Mathematical model to assess the control of Aedes aegypti mosquitoes by the sterile insect technique

Esteva, Luis; Yang, Hyun Mo

doi:10.1016/j.mbs.2005.06.004

Cited by 133 publications

(138 citation statements)

References 14 publications

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“…In Table 1 we summarize the stability analysis of P 2 , P 3+ and P 3− . The stability analysis of equilibrium points P 3+ and P 3− is quite similar to that presented elsewhere [5]. α µ T R existence stable unstable Table 1.…”

Section: Analysis Of the Modelsupporting

confidence: 63%

Control of Dengue Vector by the Sterile Insect Technique Considering Logistic Recruitment

Esteva

Yang²

2006

TEMA - Tendências Em Matemática Aplicada E Computacional

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Abstract. We propose a mathematical model to assess the effects of irradiated male insects introduction in a previously infested region, taking into account the logistic recruitment of sterile male insects. The release of sterile male insects aims to displace gradually the natural (or wild) insect from the habitat. We discuss the suitability of this release technique when applied to peridomestic adapted Aedes aegypti mosquitoes which are transmitters of Yellow Fever and Dengue disease.

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Section: Analysis Of the Modelsupporting

confidence: 63%

Control of Dengue Vector by the Sterile Insect Technique Considering Logistic Recruitment

Esteva

Yang²

2006

TEMA - Tendências Em Matemática Aplicada E Computacional

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“…Other models have considered the role of a unique vector in the transmission of multiple diseases, as more than one dengue serotype [21,23,24] or the concurrent transmission of yellow fever in dengue infested areas [25]. Finally, the effect of vector control have already been explicitly analyzed in ODE models [23,24,26].…”

Section: The Modelmentioning

confidence: 99%

Periodic forcing in a three-level cellular automata model for a vector-transmitted disease

et al. 2009

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The transmission of vector infectious diseases, which produces complex spatiotemporal patterns, is analyzed by a periodically forced two-dimensional cellular automata model. The system, which comprises three population levels, is introduced to describe complex features of the dynamics of the vector transmitted dengue epidemics, known to be very sensitive to seasonal variables. The three coupled levels represent the human, the adult and immature vector populations. The dynamics includes external seasonality forcing (rainfall intensity data), human and mosquito mobility, and vector control effects. The model parameters, even if bounded to well defined intervals obtained from reported data, can be selected to reproduce specific epidemic outbursts. In the current study, explicit results are obtained by comparison with actual data retrieved from the time-series of dengue epidemics in two cities in Brazil. The results show fluctuations that are not captured by mean-field models. It also reveals the qualitative behavior of the spatiotemporal patterns of the epidemics. In the extreme situation of absence of external periodic drive, the model predicts completely distinct long time evolution. The model is robust in the sense that it is able to reproduce the time series of dengue epidemics of different cities, provided the forcing term takes into account the local rainfall modulation. Finally, the dependence between epidemics threshold and vector control undergoes a transition from power law to stretched exponential behavior due to human mobility effect.

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“…[19]) are the global nature of the properties and the irrelevance of the Lyapunov function. (For an alternative approach see [19])…”

Section: Population Dynamics Of Anopheles Mosquitomentioning

confidence: 99%

“…Since the first field releases, various modelling and/or mathematical works have been done on SIT using either discrete models [12,29], or continuous temporal models with continuous release (see for instance [5,6,19,20,28,29,38] and references therein), with pulsed releases [17,42], or spatio-temporal models with one dimensional spatial component and continuous (proportional) releases [20,34,39]. See also [7] for an overview on SIT mathematical modelling.…”

Section: Introductionmentioning

confidence: 99%

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Mathematical Modeling of Sterile Insect Technology for Control of Anopheles Mosquito

Anguelov

Dumont

Lubuma

2011

AIP Conference Proceedings

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The Sterile Insect Technology (SIT) is a nonpolluting method of control of the invading insects that transmit the disease. The method relies on the release of sterile or treated males in order to reduce the wild population of anopheles mosquito. We propose two mathematical models. The first model governs the dynamics of anopheles mosquito. The second model, the SIT model, deals with the interaction between treated males and wild female anopheles. Using the theory of monotone operators, we obtain dynamical properties of global nature that can be summarized as follows. Both models are dissipative dynamical systems on the positive cone R 4 + . The value R = 1 of the basic offspring number R is a forward bifurcation for the model of the anopheles mosquito, with the trivial equilibrium 0 being globally asymptotically stable (GAS) when R ≤ 1, whereas 0 becomes unstable and one stable equilibrium is born with well determined basins of attraction when R > 1. For the SIT model, we obtain a threshold numberλ of treated male mosquitos above which the control of wild female mosquitos is effective. That is, for λ >λ the equilibrium 0 is GAS. When 0 < λ ≤λ, the number of equilibria and their stability are described together with their precise basins of attraction. These theoretical results are rephrased in terms of possible strategies for the control of the anopheles mosquito and they are illustrated by numerical simulations.

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Mathematical model to assess the control of Aedes aegypti mosquitoes by the sterile insect technique

Cited by 133 publications

References 14 publications

Control of Dengue Vector by the Sterile Insect Technique Considering Logistic Recruitment

Control of Dengue Vector by the Sterile Insect Technique Considering Logistic Recruitment

Periodic forcing in a three-level cellular automata model for a vector-transmitted disease

Mathematical Modeling of Sterile Insect Technology for Control of Anopheles Mosquito

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