Predator-prey model with age structure

Jairaj Promrak, Graeme Charles Wake, Chontita Rattanakul

Abstract


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

Keywords


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



DOI: http://dx.doi.org/10.21914/anziamj.v59i0.11568



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.