### Mathematical Biosciences and Engineering

2020, Issue 5: 5686-5708. doi: 10.3934/mbe.2020306
Research article Special Issues

# Explicit solution of a Lotka-Sharpe-McKendrick system involving neutral delay differential equations using the r-Lambert W function

• Received: 25 June 2020 Accepted: 03 August 2020 Published: 28 August 2020
• Structured population models, which account for the state of individuals given features such as age, gender, and size, are widely used in the fields of ecology and biology. In this paper, we consider an age-structured population model describing the population of adults and juveniles. The model consists of a system of ordinary and neutral delay differential equations. We present an explicit solution to the model using a generalization of the Lambert W function called the r-Lambert W function. Numerical simulations with varying parameters and initial conditions are done to illustrate the obtained solution. The proposed method is also applied to an insect population model with long larval and short adult phases.

Citation: Cristeta U. Jamilla, Renier G. Mendoza, Victoria May P. Mendoza. Explicit solution of a Lotka-Sharpe-McKendrick system involving neutral delay differential equations using the r-Lambert W function[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 5686-5708. doi: 10.3934/mbe.2020306

### Related Papers:

• Structured population models, which account for the state of individuals given features such as age, gender, and size, are widely used in the fields of ecology and biology. In this paper, we consider an age-structured population model describing the population of adults and juveniles. The model consists of a system of ordinary and neutral delay differential equations. We present an explicit solution to the model using a generalization of the Lambert W function called the r-Lambert W function. Numerical simulations with varying parameters and initial conditions are done to illustrate the obtained solution. The proposed method is also applied to an insect population model with long larval and short adult phases.

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沈阳化工大学材料科学与工程学院 沈阳 110142

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