Modelling and analysis of a cocktail phage therapy with coinfection
We analyze a delay differential model for phage therapy in which a cocktail of $n$ different types of bacteriophages, each with its own latency period, is administered and coinfection is allowed. We prove the global existence, uniqueness and nonnegativity of solutions, and the existence of an invariant region, under suitable conditions, in which the bacteria are eradicated exponentially fast. We determine the stability of the bacteria-free equilibrium in terms of the administered doses and give sufficient conditions for the nonexistence of coexistence equilibria, showing that coinfection may allow bacteria and phages to coexist even when the doses are large. For a cocktail of two phage types with the same latency period, we obtain a complete description of the biologically feasible coexistence equilibria, which may be zero, one or two. Numerical simulations illustrate the theoretical results.