borne microparasitic infections.

Spatially-Explicit Simulation Modeling of Ecological Response to Climate Change: Methodological Considerations in Predicting Shifting Population Dynamics of Infectious Disease Vectors

Poikilothermic disease vectors can respond to altered climates through spatial changes in both population size and phenology. Quantitative descriptors to characterize, analyze and visualize these dynamic responses are lacking, particularly across large spatial domains. In order to demonstrate the value of a spatially explicit, dynamic modeling approach, we assessed spatial changes in the population dynamics of Ixodes scapularis, the Lyme disease vector, using a temperature-forced population model simulated across a grid of 4 × 4 km cells covering the eastern United States, using both modeled (Weather Research and Forecasting (WRF) 3.2.1) baseline/current (2001-2004) and projected (Representative Concentration Pathway (RCP) 4.5 and RCP 8.5; 2057-2059) climate data. Ten dynamic population features (DPFs) were derived from simulated populations and analyzed spatially to characterize the regional population response to current and future climate across the domain. Each DPF under the current climate was assessed for its ability to discriminate observed Lyme disease risk and known vector presence/absence, using data from the US Centers for Disease Control and Prevention. Peak vector population and month of peak vector population were the DPFs that performed best as predictors of current Lyme disease risk. When examined under baseline and projected climate scenarios, the spatial and temporal distributions of DPFs shift and the seasonal cycle of key questing life stages is compressed under some scenarios. Our results demonstrate the utility of spatial characterization, analysis and visualization of dynamic population responses-including altered phenology-of disease vectors to altered climate.

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.

Ecologic and sociodemographic risk determinants for dengue transmission in urban areas in Thailand

This study analyzed the association between household-level ecologic and individual-level sociodemographic determinants and dengue transmission in urban areas of Chachoengsao province, Thailand. The ecologic and sociodemographic variables were examined by univariate analysis and multivariate logistic regression. In the ecologic model, dengue risk was related to households situated in the ecotope of residential mixed with commercial and densely populated urban residential areas (RCDENPURA) (aOR = 2.23, P = 0.009), high historical dengue risk area (aOR = 2.06, P < 0.001), and presence of household window screens (aOR = 1.62, P = 0.023). In the sociodemographic model, the dengue risk was related to householders aged >45 years (aOR = 3.24, P = 0.003), secondary and higher educational degrees (aOR = 2.33, P = 0.013), household members >4 persons (aOR = 2.01, P = 0.02), and community effort in environmental management by clean-up campaign (aOR = 1.91, P = 0.035). It is possible that the preventive measures were positively correlated with dengue risk because these activities were generally carried out in particular households or communities following dengue experiences or dengue outbreaks. Interestingly, the ecotope of RCDENPURA and high historical dengue risk area appeared to be very good predictors of dengue incidences.