Dynamics of a red imported fire ant ecological system under different pulse control strategies

At present, the invasive species red imported fire ants have become a major threat to local ecosystems and the daily lives of people in China. Long-term reliance on chemical control has led to the development of resistance in red imported fire ants, resulting in unsatisfactory control effectiveness. To address this issue, this paper, from a biomathematical perspective, for the first time introduces mathematical modeling into the population control of red imported fire ants. Predators are incorporated into the model, and two different control strategies are adopted to reduce the risk of resistance development. By examining the properties of the Poincaré map and the associated fixed points, we derive the conditions ensuring the existence and stability of order-k periodic solutions. Criteria for the existence and stability of predator-free periodic solutions are also established, followed by bifurcation and sensitivity analyses with respect to key parameters. Numerical simulations are finally presented to demonstrate the validity and practical effectiveness of the proposed control strategies. Theoretical and numerical results indicate that implementing two different control strategies reduces the likelihood of resistance development in red imported fire ants, and the introduction of predators makes the control strategies more long-term and effective. This provides scientific and effective theoretical guidance for the management of a red imported fire ant populations.