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While disease propagation is a main focus of network science, its coevolution with treatment has yet to be studied in this framework. We present a mean-field and stochastic analysis of an epidemic model with antiviral administration and resistance development. We show how this model maps to a coevolutive competition between site and bond percolation featuring hysteresis and both second- and first-order phase transitions. The latter, whose existence on networks is a long-standing question, imply that a microscopic change in infection rate can lead to macroscopic jumps in expected epidemic size.
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