Researchers built a delay‑differential model that includes a cocktail of n phage types, each with its own latency period. The model allows phages to infect the same bacterium (coinfection). The authors proved that, under reasonable parameter and initial‑condition assumptions, solutions exist for all time and stay nonnegative. They found an invariant set in which the susceptible bacteria never grow and actually decline to zero exponentially fast, thanks to the administered phage doses. The formula for the exponential rate involves the phage decay, latency, and infection parameters. Importantly, the model generalises previous single‑phage works and shows that coinfection can keep bacteria and phages alive together even when doses are large. In the no‑coinfection version, coexistence only happens with very small doses. Numerical simulations confirm the theory but also reveal that the deterministic equations can predict bacterial numbers that are effectively extinct – a limitation that suggests stochastic effects would be needed for realistic predictions of bacterial survival.