Medical prescribing and antibiotic resistance: A game-theoretic analysis of a potentially catastrophic social dilemma

Abstract

The availability of antibiotics presents medical practitioners with a prescribing dilemma. On the one hand, antibiotics provide a safe and effective treatment option for patients with bacterial infections, but at a population level, over-prescription reduces their effectiveness by facilitating the evolution of bacteria that are resistant to antibiotic medication. A game-theoretic investigation, including analysis of equilibrium strategies, evolutionarily stability, and replicator dynamics, reveals that rational doctors, motivated to attain the best outcomes for their own patients, will prescribe antibiotics irrespective of the level of antibiotic resistance in the population and the behavior of other doctors, although they would achieve better long-term outcomes if their prescribing were more restrained. Ever-increasing antibiotic resistance may therefore be inevitable unless some means are found of modifying the payoffs of this potentially catastrophic social dilemma.

Fig 1. Payoff functions.

Payoffs from T (treat with antibiotics) and U (do not treat with antibiotics) for a representative probability of bacterial infection of ϕ = .5, showing T as a dominant strategy. For different values of ϕ > 0, only the slope of the function changes. The values used to generate the graph are given in S1 Table.

Fig 2. Replicator dynamics.

Three-dimensional plot of the dynamic of the antibiotic prescribing game determined by the replicator equation. The ϕ axis represents the probability that a symptomatic patient has a bacterial infection, and the q axis represents the proportion of symptomatic patients in the population receiving antibacterial medication. The vertical axis is the value of $\dot{q}$ = dq/dt.

Fig 3. Replicator dynamics.

The set of points determined by values of ϕ and q, illustrating the basin of attraction and typical trajectories of the replicator dynamics, with an unstable rest point where ϕ = q = 0 and stable rest point and global attractor at ϕ = q = 1. The shading indicates most rapid change at high values of ϕ and q = 1/3.