Modeling the effects of climate change on the population dynamics of mosquitoes that are vectors of infectious diseases




almost periodic function, cooperative systems, skip oviposition, vector-borne diseases


We incorporate almost periodic functions in a mosquito model to take into account a loss of synchronicity in the population dynamics of mosquitoes due to climate change. The model takes into account the skip oviposition strategy that is associated with the mosquitoes that are vectors of infectious diseases as dengue, malaria and leishmaniasis.

We prove existence and uniqueness of a stable almost periodic solution for some conditions over the parameters of the model. Numerical simulations are performed using values estimated for the life cycle of Aedes albopictus gathered in literature. The results show that the vector population can be underestimated or overestimated if an almost periodic dynamics is approximated by a periodic dynamics. Therefore, using an almost seasonal model can be more adequate to design breeding habitat-targeted mosquito control strategies when seasonal drivers are modeled since climate-mediated shifts can induce a loss of periodicity in environmental drivers.

Author Biographies

Homero Díaz-Marín, Universidad Michoacana.

Facultad de Ciencias Físico-Matemáticas.

Osvaldo Osuna, Universidad Michoacana.

Instituto de Física y Matemáticas.

Geiser Villavicencio-Pulido, Universidad Autónoma Metropolitana.

División de Ciencias Biológicas y de la Salud, Depto. de Ciencias Ambientales.


H. Bohr, Almost Periodic Functions. New York, N. Y.: Chelsea Publishing Company, 1947.

A. Bomblies, “Modeling the role of rainfall patterns in seasonalmalaria transmission”, Climatic Change, vol. 112, pp. 673-685, 2012.

H. Chen and U. Fillinger and G. Yan, “Oviposition behavior of female Anopheles gambiae in western Kenya inferred from microsatellite markers”, The American Journal of Tropical Medicine and Hygiene, vol. 75, no. 2, pp. 246-250, 2006.

C. Corduneanu, N. Gheorghiu and V. Barbu, Almost periodic functions. New York: Interscience Publishers, 1968.

H. Delatte and G. Gimonneau and A. Triboire and D. Fontenille, “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, vol. 46, n. 1, pp. 33-41, 2009.

B. Dembele, A. Friedman and A. Yakubu, “Malaria model with periodic mosquito birth and death rates”, Journal of biological dynamics, vol. 3, no. 4, pp. 430-445, 2009.

H. G. Díaz-Marín, F. López-Hernández and O. Osuna, “Almost periodic solutions for seasonal cooperative systems”, Annales Polonici Mathematic, vol. 128, no. 1, pp. 1-14, 2022.

C. Duffourd and Y. Dumont, “Impact of environmental factors on mosquito dispersal in the prospect of sterile insect technique control”, Computers and Mathematics with Applications, vol. 66, pp. 1695-1715, 2013.

Y. Dumont and J. Thulliez, “Human behaviors: A threat to mosquito control?”, Mathematical Biosciences, vol. 281, pp. 9-23, 2016.

S. E. Eikenberry and A. B. Gummel, “Mathematical modeling of climate change and malaria transmission dynamics: a historical review”, Mathematical Biology, vol. 77, pp. 857-933, 2018.

A. Elaagip, A. Ahmed, M. D. Wilson, D. A. Boakye and M. M. Abdel-Hamid “Studies of host preferences of wild-caught Phlebotomus orientalis and Ph. papatasi vectors of leishmaniasis in Sudan”, PLoS ONE, vol. 15, no. 7, pp. 1-6, 2020.

A. Karmaou, “Seasonal Distribution of Phlebotomus papatasi, Vector of Zoonotic Cutaneous Leishmaniasis”, Acta Parasitologica, vol. 65, no. 3, pp. 585-598, 2020.

C. J. M. Koenraadt, A. K. Githeko and W. Takken, “The effects of rainfall and evapotranspiration on the temporal dynamics of Anopheles gambiae s.s. and Anopheles arabiensis in a Kenyan village”, Acta Tropica, vol. 90, no. 2, pp. 141-153, 2004.

G. L. McLaughlin and G. Wasserberg, “Spatial Bet Hedging in Sand Fly Oviposition: Factors Affecting Skip Oviposition in Phlebotomus papatasi Sand Flies”, Vector-Borne and Zoonotic Diseases, vol. 21, no. 4, pp. 280-288, 2021.

V. S. Mwingira, J. Spitzen, L. G. E. Mboera, J. L. Torres-Estrada and W. Takken, “The Influence of Larval Stage and Density on Oviposition Site-Selection Behavior of the Afrotropical Malaria Mosquito Anopheles coluzzii (Diptera: Culicidae)”, Journal of Medical Entomology, vol. 573, no. 3, pp. 657-666, 2020.

J. O. Odero, U. Fillinger, E. J. Rippon, D. K. Masiga and D. Weetman, “Using sibship reconstructions to understand the relationship between larval habitat productivity and oviposition be haviour in Kenyan Anopheles arabiensis”, Malaria Journal, vol. 18, 2019.

M. N. Otal, J. M Lindh, S. J Torr, E. Masinde, B. Orindi, S. W Lindsay and U. Fillinger, “Analysing the oviposition behaviour of malaria mosquitoes: design considerations for improving two-choice egg count experiments”, Malaria Journal, vol. 205, 2015.

P. E. Parham and E. Michael, “Modeling the Effects of Weather and Climate Change on Malaria Transmission”, Environmental Health Perspectives, vol. 118, no. 5, pp. 620-626, 2010.

L. Qiang and B. G. Wang, “An almost periodic Malaria transmission model with time delayed input of vector”, Discrete and continuous dynamical systems series B, vol. 22, no. 4, pp. 1525-1546, 2017.

J. Rajarethinam, J. Ong, Z. W. Neo, L. C. Ng and J. Aik, “Distribution and seasonal fluctuations of Ae. aegypti and Ae. albopictus larval and pupae in residential areas in an urban landscape”, PLoS Neglected Tropical Diseases, vol. 14, no. 4, 2020.

H. L. Smith, Monotone Dynamical Systems: an introduction to the theory of competitive and cooperative systems. Mathematical Surveys and Monographs, vol. 41. AMS: 1995.

H. L. Smith, “Dynamics of competition,” in Mathematics Inspired by Biology, V. Capasso, Ed. Berlin: Springer, 1999, pp. 191-240.

B. G. Wang, L. Qiang and Z. C. Wang, “An almost periodic Ross-Macdonald model with structured vector population in a patchy environment”, Journal of Mathematical Biology, vol. 80, pp. 835-863, 2019.

A. Wasserberg, I. Yarom and A. Warburg, “Seasonal abundance patterns of the sandfly Phlebotomus papatasi in climatically distinct foci of cutaneous leishmaniasis in Israeli deserts”, Medical and Veterinary Entomology, vol. 17, no. 4, pp. 452-456, 2003.

S. Yaredab, A. Gebresilassieb, E. Akililuc, M. Balkewa, A. Warburgd, A. Hailue and T. Gebre-Michaela, “Habitat preference and seasonal dynamics of Phlebotomus orientalis in urban and semi-urban areas of kala-azar endemic district of Kafta Humera, northwest Ethiopia”, Acta Tropica, vol. 166, pp. 25-34, 2017.



How to Cite

H. Díaz-Marín, O. Osuna, and G. Villavicencio-Pulido, “Modeling the effects of climate change on the population dynamics of mosquitoes that are vectors of infectious diseases”, Proyecciones (Antofagasta, On line), vol. 42, no. 4, pp. 1031-1049, Jul. 2023.