Theoretical assessment of the impact of temperature variations on the population dynamics of Paracoccus marginatus

Paracoccus marginatus is a polyphagous insect pest reported to cause serious damage to tropical fruits, especially papaya. This paper deals with the problem of mathematical modeling of the impact of temperature variations on the population dynamics of P. marginatus. We first propose a mathematical model describing the population dynamics of P. marginatus that takes into account the time during eggs development. Sensitivity analysis using the eFast method has been performed to show the most important parameters of the model. We also provide the theoretical result of the model. We analyze the model and show that the stability of the pest-free and pest equilibria depends on a delay dependent basic offspring number 𝒩_0 . We also investigate the hopf bifurcation of the pest equilibrium point for a positive delay. Conditions for the stability switches of the pest equilibrium point using the time delay as a bifurcation parameter are determined. After, assuming that some parameters are temperature-dependent, we extend this preliminary model by taking account climatic factors. The extinction and uniform persistence of the pest within a plantation are investigated. Numerical simulations are provided to illustrate and support theoretical results. We found that the growth of P. marginatus is strongly affected by temperature variations.