Effect of Rainfall for the Dynamical Transmission Model of the Dengue Disease in Thailand

The SEIR (Susceptible-Exposed-Infected-Recovered) model is used to describe the transmission of dengue virus. The main contribution is determining the role of the rainfall in Thailand in the model. The transmission of dengue disease is assumed to depend on the nature of the rainfall in Thailand. We analyze the dynamic transmission of dengue disease. The stability of the solution of the model is analyzed. It is investigated by using the Routh-Hurwitz criteria. We find two equilibrium states: a disease-free state and an endemic equilibrium state. The basic reproductive number (R0) is obtained, which indicates the stability of each equilibrium state. Numerical results taking into account the rainfall are obtained and they are seen to correspond to the analytical results

The impact of the demographic transition on dengue in Thailand: Insights from a statistical analysis and mathematical modeling

Background: An increase in the average age of dengue hemorrhagic fever (DHF) cases has been reported in Thailand. The cause of this increase is not known. Possible explanations include a reduction in transmission due to declining mosquito populations, declining contact between human and mosquito, and changes in reporting. We propose that a demographic shift toward lower birth and death rates has reduced dengue transmission and lengthened the interval between large epidemics. Methods and Findings: Using data from each of the 72 provinces of Thailand, we looked for associations between force of infection (a measure of hazard, defined as the rate per capita at which susceptible individuals become infected) and demographic and climactic variables. We estimated the force of infection from the age distribution of cases from 1985 to 2005. We find that the force of infection has declined by 2% each year since a peak in the late 1970s and early 1980s. Contrary to recent findings suggesting that the incidence of DHF has increased in Thailand, we find a small but statistically significant decline in DHF incidence since 1985 in a majority of provinces. The strongest predictor of the change in force of infection and the mean force of infection is the median age of the population. Using mathematical simulations of dengue transmission we show that a reduced birth rate and a shift in the population's age structure can explain the shift in the age distribution of cases, reduction of the force of infection, and increase in the periodicity of multiannual oscillations of DHF incidence in the absence of other changes. Conclusions: Lower birth and death rates decrease the flow of susceptible individuals into the population and increase the longevity of immune individuals. The increase in the proportion of the population that is immune increases the likelihood that an infectious mosquito will feed on an immune individual, reducing the force of infection. Though the force of infection has decreased by half, we find that the critical vaccination fraction has not changed significantly, declining from an average of 85% to 80%. Clinical guidelines should consider the impact of continued increases in the age of dengue cases in Thailand. Countries in the region lagging behind Thailand in the demographic transition may experience the same increase as their population ages. The impact of demographic changes on the force of infection has been hypothesized for other diseases, but, to our knowledge, this is the first observation of this phenomenon

The 2012 Madeira dengue outbreak: epidemiological determinants and future epidemic potential

Published onlineJournal ArticleResearch Support, Non-U.S. Gov'tDengue, a vector-borne viral disease of increasing global importance, is classically associated with tropical and sub-tropical regions around the world. Urbanisation, globalisation and climate trends, however, are facilitating the geographic spread of its mosquito vectors, thereby increasing the risk of the virus establishing itself in previously unaffected areas and causing large-scale epidemics. On 3 October 2012, two autochthonous dengue infections were reported within the Autonomous Region of Madeira, Portugal. During the following seven months, this first 'European' dengue outbreak caused more than 2000 local cases and 81 exported cases to mainland Europe. Here, using an ento-epidemiological mathematical framework, we estimate that the introduction of dengue to Madeira occurred around a month before the first official cases, during the period of maximum influx of airline travel, and that the naturally declining temperatures of autumn were the determining factor for the outbreak's demise in early December 2012. Using key estimates, together with local climate data, we further propose that there is little support for dengue endemicity on this island, but a high potential for future epidemic outbreaks when seeded between May and August-a period when detection of imported cases is crucial for Madeira's public health planning.The work was funded by the Royal Society (URF to MR)

MATHEMATICAL MODEL OF DENGUE CONTROL WITH CONTROL OF MOSQUITO LARVAE AND MOSQUITO AFFECTED BY CLIMATE CHANGE

Consider a SIR model for the spread of dengue hemorrhagic fever involving three populations, mosquito eggs, mosquitoes, and humans. The parameters of the SIR model were estimated using rainfall data and air temperature for the cities of Pekanbaru and Solok. The main aim of this paper is to determine the effect of mosquito larvae and adult mosquito control on the spread of the dengue virus. Numerical solutions were also presented by using the Runge-Kutta method of order 4. Based on the results, the SIR model was obtained by involving the control parameters of mosquito larvae and adult mosquitoes. Besides, the mosquito population is affected by changes in temperature, rainfall, and fog. Numerical simulations illustrate that the number of infected mosquitoes and infected humans is influenced by the parameters of the percentage of mortality of mosquito larvae and adult mosquitoes

Forcing Versus Feedback: Epidemic Malaria and Monsoon Rains in Northwest India

Malaria epidemics in regions with seasonal windows of transmission can vary greatly in size from year to year. A central question has been whether these interannual cycles are driven by climate, are instead generated by the intrinsic dynamics of the disease, or result from the resonance of these two mechanisms. This corresponds to the more general inverse problem of identifying the respective roles of external forcings vs. internal feedbacks from time series for nonlinear and noisy systems. We propose here a quantitative approach to formally compare rival hypotheses on climate vs. disease dynamics, or external forcings vs. internal feedbacks, that combines dynamical models with recently developed, computational inference methods. The interannual patterns of epidemic malaria are investigated here for desert regions of northwest India, with extensive epidemiological records for Plasmodium falciparum malaria for the past two decades. We formulate a dynamical model of malaria transmission that explicitly incorporates rainfall, and we rely on recent advances on parameter estimation for nonlinear and stochastic dynamical systems based on sequential Monte Carlo methods. Results show a significant effect of rainfall in the inter-annual variability of epidemic malaria that involves a threshold in the disease response. The model exhibits high prediction skill for yearly cases in the malaria transmission season following the monsoonal rains. Consideration of a more complex model with clinical immunity demonstrates the robustness of the findings and suggests a role of infected individuals that lack clinical symptoms as a reservoir for transmission. Our results indicate that the nonlinear dynamics of the disease itself play a role at the seasonal, but not the interannual, time scales. They illustrate the feasibility of forecasting malaria epidemics in desert and semi-arid regions of India based on climate variability. This approach should be applicable to malaria in other locations, to other infectious diseases, and to other nonlinear systems under forcing

Dengue outlook for the World Cup in Brazil: an early warning model framework driven by real-time seasonal climate forecasts.

PublishedJournal ArticleResearch Support, Non-U.S. Gov'tBACKGROUND: With more than a million spectators expected to travel among 12 different cities in Brazil during the football World Cup, June 12-July 13, 2014, the risk of the mosquito-transmitted disease dengue fever is a concern. We addressed the potential for a dengue epidemic during the tournament, using a probabilistic forecast of dengue risk for the 553 microregions of Brazil, with risk level warnings for the 12 cities where matches will be played. METHODS: We obtained real-time seasonal climate forecasts from several international sources (European Centre for Medium-Range Weather Forecasts [ECMWF], Met Office, Meteo-France and Centro de Previsão de Tempo e Estudos Climáticos [CPTEC]) and the observed dengue epidemiological situation in Brazil at the forecast issue date as provided by the Ministry of Health. Using this information we devised a spatiotemporal hierarchical Bayesian modelling framework that enabled dengue warnings to be made 3 months ahead. By assessing the past performance of the forecasting system using observed dengue incidence rates for June, 2000-2013, we identified optimum trigger alert thresholds for scenarios of medium-risk and high-risk of dengue. FINDINGS: Our forecasts for June, 2014, showed that dengue risk was likely to be low in the host cities Brasília, Cuiabá, Curitiba, Porto Alegre, and São Paulo. The risk was medium in Rio de Janeiro, Belo Horizonte, Salvador, and Manaus. High-risk alerts were triggered for the northeastern cities of Recife (p(high)=19%), Fortaleza (p(high)=46%), and Natal (p(high)=48%). For these high-risk areas, particularly Natal, the forecasting system did well for previous years (in June, 2000-13). INTERPRETATION: This timely dengue early warning permits the Ministry of Health and local authorities to implement appropriate, city-specific mitigation and control actions ahead of the World Cup. FUNDING: European Commission's Seventh Framework Research Programme projects DENFREE, EUPORIAS, and SPECS; Conselho Nacional de Desenvolvimento Científico e Tecnológico and Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro.DENFREE projectEUPORIAS projectSPECS projectEuropean Commission's Seventh Framework Research ProgrammeConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado do Rio de Janeir

The effects of temperature forcing on dengue dynamics via the extrinsic incubation period

Dengue fever is a mosquito-transmitted disease that is endemic in many parts of the tropical world and affects a significant proportion of the human population. Temperature is known to influence aspects of the dengue transmission cycle, which has consequences for disease dynamics. Previous work has explored the effects of temperature on the mortality rate of the mosquito and the resulting population change. However, there is substantial evidence that the extrinsic incubation period (EIP) of the pathogen within the vector host, Aedes aegypti, is also temperature dependent. This dependence has not been thoroughly researched. We present a single serotype compartmental model with a gamma-distributed exposed vector class to account for a temperature-dependent EIP. Where appropriate, temperature-dependent vector mortality is convolved with the temperature dependent EIP using the mortality function presented by Yang et al. [49]. Both seasonal and diurnal temperature changes are examined for their potential effects upon dengue persistence. The mean and range of temperature fluctuations that facilitate persistence are presented based upon the EIP function, initial conditions, seasonal temperature forcing with and without vector mortality, as well as seasonal and diurnal temperature forcing with and without vector mortality. With seasonal forcing and temperature dependence only in the EIP, all simulations with mean temperatures above 26 C show persistence. However, if vector mortality is also variable, persistence is no longer possible in higher temperatures with higher temperature ranges. Diurnal forcing exacerbates this effect limiting persistence to mean temperatures of 23 C to 34 C with variable temperature ranges. It is clear that more data are needed to reduce the uncertainty in estimating the relationships between both EIP and vector mortality because these relationships can have large effects on disease dynamics. Additionally, this work demonstrates that when modeling temperature-dependent effects, it is vital to not only include seasonal variation in temperature but also diurnal variation

Mathematics of Climate Change and Mosquito-borne Disease Dynamics

abstract: The role of climate change, as measured in terms of changes in the climatology of geophysical variables (such as temperature and rainfall), on the global distribution and burden of vector-borne diseases (VBDs) remains a subject of considerable debate. This dissertation attempts to contribute to this debate via the use of mathematical (compartmental) modeling and statistical data analysis. In particular, the objective is to find suitable values and/or ranges of the climate variables considered (typically temperature and rainfall) for maximum vector abundance and consequently, maximum transmission intensity of the disease(s) they cause. Motivated by the fact that understanding the dynamics of disease vector is crucial to understanding the transmission and control of the VBDs they cause, a novel weather-driven deterministic model for the population biology of the mosquito is formulated and rigorously analyzed. Numerical simulations, using relevant weather and entomological data for Anopheles mosquito (the vector for malaria), show that maximum mosquito abundance occurs when temperature and rainfall values lie in the range [20-25]C and [105-115] mm, respectively. The Anopheles mosquito ecology model is extended to incorporate human dynamics. The resulting weather-driven malaria transmission model, which includes many of the key aspects of malaria (such as disease transmission by asymptomatically-infectious humans, and enhanced malaria immunity due to repeated exposure), was rigorously analyzed. The model which also incorporates the effect of diurnal temperature range (DTR) on malaria transmission dynamics shows that increasing DTR shifts the peak temperature value for malaria transmission from 29C (when DTR is 0C) to about 25C (when DTR is 15C). Finally, the malaria model is adapted and used to study the transmission dynamics of chikungunya, dengue and Zika, three diseases co-circulating in the Americas caused by the same vector (Aedes aegypti). The resulting model, which is fitted using data from Mexico, is used to assess a few hypotheses (such as those associated with the possible impact the newly-released dengue vaccine will have on Zika) and the impact of variability in climate variables on the dynamics of the three diseases. Suitable temperature and rainfall ranges for the maximum transmission intensity of the three diseases are obtained.Dissertation/ThesisDoctoral Dissertation Applied Mathematics 201