Resumen de Bifurcations in a Dynamical Model of the Innate Immune System Response to Initial Pulmonary Infection

Juan Su, Min Lu, Jicai Huang

• We revisit a dynamical model of the innate immune system response to initial pulmonary infection. By supposing that large pathogen load may not be able to overcome the innate system, a complete analysis on bifurcations with high codimension is given in this paper. It is shown that the highest codimension of a nilpotent cusp is 3, and a center-type equilibrium is a weak focus with order at most 2. As parameters vary, the model can undergo degenerate Bogdanov–Takens bifurcation of codimension 3 and Hopf bifurcation of codimension 2. Finally, numerical simulations, including the coexistence of a limit cycle and a homoclinic cycle, two limit cycles, tristability, are presented to illustrate the theoretical results. Our results indicate the complexity of the interaction between the innate immune system and initial pulmonary bacterial infection.