7,657 research outputs found

    Dengue disease, basic reproduction number and control

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    Dengue is one of the major international public health concerns. Although progress is underway, developing a vaccine against the disease is challenging. Thus, the main approach to fight the disease is vector control. A model for the transmission of Dengue disease is presented. It consists of eight mutually exclusive compartments representing the human and vector dynamics. It also includes a control parameter (insecticide) in order to fight the mosquito. The model presents three possible equilibria: two disease-free equilibria (DFE) and another endemic equilibrium. It has been proved that a DFE is locally asymptotically stable, whenever a certain epidemiological threshold, known as the basic reproduction number, is less than one. We show that if we apply a minimum level of insecticide, it is possible to maintain the basic reproduction number below unity. A case study, using data of the outbreak that occurred in 2009 in Cape Verde, is presented.Comment: This is a preprint of a paper whose final and definitive form has appeared in International Journal of Computer Mathematics (2011), DOI: 10.1080/00207160.2011.55454

    The Effects of Fogging and Mosquito Repellent on the Probability of Disease Extinction for Dengue Fever

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    A Continuous-Time Markov Chain model is constructed based on the a deterministic model of dengue fever transmission including mosquito fogging and the use of repellent. The basic reproduction number (R0) for the corresponding deterministic model is obtained. This number indicates the possible occurrence of an endemic at the early stages of the infection period. A multitype branching process is used to approximate the Markov chain. The construction of offspring probability generating functions related to the infected states is used to calculate the probability of disease extinction and the probability of an outbreak (P0). Sensitivity analysis is shown for variation of control parameters and for indices of the basic reproduction number. These results allow for a better understanding of the relation of the basic reproduction number with other indicators of disease transmission

    Modeling and optimal control of dengue disease with screening and information

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    This study presents a mathematical model for dengue transmission which quantifies two very important aspects: one, the impact of information-based behavioural response, and the other, the segregation of infected human population into two subclasses, ‘detected’ and ‘undetected’. For the proposed model, the sensitivity analysis is conducted to identify the key model parameters which not only influence the basic reproduction number, but also regulate the transmission of dengue. Further, in order to find the optimal pathways for suitable control interventions that reduce the dengue prevalence and economic burden, an optimal control problem is proposed by considering information-induced behavioural change, quarantine, screening, use of repulsive measures and culling of mosquitoes as control interventions. A weighted sum of various costs incurred in applied controls and the cost due to dengue disease (productivity loss) is incorporated in the proposed cost functional. The analysis of control system using Pontryagin’s maximum principle leads the existence of the optimal control profiles. Further, an exhaustive comparative study for seven different control strategies is conducted numerically. Our findings emphasize that every individual control strategy has their own impact on reducing the cumulative count of infection as well as cost. The combined impact of all control interventions is highly effective and economically viable in controlling the prevalence of dengue. We also investigated the effect of the basic reproduction number on the designed control strategies and observed that the comprehensive use of controls keeps a strong tab on the infective even if the severity of epidemic is high

    Optimal control on education, vaccination, and treatment in the model of dengue hemorrhagic fever

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    Dengue hemorrhagic fever (DHF) is an infection caused by the dengue virus which is transmitted by the Aedes aegypti mosquito. In this paper, a model of the spread of dengue disease is developed using optimal control theory by dividing the population into Susceptible, Exposed, Infected, and Recovered (SEIR) sub-populations. The Pontryagin minimum principle of the fourth-order Runge-Kutta method is used in the model of the spread of dengue disease by incorporating control factors in the form of education and vaccination of susceptible human populations, as well as treatment of infected human populations. Optimum control aims to minimize the infected human population in order to reduce the spread of DHF. Simulations were carried out for two cases, namely when the basic reproduction number   is less than one for disease-free conditions and  greater than one for endemic conditions. Based on numerical simulations of the SEIR epidemic model with controls, it results that the optimal strategy is achieved if education controls, vaccinations, and medication are used

    A patchy model for Chikungunya-like diseases

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    We consider a n-patches model, to study the impact of human population movements between cities (patches) in the spread of Chikungunya or even Dengue diseases. In previous works, it was showed that the basic reproduction number can vary from place to place, but this result was obtained without taking into account human movements. We provide a theoretical study of the patchy model, and derive the basic reproduction number, which may depend on Human movement rates between the patches and on local population sizes. We show that the basic reproduction number is bounded by the maximum of local basic reproduction number. We also show that there exists a disease-free equilibrium (DFE) that is locally asymptotically stable whenever the basic reproduction number is less than 1. Under suitable assumptions, DFE is even globally asymptotically stable. We emphasize that Human movements are of particular importance to evaluate the spreading or not of Chikungunya or Dengue diseases, and thus movement rates have to be estimated very accurately. We confirm also the importance of the local basic reproduction numbers and show that even local field interventions can be of benefit to control/reduce the spread of a disease. A complete analytical study for a 2-patches model and several examples are provided to illustrate our conclusion

    Control of dengue disease: a case study in Cape Verde

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    Preprint. The published version is: Proceedings of the 10th International Conference on Computational and Mathematical Methods in Science and Engineering (CMMSE 2010), Almería (Andalucía), Spain, June 26-30 2010, 816–822.A model for the transmission of dengue disease is presented. It consists of eight mutually-exclusive compartments representing the human and vector dynamics. It also includes a control parameter (adulticide spray) in order to combat the mosquito. The model presents three possible equilibria: two disease-free equilibria (DFE) — where humans, with or without mosquitoes, live without the disease — and another endemic equilibrium (EE). In the literature it has been proved that a DFE is locally asymptotically stable, whenever a certain epidemiological threshold, known as the basic reproduction number, is less than one. We show that if a minimum level of insecticide is applied, then it is possible to maintain the basic reproduction number below unity. A case study, using data of the outbreak that occured in 2009 in Cape Verde, is presented.Fundação para a Ciência e a Tecnologia (FCT

    ANALISIS MODEL SIR-ASI PADA PENYAKIT DEMAM BERDARAH DENGUE

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    Dengue Hemorrhagic Fever (DHF) is a disease caused by dengue virus infection through the bite of the Aedes Aegypti mosquito. The high number of cases of DBD from year to year has become a major health problem in Indonesia. DBD can be modeled using mathematical modeling to understand the dynamics of disease spread through the stability of the equilibrium point and optimal control of the problem of DBD transmission. The DBD model is classified into 2 types of classes: the human population class and the mosquito class. There are three subclasses for the human population class: the susceptible population, the infected population, and the recovered population. Meanwhile, the mosquito population class is divided into three subclasses, namely the aquatic population, the susceptible population, and the infected population. The aims of this study were to determine a mathematical model for the spread of Dengue Hemorrhagic Fever, to reconstruct the model, to determine the optimal control form for DBD, and to perform numerical simulations. The result of this study is the formation of the SIR-ASI model for DBD. Based on this model, two equilibrium points are obtained, namely a disease-free equilibrium point and an endemic equilibrium point. Then the basic reproduction number (R_0 ) is obtained through the Next Generation Matrix method

    Refining baseline estimates of dengue transmissibility and implications for control

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    Climate change, globalisation and increased travel, increasing urban populations, overcrowding, continued poverty, and the breakdown of public health infrastructure are among the factors contributing to the 30-fold increase in total dengue incidence in the past 50 years. Consequently, with an estimated 40% of the world’s population at risk of infection, dengue is now the world’s most important mosquito-borne viral infection. However estimates of dengue transmissibility and burden remain ambiguous. Since the majority of infections are asymptomatic, surveillance systems substantially underestimate true rates of infection. With advances in the development of novel control measures and the recent licensing of the Sanofi Dengvaxia® dengue vaccine, obtaining robust estimates of average dengue transmission intensity is key for estimating both the burden of disease from dengue and the likely impact of interventions. Given the highly spatially heterogeneous nature of dengue transmission, future planning, implementation, and evaluation of control programs are likely to require a spatially targeted approach. Here we collate existing age-stratified seroprevalence and incidence data and develop catalytic models to estimate the burden of dengue as quantified by the force of infection and basic reproduction number. We identified a paucity of serotype-specific age stratified seroprevalence surveys in particular but showed that non-serotype specific data could give robust estimates of baseline transmission. Chapters explore whether estimates derived from different data types are comparable. Using these estimates we mapped the estimated number of dengue cases across the globe at a high spatial resolution allowing us to assess the likely impact of targeted control measures.Open Acces
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