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Analysis of the invasion of a city by Aedes aegypti via mathematical models and Bayesian statistics

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Abstract

We analysed data from the invasion of a city by Aedes aegypti by using a series of models based on Fisher’s reaction–diffusion equation with Richard’s growth model and Bayesian statistics. The model that best explains the invasion of the city was defined through a step-by-step process of model selection based on a series of candidate models. As explanatory variables, we used the effect of urbanization type and climate variables on the parameters of Fisher’s equation: carrying capacity (K), population growth rate (r), and the diffusion coefficient (D). The resulting model is a reaction–diffusion equation with a near-zero shape parameter, similar to a Gompertz-type growth. The population advance rate of 60.19 m/day allowed Aedes aegypti to fully occupy a medium-sized city in 5 months from the estimated date of colonization. We found that the carrying capacity was dependent on temperature and urbanization type. While the results are coherent with existing literature on this species, most of the theory on population dynamics of Aedes aegypti usually assumes a logistic growth instead of Gompertz population dynamics. This type of growth is faster than logistic at densities lower than the inflexion point but slower at higher densities. Therefore, it is possible that in a regime in which the K depends on the climate, Gompertz dynamics could stabilize the population of this species of mosquito faster than assumed by the existing theory.

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Data availability

Data is available at GitHub (https://github.com/okktawio/paper-mosquito-invasion-concordia-data).

Code availability

Custom code is available at GitHub (https://github.com/okktawio/paper-mosquito-invasion-concordia-data).

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Acknowledgements

We thank Arabella Peard, Guillermo Logarzo, Belén Aguirre, and Nora Burroni for their thoughtful comments on the manuscript and Nicolas Schweigmann for the support to this study. We also thank Dr. Hernan Rossi, who was the Director of the “Felipe Heras” Hospital during the study, Dr. Elena Ostrowsky who was Secretary of Health for the municipality, the hospital staff, and the secretary of health who collaborated with the study.

Funding

During the data collection, there was no specific financing; in the analysis stage, this work was supported by “IBIAL — Integrative Biology of Insects Affecting human Life” (FP7-Marie Curie-PEOPLE-IRSES 319015).

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Authors and Affiliations

  1. IFAB, Instituto Nacional de Tecnología Agropecuaria (INTA), Estación Experimental Agropecuaria Bariloche, Av. Modesta Victoria 4450 (8400), San Carlos de Bariloche, 277, Río Negro, CC, Argentina

    Octavio Augusto Bruzzone

  2. Consejo Nacional de Investigaciones Científicas Y Técnicas (CONICET), Buenos Aires, Argentina

    Octavio Augusto Bruzzone

  3. Centro Nacional de Diagnóstico E Investigación en Endemo-Epidemias (CeNDIE), ANLIS “Dr. C. G. Malbrán”, de Salud de La Nación, Buenos Aires, Ministerio, Argentina

    María Eugenia Utgés

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  1. Octavio Augusto Bruzzone
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Octavio Augusto Bruzzone: collected the field data, developed the model, and wrote the paper; María Eugenia Utgés: analysed, interpreted the data, and wrote the paper. Both authors read and approved the final manuscript.

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Correspondence to Octavio Augusto Bruzzone.

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Bruzzone, O.A., Utgés, M.E. Analysis of the invasion of a city by Aedes aegypti via mathematical models and Bayesian statistics. Theor Ecol 15, 65–80 (2022). https://doi.org/10.1007/s12080-022-00528-y

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