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Impact of environmental factors on mosquito dispersal in the prospect of sterile insect technique control. (English) Zbl 1345.34105
Summary: The aim of this paper is to develop a mathematical model to simulate mosquito dispersal and its control taking into account environmental parameters, like wind, temperature, or landscape elements. We particularly focus on the Aedes albopictus mosquito which is now recognized as a major vector of human arboviruses, like chikungunya, dengue, or yellow fever. One way to prevent those epidemics is to control the vector population. Biological control tools, like the Sterile Insect Technique (SIT), are of great interest as an alternative to chemical control tools which are very detrimental to the environment. The success of SIT is based not only on a good knowledge of the biology of the insect, but also on an accurate modeling of the insect’s distribution. We consider a compartmental approach and derive temporal and spatio-temporal models, using Advection-Diffusion-Reaction equations to model mosquito dispersal. Periodic releases of sterilized males are modeled with an impulse differential equation. Finally, using the splitting operator approach, and well-suited numerical methods for each operator, we provide numerical simulations for mosquito spreading, and test different vector control scenarios. We show that environmental parameters, like vegetation, can have a strong influence on mosquito distribution and in the efficiency of vector control tools, like SIT.

MSC:
34D20 Stability of solutions to ordinary differential equations
34A37 Ordinary differential equations with impulses
92D25 Population dynamics (general)
Software:
TR-BDF2; R; Scilab; pchip
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References:
[1] Ross, R., The relationship of malaria and the mosquito, Lancet, 2, 48-50, (1900)
[2] Ross, R., Malaria and mosquitoes, Nature, 63, 440, (1901)
[3] Ross, R., The possibility of reducing mosquitoes, Nature, 72, 151, (1905)
[4] Dumont, Y.; Chiroleu, F.; Domerg, C., On a temporal model for the chikungunya disease: modeling, theory and numerics, Mathematical Biosciences, 213, 80-91, (2008) · Zbl 1135.92028
[5] Dumont, Y.; Chiroleu, F., Vector control for the chikungunya disease, Mathematical Biosciences and Engineering, 7, 313-345, (2010) · Zbl 1259.92071
[6] S. Bowong, Y. Dumont, J.-J. Tewa, A patchy model for chikungunya-like diseases, BIOMATH (submitted for publication). · Zbl 1368.92166
[7] Benedict, M.; Levine, R.; Hawley, W.; Lounibos, L., Spread of the tiger: global risk of invasion by the mosquito aedes albopictus, Vector-Borne and Zoonotic Diseases, 7, 76-85, (2007)
[8] Paupy, C.; Delatte, H.; Bagny, L.; Corbel, V.; Fontenille, D., aedes albopictus, an arbovirus vector: from the darkness to the light, Microbres and Infection, 11, 1177-1185, (2009)
[9] Gratz, N., Critical review of the vector status of aedes albopictus, Medical and Veterinary Entomology, 18, 215-227, (2004)
[10] Delatte, H.; Paupy, C.; Dehecq, J.; Thiria, J.; Failloux, A.; Fontenille, D., aedes albopictus, vector of chikungunya and dengue viruses in Réunion island: biology and control, Parasite (Paris, France), 15, 3, (2008)
[11] Paupy, C.; Ollomo, B.; Kamgang, B.; Moutailler, S.; Rousset, D.; Demanou, M.; Herve, J.-P.; Leroy, E.; Simard, F., Comparative role of aedes albopictus and aedes aegypti in the emergence of dengue and chikungunya in central africa, Vector-Borne and Zoonotic Diseases, 10, 259-266, (2010)
[12] Knipling, E., Sterile-male method of population control, Science, 130, 902-904, (1959)
[13] Barclay, H., Mathematical models for the use of sterile insects, (Dyck, V.; Hendrichs, J.; Robinson, A., Sterile Insect Technique, (2005), Springer Netherlands), 147-174
[14] Anguelov, R.; Dumont, Y.; Lubuma, J., Mathematical modeling of sterile insect technology for control of anopheles mosquito, Computers and Mathematics with Applications, 64, 374-389, (2012) · Zbl 1252.92044
[15] Dumont, Y.; Tchuenche, J., Mathematical studies on the sterile insect technique for the chikungunya disease and aedes albopictus, Journal of Mathematical Biology, 65, 809-855, (2012) · Zbl 1311.92175
[16] Manoranjan, V. S.; Driessche, P. V.D., On a diffusion model for sterile insect release, Mathematical Biosciences, 79, 199-208, (1986) · Zbl 0585.92022
[17] Lewis, M.; Driessche, P. V.D., Waves of extinction from sterile insect release, Mathematical Biosciences, 116, 221-247, (1993) · Zbl 0778.92024
[18] Dufourd, C.; Dumont, Y., Modeling and simulations of mosquito dispersal. the case of aedes albopictus, BIOMATH, 1, (2012) · Zbl 1368.92141
[19] Delatte, H.; Gimonneau, G.; Triboire, A.; Fontenille, D., Influence of temperature on immature development, survival, longevity, fecundity, and gonotrophic cycles of aedes albopictus, vector of chikungunya and dengue in the indian Ocean, Journal of Medical Entomology, 46, 33-41, (2009)
[20] Y. Dumont, C. Dufourd, Spatio-temporal modeling of mosquito distribution, in: AIP Conference Proceedings—American Institute of Physics, vol. 1404, pp. 162-165.
[21] Clements, A., The biology of mosquitoes: development, nutrition, and reproduction, (The Biology of Mosquitoes, (1992), Chapman & Hall)
[22] Boyer, S.; Gilles, J.; Merancienne, D.; Lemperiere, G.; Fontenille, D., Sexual performance of male mosquito aedes albopictus, Medical and Veterinary Entomology, 25, 454-459, (2011)
[23] Fritsch, F.; Carlson, R., Monotone piecewise cubic interpolation, SIAM Journal on Numerical Analysis, 238-246, (1980) · Zbl 0423.65011
[24] Farina, L.; Rinaldi, S., (Positive Linear Systems: Theory and Applications, Pure and Applied Mathematics (New York), (2000), Wiley-Interscience New York), Theory and applications · Zbl 0988.93002
[25] Teixeira, J.; Borges, M. J., Existence of periodic solutions of ordinary differential equations, Journal of Mathematical Analysis and Applications, 385, 414-422, (2012) · Zbl 1242.34073
[26] Balestrino, F.; Medici, A.; Candini, G.; Carrieri, M.; Maccagnani, B.; Calvitti, M.; Maini, S.; Bellini, R., Gamma ray dosimetry and mating capacity studies in the laboratory on aedes albopictus males, Journal of Medical Entomology, 47, 581-591, (2010)
[27] Bellini, R.; Calvitti, M.; Medici, A.; Carrieri, M.; Celli, G.; Maini, S., Use of the sterile insect technique against aedes albopictus in Italy: first results of a pilot trial, Area-Wide Control of Insect Pests, 505-515, (2007)
[28] Oliva, C. F.; Jacquet, M.; Gilles, J.; Lemperiere, G.; Maquart, P.-O.; Quilici, S.; Schooneman, F.; Vreysen, M. J.B.; Boyer, S., The sterile insect technique for controlling populations of aedes albopictus (diptera: culicidae) on Réunion island: mating vigour of sterilized males, PLoS One, 7, e49414, (2012)
[29] Mickens, R., Nonstandard finite difference models of differential equations, (1994), World Scientific Pub. Co. Inc. · Zbl 0810.65083
[30] Anguelov, R.; Dumont, Y.; Lubuma, J. M.-S., On nonstandard finite difference schemes in biosciences, AIP Conference Proceedings, 1487, 212-223, (2012)
[31] Anguelov, R.; Dumont, Y.; Lubuma, J.; Mureithi, E., Stability analysis and dynamics preserving non-standard finite difference schemes for a malaria model, Mathematical Population Studies, 20, 2, 101-122, (2013) · Zbl 1409.92221
[32] R. Anguelov, Y. Dumont, J.M.-S. Lubuma, M. Shillor, Dynamically consistent nonstandard finite difference schemes for epidemiological models, Journal of Computational and Applied Mathematics, Available online 6 May 2013, http://dx.doi.org/10.1016/j.cam.2013.04.042 (http://www.sciencedirect.com/science/article/pii/S0377042713002380). · Zbl 1291.92097
[33] Dumont, Y.; Russel, R.; Lecomte, V.; Le Corre, M., Conservation of endangered endemic seabirds within a multi-predator context: the barau’s petrel in Réunion island, Natural Resource Modelling, 23, 381-436, (2010) · Zbl 1402.92340
[34] Dumont, Y.; Lubuma, J. M.-S., Non-standard finite-difference methods for vibro-impact problems, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 461, 1927-1950, (2005) · Zbl 1139.70300
[35] Daykin, P.; Kellogg, F.; Wright, R., Host-finding and repulsion of aedes aegypti, The Canadian Entomologist, 97, 239-263, (1965)
[36] G. Lemperiere, J. Boyer, S. Dehecq, C. Dufourd, Y. Dumont, Influence of rural landscape structures on the dispersal of the Asian tiger mosquito Aedes albopictus: a study case at la Réunion Island, in: 8th IALE (International Association of Landscape Ecology World Congress) Beijing, China, August 18-23, 2011.
[37] Younes, A.; Ackerer, P., Solving the advection-diffusion equation with the eulerian-Lagrangian localized adjoint method on unstructured meshes and non uniform time stepping, Journal of Computational Physics, 208, 384-402, (2005) · Zbl 1073.65107
[38] Gillies, M., The role of carbon dioxide in host-finding by mosquitoes (diptera: culicidae): a review, Bulletin of Entomological Research, 70, 525-532, (1980)
[39] Cummins, B.; Cortez, R.; Foppa, I.; Walbeck, J.; Hyman, J., A spatial model of mosquito host-seeking behavior, PLoS Computational Biology, 8, e1002500, (2012)
[40] Ladyžhenskaya, O.; Solonnikov, V.; Ural’tseva, N., Linear and quasi-linear equations of parabolic type, vol. 23, (1968), Amer. Mathematical Society · Zbl 0174.15403
[41] Hundsdorfer, W.; Verwer, J., Numerical solution of time-dependent advection-diffusion-reaction equations, vol. 33, (2007), Springer Verlag
[42] Lanser, D.; Verwer, J. G., Analysis of operator splitting for advection-diffusion-reaction problems from air pollution modelling, Journal of Computational and Applied Mathematics, 111, 201-216, (1999), Numerical methods for differential equations (Coimbra, 1998) · Zbl 0949.65090
[43] Colella, P., Multidimensional upwind methods for hyperbolic conservation laws, Journal of Computational Physics, 87, 171-200, (1990) · Zbl 0694.65041
[44] Hosea, M.; Shampine, L., Analysis and implementation of tr-bdf2, Applied Numerical Mathematics, 20, 21-37, (1996) · Zbl 0859.65076
[45] Scilab Enterprises, Scilab: le logiciel open source gratuit de calcul numérique, Scilab Enterprises, Orsay, France, 2012. http://www.scilab.org.
[46] R Development Core Team, R: a language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria, 2011. http://www.R-project.org/.
[47] Oliva, C. F.; Maier, M. J.; Gilles, J.; Jacquet, M.; Lemperiere, G.; Quilici, S.; Vreysen, M. J.; Schooneman, F.; Chadee, D. D.; Boyer, S., Effects of irradiation, presence of females, and sugar supply on the longevity of sterile males aedes albopictus (skuse) under semi-field conditions on Réunion island, Acta Tropica, 125, 287-293, (2013)
[48] Lacroix, R.; Delatte, H.; Hue, T.; Reiter, P., Dispersal and survival of male and female aedes albopictus (diptera: culicidae) on Réunion island, Journal of Medical Entomology, 46, 1117-1124, (2009)
[49] White, S. M.; Rohani, P.; Sait, S. M., Modelling pulsed releases for sterile insect techniques: fitness costs of sterile and transgenic males and the effects on mosquito dynamics, Journal of Applied Ecology, (2010)
[50] Shu, C.-W., High order weighted essentially nonoscillatory schemes for convection dominated problems, SIAM Review, 51, 82-126, (2009) · Zbl 1160.65330
[51] Varga, R., Matrix iterative analysis, (1962), Prentice-Hall Englewoods Cliffs, NJ · Zbl 0133.08602
[52] Vidyasagar, M., Decomposition techniques for large-scale systems with nonadditive interactions: stability and stabilization, IEEE Transactions on Automatic Control, 25, 773-779, (1980) · Zbl 0478.93044
[53] Isidori, A., (Nonlinear Control Systems. II, Communications and Control Engineering Series, (1999), Springer-Verlag London Ltd. London)
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