An SIR-Dengue transmission model with seasonal effects and impulsive control

Chávez, Joseph Páez; Götz, Thomas; Siegmund, Stefan; Wijaya, Karunia Putra

doi:10.1016/j.mbs.2017.04.005

Cited by 45 publications

(42 citation statements)

References 29 publications

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“…The model divides the population of interest based on their health status [ 25 ], for example, susceptible (S), exposed (E), infectious (I) and recovered (R). The compartmental model has been employed in the study of transmission dynamics in many vector-borne diseases such as Dengue [ 26 , 27 ] and Malaria [ 28 ]. In the ZIKV study, this modeling architecture has also been constructed [ 29 – 33 ].…”

Section: Introductionmentioning

confidence: 99%

A mathematical model for Zika virus transmission dynamics with a time-dependent mosquito biting rate

Suparit

Wiratsudakul

Modchang

2018

Theor Biol Med Model

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BackgroundMathematical modeling has become a tool used to address many emerging diseases. One of the most basic and popular modeling frameworks is the compartmental model. Unfortunately, most of the available compartmental models developed for Zika virus (ZIKV) transmission were designed to describe and reconstruct only past, short-time ZIKV outbreaks in which the effects of seasonal change to entomological parameters can be ignored. To make an accurate long-term prediction of ZIKV transmission, the inclusion of seasonal effects into an epidemic model is unavoidable.MethodsWe developed a vector-borne compartmental model to analyze the spread of the ZIKV during the 2015–2016 outbreaks in Bahia, Brazil and to investigate the impact of two vector control strategies, namely, reducing mosquito biting rates and reducing mosquito population size. The model considered the influences of seasonal change on the ZIKV transmission dynamics via the time-varying mosquito biting rate. The model was also validated by comparing the model prediction with reported data that were not used to calibrate the model.ResultsWe found that the model can give a very good fit between the simulation results and the reported Zika cases in Bahia (R-square = 0.9989). At the end of 2016, the total number of ZIKV infected people was predicted to be 1.2087 million. The model also predicted that there would not be a large outbreak from May 2016 to December 2016 due to the decrease of the susceptible pool. Implementing disease mitigation by reducing the mosquito biting rates was found to be more effective than reducing the mosquito population size. Finally, the correlation between the time series of estimated mosquito biting rates and the average temperature was also suggested.ConclusionsThe proposed ZIKV transmission model together with the estimated weekly biting rates can reconstruct the past long-time multi-peak ZIKV outbreaks in Bahia.Electronic supplementary materialThe online version of this article (10.1186/s12976-018-0083-z) contains supplementary material, which is available to authorized users.

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Section: Introductionmentioning

confidence: 99%

A mathematical model for Zika virus transmission dynamics with a time-dependent mosquito biting rate

Suparit

Wiratsudakul

Modchang

2018

Theor Biol Med Model

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“…It would also break down in the presence of changing control efforts such as school closure [71] or novel vector control [72]. In such situations, a mechanistic modelling approach [73] may be better able to predict the epidemic dynamics until sufficient training data are available.…”

Section: Limitationsmentioning

confidence: 99%

The utility of LASSO-based models for real time forecasts of endemic infectious diseases: A cross country comparison

Chen

Chu

Chen

et al. 2018

Journal of Biomedical Informatics

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“…Given these constraints, mathematical models can serve as important tools for predicting the effects of control efforts and optimizing control efficacies and costs. Indeed, the efficacies of adult and larval control measure have been assessed and optimized using both simple, deterministic epidemic models [2,3,4,5] and complex disease models with features such as stochasticity [6,7], seasonality [8,9,10,11], host heterogeneity [11,12,13,14], and spatial structure [6,7,13].…”

Section: Introductionmentioning

confidence: 99%

“…Models of this class incorporate control only implicitly through it's overall gross effects on model parameters; these will be referred as "implicit" control models throughout this paper. A second, more complicated method for incorporating control into vector-borne disease models is to directly model the effects of control on vector populations or environmental parameters [3,7,8,9,10,11,22]. For example, an area-wide adulticide spray could be modeled as a sudden, direct decrease in the adult vector population at the time of application.…”

Section: Introductionmentioning

confidence: 99%

Implicit versus explicit control strategies in models for vector-borne disease epidemiology

Demers

Bewick

et al. 2019

Preprint

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Throughout the vector-borne disease modeling literature, there exist two general frameworks for incorporating vector management strategies (e.g. area-wide adulticide spraying and larval source reduction campaigns) into vector population models, namely, the "implicit" and "explicit" control frameworks. The more simplistic "implicit" framework facilitates derivation of mathematically rigorous results on disease suppression and optimal control, but the biological connection of these results to realworld "explicit" control actions that could guide specific management actions is vague at best. Here, we formally define the biological and mathematical relationships between implicit and explicit control, and we provide detailed mathematical expressions relating the strength of implicit control to management-relevant properties of explicit control for four common intervention strategies. These expressions allow optimal control and sensitivity analysis results in existing implicit control studies to be interpreted in terms of real world actions. Our work reveals a previously unknown fact: implicit control is a meaningful approximation of explicit control only when resonance-like synergistic effects between multiple controls have a negligible effect on average population reduction. When non-negligible synergy exists, implicit control results, despite their mathematical tidiness, fail to provide accurate predictions regarding vector control and disease spread. The methodology we establish can be applied to study the interaction of phenological effects with control strategies, and we present a new technique for finding impulse control strategies that optimally reduce a vector population in the presence of seasonally oscillating model parameters. Collectively, these elements build an effective bridge between analytically interesting and mathematically tractable implicit control and the challenging, action-oriented explicit control.

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An SIR-Dengue transmission model with seasonal effects and impulsive control

Cited by 45 publications

References 29 publications

A mathematical model for Zika virus transmission dynamics with a time-dependent mosquito biting rate

A mathematical model for Zika virus transmission dynamics with a time-dependent mosquito biting rate

The utility of LASSO-based models for real time forecasts of endemic infectious diseases: A cross country comparison

Implicit versus explicit control strategies in models for vector-borne disease epidemiology

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