When Does Overuse of Antibiotics Become a Tragedy of the Commons?

<div><h3>Background</h3><p>Over-prescribing of antibiotics is considered to result in increased morbidity and mortality from drug-resistant organisms. A resulting common wisdom is that it would be better for society if physicians would restrain their prescription of antibiotics. In this view, self-interest and societal interest are at odds, making antibiotic use a classic “tragedy of the commons”.</p> <h3>Methods and Findings</h3><p>We developed two mathematical models of transmission of antibiotic resistance, featuring <em>de novo</em> development of resistance and transmission of resistant organisms. We analyzed the decision to prescribe antibiotics as a mathematical game, by analyzing individual incentives and community outcomes.</p> <h3>Conclusions</h3><p>A conflict of interest may indeed result, though not in all cases. Increased use of antibiotics by individuals benefits society under certain circumstances, despite the amplification of drug-resistant strains or organisms. In situations where increased use of antibiotics leads to less favorable outcomes for society, antibiotics may be harmful for the individual as well. For other scenarios, where a conflict between self-interest and society exists, restricting antibody use would benefit society. Thus, a case-by-case assessment of appropriate use of antibiotics may be warranted.</p> </div

Distribution parameter estimates with 95% confidence intervals.

<p>*Shape parameter for the truncated mixed exponential refers to the proportion parameter</p><p>**Shape parameter for the truncated normal and Gumbel distributions refers to the location parameter</p><p>***Parameter 3 for the generalized gamma refers to the second shape parameter</p><p>Distribution parameter estimates with 95% confidence intervals.</p

Antibiotic use modeled as a mathematical game.

<p>Each row corresponds to the strategy of a particular individual, and each column corresponds to a unanimous strategy chosen by the rest of the population. The welfare or utility of the individual player is represented in each cell (, , , or ), and can be calculated directly from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0046505#pone.0046505.e108" target="_blank">Equation 17</a> by substituting the individual's choice of treatment rate and the forces of infection and resulting from the community choice of . See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0046505#pone.0046505.s001" target="_blank">Text S1</a> for details.</p

Numerical scenarios for Figure 2.

<p>In all scenarios, , , and . The first column refers to the panel in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0046505#pone-0046505-g002" target="_blank">Figure 2</a>. Subsequent columns give the particular parameters chosen for the panel. The final two columns provide the minimum equilibrium prevalence and the maximum equilibrium prevalence of the severe state (from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0046505#pone.0046505.e072" target="_blank">Equation (7)</a> in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0046505#pone.0046505.s001" target="_blank">Text S1</a>), respectively, for the parameters in the panel.</p

Exponential distribution and other distributions which mimic the exponential, fit to Tanzanian data.

<p>This figure shows the Tanzanian trachoma prevalence data as a histogram in the background along with the fits of various distributions which can mimic the exponential. The black line indicates the exponential distribution fit to the data, along with the 95% confidence interval as gray shading. All the other distributions give their best fit to the data when taking on parameter values that are consistent with the exponential, as shown by their fit within the 95% confidence interval (gray shading) of the exponential curve.</p

Relative fraction of time spent in the severe disease under six different scenarios.

<p>The -axes are the community level of treatment, i.e. the strategy assumed chosen by all other members of the community. The -axes are the level of treatment chosen by an individual within the community. The contour plot shows the fraction of time spent by this person, in the severe state; each panel has been scaled so that the minimum value is zero (blue) and the maximum value is 1 (red). The numerical parameter choices are given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0046505#pone-0046505-t002" target="_blank">Table 2</a>, and the minimum and maximum values for each panel.</p

Assessment of the effect of over-treatment of mild infection on the treatment of mild infections.

<p>It was assumed that severely infected individuals do not transmit, and that drug resistance does not develop during treatment of severe infections. The mean time to treatment is set at 5 (arbitrary units) for mild infection, and 1/3 units for severe infection. All other expected waiting times (recovery, progression) are equal to 1. The reproduction number for the drug-sensitive organism is 1.5. See Text for full details of Model 2. Under these assumptions, the drug-resistant organism competitively excludes the drug-sensitive organism whenever the relative transmissibility exceeds 10/11 (91%) (grey area, labeled “No sensitive strain”). The parameters are , , , , , , and . The horizontal axis corresponds to and the vertical axis to .</p

Compartmental flow diagram for Model 2.

<p>Each circle represents a state variable; each arrow a transition. The state variables are: —the number of uninfected individuals, —the number of individuals with mild infection by the drug-sensitive organism, —the number of individuals with severe infection by the drug-sensitive organism, —the number of individuals with mild infection by the drug-resistant organism, and —the number of individuals with severe infection by the drug-resistant organism. Treatment rates for the mild and severe state are given by and , respectively. The arrows are labeled with per-individual flow rates; the total flow rate from each state along each arrow is given by the label of the arrow times the number of individuals in the state. The explicit differential equations and parameter definitions are given in the main text.</p

Fit of distributions, ranked by corrected Akaike Information Criteria (AIC_c).

<p>*All distributions were truncated between a prevalence of 0 and 1</p><p>Fit of distributions, ranked by corrected Akaike Information Criteria (AIC_c).</p

Reasons listed as obstacles to eradication.

<p><i>P</i> = 0.22 comparing the distribution of responses between the five neglected tropical diseases.</p