Transmission dynamics of an influenza model with vaccination and antiviral treatment

In this paper, we propose a novel compartmental model integrating dual intervention strategies (vaccination and antiviral treatment) to investigate influenza transmission dynamics. The mathematical analysis demonstrates that the basic reproduction number [Formula: see text] serves as an epidemiological threshold governing system behavior: If [Formula: see text], global stability of the disease-free equilibrium ensures pathogen elimination; if [Formula: see text], stability of the resistant-strain-dominant equilibrium suggests competitive exclusion of drug-sensitive variants; while if [Formula: see text], stability of the endemic equilibrium indicates long-term circulation of sensitive strains. Epidemiologically, we identify two critical intervention insights: (i) Vaccination coverage positively correlates with infection reduction efficiency, exhibiting nonlinear dose-response characteristics; (ii) Antiviral treatment efficacy depends on time-dependent adaptive deployment, requiring dynamic balancing between drug resistance risks and outbreak containment benefits. These findings provide quantitative guidance for designing phased intervention strategies during influenza outbreaks, particularly in optimizing resource allocation between prophylactic vaccination and therapeutic protocols.