Predator-prey model with age structure


  • Jairaj Promrak Mahidol University,
  • Graeme Charles Wake Massey University
  • Chontita Rattanakul Mahidol University



Sharpe–Lotka–McKendrick equation, predator–prey model, steady age distribution, mealybugs.


Mealybug is an important pest of cassava plant in Thailand and tropical countries, leading to severe damage of crop yield. One of the most successful controls of mealybug spread is using its natural enemies such as green lacewings, where the development of mathematical models forecasting mealybug population dynamics improves implementation of biological control. In this work, the Sharpe–Lotka–McKendrick equation is extended and combined with an integro-differential equation to study population dynamics of mealybugs (prey) and released green lacewings (predator). Here, an age-dependent formula is employed for mealybug population. The solutions and the stability of the system are considered. The steady age distributions and their bifurcation diagrams are presented. Finally, the threshold of the rate of released green lacewings for mealybug extermination is investigated. doi:10.1017/S1446181117000360

Author Biographies

Jairaj Promrak, Mahidol University,

Mathematics Department, Teaching Assistant and Postgraduate Student

Graeme Charles Wake, Massey University

Institute of Natural and Mathematical Sciences, Professor Emeritus

Chontita Rattanakul, Mahidol University

Mathematics Department, Associate Professor





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