Comparing vector–host and SIR models for dengue transmission

Various simple mathematical models have been used to investigate dengue transmission. Some of these models explicitly model the mosquito population, while others model the mosquitoes implicitly in the transmission term. We study the impact of modeling assumptions on the dynamics of dengue in Thailand by fitting dengue hemorrhagic fever (DHF) data to simple vector–host and SIR models using Bayesian Markov chain Monte Carlo estimation. The parameter estimates obtained for both models were consistent with previous studies. Most importantly, model selection found that the SIR model was substantially better than the vector–host model for the DHF data from Thailand. Therefore, explicitly incorporating the mosquito population may not be necessary in modeling dengue transmission for some populations.     

Follow up estimation of Aedes aegypti entomological parameters and mathematical modellings

The dengue virus is a vector-borne disease transmitted by mosquito Aedes aegypti and the incidence is strongly influenced by temperature and humidity which vary seasonally. To assess the effects of temperature on dengue transmission, mathematical models are developed based on the population dynamics theory. However, depending on the hypotheses of the modelling, different outcomes regarding to the risk of epidemics are obtained. We address this question comparing two simple models supplied with model's parameters estimated from temperature-controlled experiments, especially the entomological parameters regarded to the mosquito's life cycle in different temperatures. Once obtained the mortality and transition rates of different stages comprising the life cycle of mosquito and the oviposition rate, we compare the capacity of vector reproduction (the basic offspring number) and the risk of infection (basic reproduction number) provided by two models. The extended model, which is more realistic, showed that both mosquito population and dengue risk are situated at higher values than the simplified model, even that the basic offspring number is lower.     

An ensemble forecast system for tracking dynamics of dengue outbreaks and its validation in China

As a common vector-borne disease, dengue fever remains challenging to predict due to large variations in epidemic size across seasons driven by a number of factors including population susceptibility, mosquito density, meteorological conditions, geographical factors, and human mobility. An ensemble forecast system for dengue fever is first proposed that addresses the difficulty of predicting outbreaks with drastically different scales. The ensemble forecast system based on a susceptible-infected-recovered (SIR) type of compartmental model coupled with a data assimilation method called the ensemble adjusted Kalman filter (EAKF) is constructed to generate real-time forecasts of dengue fever spread dynamics. The model was informed by meteorological and mosquito density information to depict the transmission of dengue virus among human and mosquito populations, and generate predictions. To account for the dramatic variations of outbreak size in different seasons, the effective population size parameter that is sequentially updated to adjust the predicted outbreak scale is introduced into the model. Before optimizing the transmission model, we update the effective population size using the most recent observations and historical records so that the predicted outbreak size is dynamically adjusted. In the retrospective forecast of dengue outbreaks in Guangzhou, China during the 2011–2017 seasons, the proposed forecast model generates accurate projections of peak timing, peak intensity, and total incidence, outperforming a generalized additive model approach. The ensemble forecast system can be operated in real-time and inform control planning to reduce the burden of dengue fever.     

Assessing the suitability for Aedes albopictus and dengue transmission risk in China with a delay differential equation model

Dengue is considered non-endemic to mainland China. However, travellers frequently import the virus from overseas and local mosquito species can then spread the disease in the population. As a consequence, mainland China still experiences large dengue outbreaks. Temperature plays a key role in these outbreaks: it affects the development and survival of the vector and the replication rate of the virus. To better understand its implication in the transmission risk of dengue, we developed a delay differential equation model that explicitly simulates temperature-dependent development periods and tested it with collected field data for the Asian tiger mosquito, Aedes albopictus. The model predicts mosquito occurrence locations with a high accuracy (Cohen’s κ of 0.78) and realistically replicates mosquito population dynamics. Analysing the infection dynamics during the 2014 dengue outbreak that occurred in Guangzhou showed that the outbreak could have lasted for another four weeks if mosquito control interventions had not been undertaken. Finally, we analyse the dengue transmission risk in mainland China. We find that southern China, including Guangzhou, can have more than seven months of dengue transmission per year while even Beijing, in the temperate north, can have dengue transmission during hot summer months. The results demonstrate the importance of using detailed vector and infection ecology, especially when vector-borne disease transmission risk is modelled over a broad range of climatic zones.     

Describing the geographic spread of dengue disease by traveling waves

Dengue is a human disease transmitted by the mosquito Aedes aegypti. For this reason geographical regions infested by this mosquito species are under the risk of dengue outbreaks. In this work, we propose a mathematical model to study the spatial dissemination of dengue using a system of partial differential reaction-diffusion equations. With respect to the human and mosquito populations, we take into account their respective subclasses of infected and uninfected individuals. The dynamics of the mosquito population considers only two subpopulations: the winged form (mature female mosquitoes), and an aquatic population (comprising eggs, larvae and pupae). We disregard the long-distance movement by transportation facilities, for which reason the diffusion is considered restricted only to the winged form. The human population is considered homogeneously distributed in space, in order to describe localized dengue dissemination during a short period of epidemics. The cross-infection is modeled by the law of mass action. A threshold value as a function of the model's parameters is obtained, which determines the rate of dengue dissemination and the risk of dengue outbreaks. Assuming that an area was previously colonized by the mosquitoes, the rate of disease dissemination is determined as a function of the model's parameters. This rate of dissemination of dengue disease is determined by applying the traveling wave solutions to the corresponding system of partial differential equations.     

Modelling and analysis of impulsive releases of sterile mosquitoes

To study the impact of releasing sterile mosquitoes on mosquito-borne disease transmissions, we propose two mathematical models with impulsive releases of sterile mosquitoes. We consider periodic impulsive releases in the first model and obtain the existence, uniqueness, and globally stability of a wild-mosquito-eradication periodic solution. We also establish thresholds for the control of the wild mosquito population by selecting the release rate and the release period. In the second model, the impulsive releases are determined by the closely monitored wild mosquito density, or the state feedback. We prove the existence of an order one periodic solution and find a relatively small attraction region, which ensures the wild mosquito population is under control. We provide numerical analysis which shows that a smaller release rate and more frequent releases are more efficient in controlling the wild mosquito population for the periodic releases, but an early release of sterile mosquitoes is more effective for the state feedback releases.     

An accurate mathematical model predicting number of dengue cases in tropics

Dengue fever is a systemic viral infection of epidemic proportions in tropical countries. The incidence of dengue fever is ever increasing and has doubled over the last few decades. Estimated 50million new cases are detected each year and close to 10000 deaths occur each year. Epidemics are unpredictable and unprecedented. When epidemics occur, health services are over whelmed leading to overcrowding of hospitals. At present there is no evidence that dengue epidemics can be predicted. Since the breeding of the dengue mosquito is directly influenced by environmental factors, it is plausible that epidemics could be predicted using weather data. We hypothesized that there is a mathematical relationship between incidence of dengue fever and environmental factors and if such relationship exists, new cases of dengue fever in the succeeding months can be predicted using weather data of the current month. We developed a mathematical model using machine learning technique. We used Island wide dengue epidemiology data, weather data and population density in developing the model. We used incidence of dengue fever, average rain fall, humidity, wind speed, temperature and population density of each district in the model. We found that the model is able to predict the incidence of dengue fever of a given month in a given district with precision (RMSE between 18- 35.3). Further, using weather data of a given month, the number of cases of dengue in succeeding months too can be predicted with precision (RMSE 10.4—30). Health authorities can use existing weather data in predicting epidemics in the immediate future and therefore measures to prevent new cases can be taken and more importantly the authorities can prepare local authorities for outbreaks.     

Linking mosquito surveillance to dengue fever through Bayesian mechanistic modeling

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

Meteorologically Driven Simulations of Dengue Epidemics in San Juan,PR

Meteorological factors influence dengue virus ecology by modulating vector mosquito population dynamics, viral replication, and transmission. Dynamic modeling techniques can be used to examine how interactions among meteorological variables, vectors and the dengue virus influence transmission. We developed a dengue fever simulation model by coupling a dynamic simulation model for Aedes aegypti, the primary mosquito vector for dengue, with a basic epidemiological Susceptible-Exposed-Infectious-Recovered (SEIR) model. Employing a Monte Carlo approach, we simulated dengue transmission during the period of 2010–2013 in San Juan, PR, where dengue fever is endemic. The results of 9600 simulations using varied model parameters were evaluated by statistical comparison (r²) with surveillance data of dengue cases reported to the Centers for Disease Control and Prevention. To identify the most influential parameters associated with dengue virus transmission for each period the top 1% of best-fit model simulations were retained and compared. Using the top simulations, dengue cases were simulated well for 2010 (r² = 0.90, p = 0.03), 2011 (r² = 0.83, p = 0.05), and 2012 (r² = 0.94, p = 0.01); however, simulations were weaker for 2013 (r² = 0.25, p = 0.25) and the entire four-year period (r² = 0.44, p = 0.002). Analysis of parameter values from retained simulations revealed that rain dependent container habitats were more prevalent in best-fitting simulations during the wetter 2010 and 2011 years, while human managed (i.e. manually filled) container habitats were more prevalent in best-fitting simulations during the drier 2012 and 2013 years. The simulations further indicate that rainfall strongly modulates the timing of dengue (e.g., epidemics occurred earlier during rainy years) while temperature modulates the annual number of dengue fever cases. Our results suggest that meteorological factors have a time-variable influence on dengue transmission relative to other important environmental and human factors.     

Modeled response of the West Nile virus vector Culex quinquefasciatus to changing climate using the dynamic mosquito simulation model

Climate can strongly influence the population dynamics of disease vectors and is consequently a key component of disease ecology. Future climate change and variability may alter the location and seasonality of many disease vectors, possibly increasing the risk of disease transmission to humans. The mosquito species Culex quinquefasciatus is a concern across the southern United States because of its role as a West Nile virus vector and its affinity for urban environments. Using established relationships between atmospheric variables (temperature and precipitation) and mosquito development, we have created the Dynamic Mosquito Simulation Model (DyMSiM) to simulate Cx. quinquefasciatus population dynamics. The model is driven with climate data and validated against mosquito count data from Pasco County, Florida and Coachella Valley, California. Using 1-week and 2-week filters, mosquito trap data are reproduced well by the model (P < 0.0001). Dry environments in southern California produce different mosquito population trends than moist locations in Florida. Florida and California mosquito populations are generally temperature-limited in winter. In California, locations are water-limited through much of the year. Using future climate projection data generated by the National Center for Atmospheric Research CCSM3 general circulation model, we applied temperature and precipitation offsets to the climate data at each location to evaluate mosquito population sensitivity to possible future climate conditions. We found that temperature and precipitation shifts act interdependently to cause remarkable changes in modeled mosquito population dynamics. Impacts include a summer population decline from drying in California due to loss of immature mosquito habitats, and in Florida a decrease in late-season mosquito populations due to drier late summer conditions.     

Knowledge, awareness and practices regarding dengue fever among the adult population of dengue hit cosmopolitan

Background

The World health Organization (WHO) declares dengue and dengue hemorrhagic fever to be endemic in South Asia. Despite the magnitude of problem, no documented evidence exists in Pakistan which reveals the awareness and practices of the country''s adult population regarding dengue fever, its spread, symptoms, treatment and prevention. This study was conducted to assess the level of knowledge, attitudes and practices regarding dengue fever in people visiting tertiary care hospitals in Karachi, Pakistan.

Methods

A cross-sectional pilot study was conducted among people visiting tertiary care hospitals in Karachi. Through convenience sampling, a pre-tested and structured questionnaire was administered through a face-to-face unprompted interview with 447 visitors. Knowledge was recorded on a scale of 1–3.

Results

About 89.9% of individuals interviewed had heard of dengue fever. Sufficient knowledge about dengue was found to be in 38.5% of the sample, with 66% of these in Aga Khan University Hospital and 33% in Civil Hospital Karachi. Literate individuals were relatively more well-informed about dengue fever as compared to the illiterate people (p<0.001). Knowledge based upon preventive measures was found to be predominantly focused towards prevention of mosquito bites (78.3%) rather than eradication of mosquito population (17.3%). Use of anti- mosquito spray was the most prevalent (48.1%) preventive measure. Television was considered as the most important and useful source of information on the disease.

Conclusion

Adult population of Karachi has adequate knowledge related to the disease ‘dengue’ on isolated aspects, but the overall prevalence of ‘sufficient knowledge’ based on our criteria is poor. We demonstrated adequate prevalence of preventive practices against the disease. Further studies correlating the association between knowledge and its effectiveness against dengue will be helpful in demonstrating the implications of awareness campaigns.     

A decade of colonization: the spread of the Asian tiger mosquito in Pennsylvania and implications for disease risk

In recent decades, the Asian tiger mosquito expanded its geographic range throughout the northeastern United States, including Pennsylvania. The establishment of Aedes albopictus in novel areas raises significant public health concerns, since this species is a highly competent vector of several arboviruses, including chikungunya, West Nile, and dengue. In this study, we used geographic information systems (GIS) to examine a decade of colonization by Ae. albopictus throughout Pennsylvania between 2001 and 2010. We examined the spatial and temporal distribution of Ae. albopictus using spatial statistical analysis and examined the risk of dengue virus transmission using a model that captures the probability of transmission. Our findings show that since 2001, the Ae. albopictus population in Pennsylvania has increased, becoming established and expanding in range throughout much of the state. Since 2010, imported cases of dengue fever have been recorded in Pennsylvania. Imported cases of dengue, in combination with summer temperatures conducive for virus transmission, raise the risk of local disease transmission.     

Malaria model with periodic mosquito birth and death rates

In this paper, we introduce a model of malaria, a disease that involves a complex life cycle of parasites, requiring both human and mosquito hosts. The novelty of the model is the introduction of periodic coefficients into the system of one-dimensional equations, which account for the seasonal variations (wet and dry seasons) in the mosquito birth and death rates. We define a basic reproduction number R(0) that depends on the periodic coefficients and prove that if R(0)<1 then the disease becomes extinct, whereas if R(0)>1 then the disease is endemic and may even be periodic.     

Predicting Local Dengue Transmission in Guangzhou,China, through the Influence of Imported Cases,Mosquito Density and Climate Variability

Introduction

Each year there are approximately 390 million dengue infections worldwide. Weather variables have a significant impact on the transmission of Dengue Fever (DF), a mosquito borne viral disease. DF in mainland China is characterized as an imported disease. Hence it is necessary to explore the roles of imported cases, mosquito density and climate variability in dengue transmission in China. The study was to identify the relationship between dengue occurrence and possible risk factors and to develop a predicting model for dengue’s control and prevention purpose.

Methodology and Principal Findings

Three traditional suburbs and one district with an international airport in Guangzhou city were selected as the study areas. Autocorrelation and cross-correlation analysis were used to perform univariate analysis to identify possible risk factors, with relevant lagged effects, associated with local dengue cases. Principal component analysis (PCA) was applied to extract principal components and PCA score was used to represent the original variables to reduce multi-collinearity. Combining the univariate analysis and prior knowledge, time-series Poisson regression analysis was conducted to quantify the relationship between weather variables, Breteau Index, imported DF cases and the local dengue transmission in Guangzhou, China. The goodness-of-fit of the constructed model was determined by pseudo-R², Akaike information criterion (AIC) and residual test. There were a total of 707 notified local DF cases from March 2006 to December 2012, with a seasonal distribution from August to November. There were a total of 65 notified imported DF cases from 20 countries, with forty-six cases (70.8%) imported from Southeast Asia. The model showed that local DF cases were positively associated with mosquito density, imported cases, temperature, precipitation, vapour pressure and minimum relative humidity, whilst being negatively associated with air pressure, with different time lags.

Conclusions

Imported DF cases and mosquito density play a critical role in local DF transmission, together with weather variables. The establishment of an early warning system, using existing surveillance datasets will help to control and prevent dengue in Guangzhou, China.     

Interaction of Mean Temperature and Daily Fluctuation Influences Dengue Incidence in Dhaka,Bangladesh

Local weather influences the transmission of the dengue virus. Most studies analyzing the relationship between dengue and climate are based on relatively coarse aggregate measures such as mean temperature. Here, we include both mean temperature and daily fluctuations in temperature in modelling dengue transmission in Dhaka, the capital of Bangladesh. We used a negative binomial generalized linear model, adjusted for rainfall, anomalies in sea surface temperature (an index for El Niño-Southern Oscillation), population density, the number of dengue cases in the previous month, and the long term temporal trend in dengue incidence. In addition to the significant associations of mean temperature and temperature fluctuation with dengue incidence, we found interaction of mean and temperature fluctuation significantly influences disease transmission at a lag of one month. High mean temperature with low fluctuation increases dengue incidence one month later. Besides temperature, dengue incidence was also influenced by sea surface temperature anomalies in the current and previous month, presumably as a consequence of concomitant anomalies in the annual rainfall cycle. Population density exerted a significant positive influence on dengue incidence indicating increasing risk of dengue in over-populated Dhaka. Understanding these complex relationships between climate, population, and dengue incidence will help inform outbreak prediction and control.     

The climatic factors affecting dengue fever outbreaks in southern Taiwan: an application of symbolic data analysis

Background

Dengue fever is a leading cause of severe illness and hospitalization in Taiwan. This study sought to elucidate the linkage between dengue fever incidence and climate factors.

Results

The result indicated that temperature, accumulated rainfall, and sunshine play an important role in the transmission cycles of dengue fever. A predictive model equation plots dengue fever incidence versus temperature, rainfall, and sunshine, and it suggests that temperature, rainfall, and sunshine are significantly correlated with dengue fever incidence.

Conclusions

The data suggests that climate factors are important determinants of dengue fever in southern Taiwan. Dengue fever viruses and the mosquito vectors are sensitive to their environment. Temperature, rainfall and sunshine have well-defined roles in the transmission cycle. This finding suggests that control of mosquito by climatic factor during high temperature seasons may be an important strategy for containing the burden of dengue fever.

     

Threshold Conditions for a Non-Autonomous Epidemic System Describing the Population Dynamics of Dengue

A non-autonomous dynamical system, in which the seasonal variation of a mosquito vector population is modeled, is proposed to investigate dengue overwintering. A time-dependent threshold, R(t), is deduced such that when its yearly average, denoted by , is less than 1, the disease does not invade the populations and when is greater than 1 it does. By not invading the population we mean that the number of infected individuals always decrease in subsequent seasons of transmission. Using the same threshold, all the qualitative features of the resulting epidemic can be understood. Our model suggests that trans-ovarial infection in the mosquitoes facilitates dengue overwintering. We also explain the delay between the peak in the mosquitoes population and the peak in dengue cases. An erratum to this article can be found at     

Climate Change,Population Immunity,and Hyperendemicity in the Transmission Threshold of Dengue

Background

It has been suggested that the probability of dengue epidemics could increase because of climate change. The probability of epidemics is most commonly evaluated by the basic reproductive number (R₀), and in mosquito-borne diseases, mosquito density (the number of female mosquitoes per person [MPP]) is the critical determinant of the R₀ value. In dengue-endemic areas, 4 different serotypes of dengue virus coexist–a state known as hyperendemicity–and a certain proportion of the population is immune to one or more of these serotypes. Nevertheless, these factors are not included in the calculation of R₀. We aimed to investigate the effects of temperature change, population immunity, and hyperendemicity on the threshold MPP that triggers an epidemic.

Methods and Findings

We designed a mathematical model of dengue transmission dynamics. An epidemic was defined as a 10% increase in seroprevalence in a year, and the MPP that triggered an epidemic was defined as the threshold MPP. Simulations were conducted in Singapore based on the recorded temperatures from 1980 to 2009 The threshold MPP was estimated with the effect of (1) temperature only; (2) temperature and fluctuation of population immunity; and (3) temperature, fluctuation of immunity, and hyperendemicity. When only the effect of temperature was considered, the threshold MPP was estimated to be 0.53 in the 1980s and 0.46 in the 2000s, a decrease of 13.2%. When the fluctuation of population immunity and hyperendemicity were considered in the model, the threshold MPP decreased by 38.7%, from 0.93 to 0.57, from the 1980s to the 2000s.

Conclusions

The threshold MPP was underestimated if population immunity was not considered and overestimated if hyperendemicity was not included in the simulations. In addition to temperature, these factors are particularly important when quantifying the threshold MPP for the purpose of setting goals for vector control in dengue-endemic areas.     

Malaria model with periodic mosquito birth and death rates

In this paper, we introduce a model of malaria, a disease that involves a complex life cycle of parasites, requiring both human and mosquito hosts. The novelty of the model is the introduction of periodic coefficients into the system of one-dimensional equations, which account for the seasonal variations (wet and dry seasons) in the mosquito birth and death rates. We define a basic reproduction number R ₀ that depends on the periodic coefficients and prove that if R ₀<1 then the disease becomes extinct, whereas if R ₀>1 then the disease is endemic and may even be periodic.