Temperature dependent developmental time for the larva stage of Aedes aegypti

Meili Li; Rongrong Guo; Wei Ding; Junling Ma; Meili Li; Rongrong Guo; Wei Ding; Junling Ma

doi:10.3934/mbe.2022203

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 5: 4396-4406. doi: 10.3934/mbe.2022203

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Research article

Temperature dependent developmental time for the larva stage of Aedes aegypti

1.
College of Science, Donghua University, Shanghai 201620, China
2.
Mathematics and Science College, Shanghai Normal University, Shanghai, 200234, China
3.
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 2Y2, Canada

Received: 15 December 2021 Revised: 07 February 2022 Accepted: 22 February 2022 Published: 01 March 2022

We first verify that the time from the emergence of larva to the emergence of pupa (i.e., the duration of the larva stage) for Aedes aegypti is approximately gamma distributed, provided that the pupation process is successful. This is illustrated by fitting a multi-stage model to temperature-controlled pupation rate data of Aedes aegypti. We then determine the temperature dependent gamma distribution parameters, and found that both the shape and rate parameters and the survival probability are unimodal functions of temperature. We then use a Gaussian unimodal function to describe the dependence of these parameters on temperature, and fit the model to the pupation rate data. We found that the optimal pupation temperature is about 28℃, with a mean time from the emergence of larva to the emergence of pupa about 3.8 days, and standard deviation of 0.5 days. For very high and very low temperatures, the death rate is $ 1 $.
- Gaussian function,
- developmental time,
- maximum likelihood estimation,
- gamma distribution
Citation: Meili Li, Rongrong Guo, Wei Ding, Junling Ma. Temperature dependent developmental time for the larva stage of Aedes aegypti[J]. Mathematical Biosciences and Engineering, 2022, 19(5): 4396-4406. doi: 10.3934/mbe.2022203

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Abstract

We first verify that the time from the emergence of larva to the emergence of pupa (i.e., the duration of the larva stage) for Aedes aegypti is approximately gamma distributed, provided that the pupation process is successful. This is illustrated by fitting a multi-stage model to temperature-controlled pupation rate data of Aedes aegypti. We then determine the temperature dependent gamma distribution parameters, and found that both the shape and rate parameters and the survival probability are unimodal functions of temperature. We then use a Gaussian unimodal function to describe the dependence of these parameters on temperature, and fit the model to the pupation rate data. We found that the optimal pupation temperature is about 28℃, with a mean time from the emergence of larva to the emergence of pupa about 3.8 days, and standard deviation of 0.5 days. For very high and very low temperatures, the death rate is $ 1 $.

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