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ABSTRACT Predator‐prey models, such as the Leslie‐Gower model, are essential for understanding population dynamics and stability within ecosystems. These models help explain the balance between species under natural conditions, but the inclusion of factors like the Allee effect and intraspecific competition adds complexity and realism to these interactions, enhancing our ability to predict system behavior under stress. To detect early indicators of population collapse, this study investigates the intricate dynamics of a modified Leslie‐Gower predator‐prey model with both Allee effect and intraspecific competition. We analyze the existence and stability of equilibria, as well as bifurcation phenomena, including saddle‐node bifurcations of codimension 2, Hopf bifurcations of codimension 2, and Bogdanov‐Takens bifurcations of codimension at least 4. Detailed transitions between bifurcation curves–specifically saddle‐node, Hopf, homoclinic, and limit cycle bifurcations–are also examined. We observe a novel transition phenomenon, where a system jumps from saddle‐node bifurcation to homoclinic and limit cycle bifurcations. This suggests that burst oscillations may serve as an early warning of system collapse rather than simply a tipping point. Our findings indicate that moderate levels of intraspecific competition or Allee effect support coexistence of both populations, while excessive levels may destabilize the entire biological system, leading to collapse. These insights offer valuable implications for ecological management and the early detection of risks in population dynamics. 

Direct-acting antiviral agents (DAAs) are known to interfere with various intracellular stages of the hepatitis C virus (HCV) life cycle and have demonstrated efficacy in treating HCV infection. However, DAA monotherapy can lead to drug resistance due to mutations. This paper explores the impact of DAA therapy on HCV dynamics using a multiscale age-structured partial differential equation (PDE) model that incorporates intracellular viral RNA replication within infected cells and two strains of viruses representing a drug-sensitive strain and a drug-resistant mutant variant, respectively. We derived an equivalent ordinary differential equation (ODE) model from the PDE model to simplify mathematical analysis and numerical simulations. We studied the dynamics of the two virus strains before treatment and investigated the impact of mutations on the evolution kinetics of drug-sensitive and drug-resistant viruses, as well as the competition between the two strains during treatment. We also explored the role of DAAs in blocking HCV RNA replication and releasing new virus particles from cells. During treatment, mutations do not significantly influence the dynamics of various virus strains; however, they can generate low-level HCV that may be completely inhibited due to their poor fitness. The fitness of the mutant strain compared to the drug-sensitive strain determines which strain dominates the virus population. We also investigated the prevalence and drug resistance evolution of HCV variants during DAA treatment.