Modeling the Dynamic Transmission of Dengue Fever: Investigating Disease Persistence

Medeiros, Líliam César de Castro; Castilho, César; Braga, Cynthia; Souza, Wayner Vieira de; Regis, Lêda; Monteiro, Antônio Miguel Vieira

doi:10.1371/journal.pntd.0000942

Cited by 75 publications

(40 citation statements)

References 64 publications

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“…It is easy to study the one-dimensional system (8) and in particular to show that if γ 0 > 1 and y 0 = 0 then,…”

Section: Butmentioning

confidence: 99%

“…For the sake of completeness, we remark that multipartite structures find motivation in real life epidemics. For example, the dengue disease is spread between humans and Aedes Aegipty mosquitoes according to a bipartite structure, refer to [8]. Indeed, a healthy human gets infected once bitten by an infected mosquito.…”

Section: Introduction and Brief Review Of Thementioning

confidence: 99%

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Bi-Virus SIS Epidemics over Networks: Qualitative Analysis

Santos

Moura

2015

IEEE Trans. Netw. Sci. Eng.

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Abstract-The paper studies the qualitative behavior of a set of Ordinary Differential Equations that models the dynamics of bi-virus epidemics over bilayer networks. Each layer is a weighted digraph associated with a strain of virus; the weights γ z ij represent the rates of infection from node i to node j of strain z. We establish a sufficient condition on the γ's that guarantees survival of the fittest-only one strain survives. We propose an ordering of the weighted digraphs, the -order, and show that if the weighted digraph of strain y is -dominated by the weighted digraph of strain x, then y dies out in the long run. We prove that the orbits of the ODE accumulate to an attractor. Due to the coupled nonlinear high-dimension nature of the ODEs, there is no natural Lyapunov function to study their global qualitative behavior. We prove our results by combining two important properties of these ODEs: (i) monotonicity under a partial ordering on the set of graphs; and (ii) dimension-reduction under symmetry of the graphs. Property (ii) allows us to fully address the survival of the fittest for regular graphs. Then, by bounding the epidemics dynamics for generic networks by the dynamics on regular networks, we prove the result for general networks.

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“…It is easy to study the one-dimensional system (8) and in particular to show that if γ 0 > 1 and y 0 = 0 then,…”

Section: Butmentioning

confidence: 99%

Section: Introduction and Brief Review Of Thementioning

confidence: 99%

Bi-Virus SIS Epidemics over Networks: Qualitative Analysis

Santos

Moura

2015

IEEE Trans. Netw. Sci. Eng.

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“…The variation in climate factors such to dengue disease transmission. Temperature and rainfall interfere at all stages of mosquito development from the emergence and viability of eggs, to the size and longevity of adult mosquitoes, as well as their dispersal over space (Allis et al, 2011;Medeiros et al, 2011). Demographic factors such as population density, education level, human awareness and household income are also vital determinants of dengue spread.…”

Section: March 2018mentioning

confidence: 99%

A mathematical model with control to analyse the dynamics of dengue disease transmission in urban Colombo

Perera¹,

Wickramaarachchi²

2018

J. Natn. Sci. Foundation Sri Lanka

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Abstract:Dengue is a mosquito-borne disease. It has been an important public health problem particularly in the tropical and sub-tropical regions in the world, for which no vaccine or successful treatment has been found. Therefore, prevention and control play a vital role in minimising the risk of dengue in vulnerable populations.Various mathematical models such as the SIR model have been developed to understand the transmission dynamics of dengue. The main drawback of these dynamic models is the lack of predictability with respect to external factors such as climate, geography, demography and human behaviour due depends heavily on various external factors such as climate is a critical parameter of these models and is responsible for the local transmission of the disease. In this study, the mosquito density is modelled with respect to changing levels of climate favourable for mosquito reproduction. A climate risk index developed using fuzzy set theory is used to vary the mosquito density with respect to rainfall and temperature and this measure is included in the SIR model. Finally, two measures, u 1 and u 2 , are introduced to control adult mosquitoes and growing juveniles using two methods. u 1 and u 2 as random processes from uniform distribution. The second method involves continuous and constant control measures over time. The numerical results of the SIR model suggest that the dynamics of infections has changed and the number of increase.

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“…Mathematical models of pathogen population dynamics, by virtue of their ability to provide a quantitative means for integrating and simulating the impacts of multi-factorial and multi-scale disease transmission processes, may offer us a particularly pertinent methodological tool for developing such holistic predictive and investigative frameworks [7][8][9][10][11][12][13]19,25,27,[42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58]. Recent advances in incorporating the effects of climate, as well as anthropogenic alterations of ecosystems (e.g.…”

Section: Introductionmentioning

confidence: 99%

Climate, environmental and socio-economic change: weighing up the balance in vector-borne disease transmission

Parham

Waldock

Christophides

et al. 2015

Phil. Trans. R. Soc. B

246

224

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Arguably one of the most important effects of climate change is the potential impact on human health. While this is likely to take many forms, the implications for future transmission of vector-borne diseases (VBDs), given their ongoing contribution to global disease burden, are both extremely important and highly uncertain. In part, this is owing not only to data limitations and methodological challenges when integrating climate-driven VBD models and climate change projections, but also, perhaps most crucially, to the multitude of epidemiological, ecological and socio-economic factors that drive VBD transmission, and this complexity has generated considerable debate over the past 10–15 years. In this review, we seek to elucidate current knowledge around this topic, identify key themes and uncertainties, evaluate ongoing challenges and open research questions and, crucially, offer some solutions for the field. Although many of these challenges are ubiquitous across multiple VBDs, more specific issues also arise in different vector–pathogen systems.

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Modeling the Dynamic Transmission of Dengue Fever: Investigating Disease Persistence

Cited by 75 publications

References 64 publications

Bi-Virus SIS Epidemics over Networks: Qualitative Analysis

Bi-Virus SIS Epidemics over Networks: Qualitative Analysis

A mathematical model with control to analyse the dynamics of dengue disease transmission in urban Colombo

Climate, environmental and socio-economic change: weighing up the balance in vector-borne disease transmission

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