Published Jul 30, 2022


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Carmen Alicia Ramírez-Bernate

Héctor Jairo Martínez-Romero

Diana Marcela Erazo-Borja



In this work, we analyze the population dynamics of the Aedes aegypti mosquito, a transmitter of various viruses such as dengue, zika, and chikungunya, in a given area, based on the use of various control techniques. To do this, we use a reaction-diffusion model that considers various environmental characteristics such as temperature and landscape shape. Initially, we do this analysis using larvicides, insecticides, and the SIT (sterile insect release) technique separately. We simulate different control scenarios using appropriate numerical methods, test combinations of these techniques, and determine the efficiency of each strategy according to the overall reduction in the number of fertilized females due to the applied technique. Subsequently, through a cost-effectiveness analysis, we verified that the release of sterile mosquitoes at the beginning of each seasonal period is the best strategy to control the population of Aedes aegypti.


Aedes aegypti, Cost-effectiveness analysis, insecticide, larvicide, reaction-diffusion model, sterile mosquitoes

[1] Roumen A, Dumont Y, Lubuma J. Mathematical modeling of sterile insect technology for
control of anopheles mosquito. Computer and Mathematics with Applications. 64(3): 374–389, 2012.
doi: 10.1016/j.camwa.2012.02.068.

[2] Esteva L, Yang HM. Mathematical model to assess the control of Aedes aegypti mosquitoes by the sterile insect technique. Mathematical Biosciences. 198(2): 132–147, 2005.
doi: 10.1016/j.mbs.2005.06.004.

[3] Almeida L, Duprez M, Privat Y, Vauchelet N. Mosquito population control strategies for fighting against arboviruses. Mathematical Biosciences and Engineering. 16(6): 6274–6297, 2019.
doi: 10.3934/mbe.2019313.

[4] Pierre AB, Cardona D, Dumont Y, Vasilieva O. Implementation of control strategies for sterile insect techniques. Mathematical Biosciences. 314: 43–60, 2019.
doi: 10.1016/j.mbs.2019.06.002.

[5] Manoranjan VS, Van Den Driessche P. On a diffusion model for sterile insectrelease. Mathematical Biosciences. 79(2). 1986.
doi: 10.1016/0025-5564(86)90148-3.

[6] Pio Ferreira C, Yang HM, Esteva L. Assessing the suitability of sterile insect technique applied to Aedes aegypti. Journal of Biological Systems. 16(4): 565–577, 2008.
doi: 10.1142/S0218339008002691.

[7] Dufourd C, Dumont Y. Impact of environmental factors on mosquito dispersal in the prospect of sterile insect technique control. Computers and Mathematics with Applications. 66(9): 1695–1715, 2013.
doi: 10.1016/j.camwa.2013.03.024.

[8] Oléron T, Bishop S. A spatial model with pulsed releases to compare strategies for the sterile insect technique applied to the mosquito Aedes aegypti. Mathematical Biosciences. 254: 6–27, 2014.
doi: 10.1016/j.mbs.2014.06.001.

[9] Jiang W, Li X, Zou X. On a reaction–diffusion model for sterile insect release method on a bounded domain. International Journal of Biomathematics. 07(3). 2014.
doi: 10.1142/S1793524514500302.

[10] Ramírez CA. “Modelagem Matemática e Simulações Computacionais de Estratégias Combinadas de Combate a um Inseto Vetor: o caso do Aedes aegypti.” PhD thesis. UNICAMP. 2018.

[11] Hendrichs J, Robinson A. Chapter 243 - Sterile Insect Technique. San Diego: Academic Press: 953–957, 2009.

[12] Arias JH, Martínez HJ, Sepulveda LS, Vasilieva O. Estimación de los parámetros de dos modelos para la dinámica del dengue y su vector en Cali Colombia. Ingeniería y Ciencia. 14(28): 69–92, 2018.
doi: 10.17230/ingciencia.14.28.3.

[13] Yang HM, Macoris MLG, Galvani KC, Andrighetti MTM. Assessing the effects of temperature on the population of Aedes aegypti, the vector of dengue. Epidemiology and Infection. 137: 1188–1202, 2009.
doi: 10.1017/S0950268809002040.

[14] Edelstein-Keshet L. Mathematical Models in Biology. Birkhauser Mathema-tics Series. 2005.

[15] Bothe D, Fischer A, Pierre M, Rolland G. Global well-posedness for a class of reactionadvection- anisotropic-diffusion system. Journal of Evolution Equations. 17(1): 101–130, 2017.
doi: 10.1007/s00028-016-0348-0.

[16] Muir L, Kay B. Aedes aegypti survival and dispersal estimated by mark-release-recapture in northern Australia. The American Journal of Tropical Medicine and Hygiene. 58(3): 277–282, 1998.
doi: 10.4269/ajtmh.1998.58.277.

[17] OMS. Lucha contra el dengue. Technical report. Organización Mundial de la Salud. 2013.

[18] Pio Ferreira C, Pulino P, Yang HM, Takahashi LT. Controlling Dispersal Dynamics of Aedes aegypti. Mathematical Population Studies. 13(4): 215–236, 2006.
doi: 10.1080/08898480600950515.

[19] Verdonschot PFM, Besse-Lototskayaa AA. Flight distance of mosquitoes (Culicidae): A metadata analysis to support the management of barrier zones around rewetted and newly constructed wetlands. Limnologica. 45. 2014.
doi: 10.1016/j.limno.2013.11.002.

[20] Russell RC, Webb CE, Williams CR, Ritchie SA. Mark-release-recapture study to measure dispersal of the mosquito Aedes aegypti in Cairns, Queensland, Australia. Med Vet Entomol. 19(4). 2005.
doi: 10.1111/j.1365-2915.2005.00589.x.

[21] Silva MR, Lugao PHG, Chapiro G. Modeling and simulation of the spatial population dynamics of the Aedes aegypti mosquito with an insecticide application. Parasites Vectors. 13(550). 2020.
doi: 10.1186/s13071-020-04426-2.

[22] Carvalho SA, Da Silva SO, Da Cunha Charret I. Mathematical modeling of dengue epidemic: control methods and vaccination strategies. Theory in Biosciences. 138(2): 223–239, 2019.
doi: 10.1007/s12064-019-00273-7.

[23] PAHO. Evaluation of Innovative Strategies for Aedes aegypti Control: Challenges for their Introduction and Impact Assessment. Pan American Health Organization. 2019.

[24] Kinipling EF. Possibilities of insect control or eradication through the use of sexually sterile males. Journal of Economic Entomology. 48(4): 459–462, 1955.
doi: 10.1093/jee/48.4.459.

[25] Hughes TJR. The finite element method: linear static and dynamic finite element analysis. Mineola, New York: Dover Publications, INC. 1987.

[26] LeVeque RJ. Finite difference methods for ordinary and partial differential equations: steadystate and time-dependent problems. Society for Industrial and Applied Mathematics. 2007.

[27] Douglas J, Dupont T. Galerkin methods for parabolic equations. SIAM Journal on Numerical Analysis. 7(4): 575–626, 1970.
doi: 10.1137/0707048.

[28] Chadee D. Studies on the post-oviposition blood-feeding behaviour of Aedes aegypti (L.) (Diptera: Culicidae) in the laboratory. Pathogens and Global Health. 106(7): 413–417, 2012.

[29] Phillips C. What is cost-effectiveness? Technical report. Health economics. 2009.

[30] PAHO. Dengue cases in the Americas top 1.6 million, highlighting need for mosquito control during COVID-19 pandemic. Technical report. Pan American Health Organization. 2020.

[31] Márquez Y, Monroy KJ, Martínez EG, Peña VH, L MA. Influencia de la temperatura ambiental en el mosquito Aedes aegypti y la transmisión del virus del dengue. CES Medicina. 33(1). 2019.

[32] Cianci D, Van Den Broek J, Caputo B, Marini F, Della Torre A, H H, Hartemink N. Estimating mosquito population size from mark release recapture data. Journal of Medical Entomology. 50(3): 533–542, 2013.
doi: 10.1603/ME12126.
How to Cite
Ramírez-Bernate, C. A., Martínez-Romero, H. J. ., & Erazo-Borja, D. M. (2022). Control strategies in the spatial population dynamics of Aedes aegypti vector using sterile mosquitoes and insecticides. Universitas Scientiarum, 27(2), 206–232.
Matemáticas y Estadística / Mathematics and Statistics / Matemática e Estatística