Mathematical models play an essential role in current evolutionary biology, and evolutionary epidemiology is not an exception . While the issues of virulence evolution and drug-resistance evolution resonate in the literature for quite some time [2, 3], the study by Alizon  is one of a few that consider co-evolution of both these traits . The idea behind this study is the following: treating individuals with more severe symptoms at a higher rate (which appears to be quite natural) leads to an appearance of virulent drug-resistant strains, via treatment failure. The author then shows that virulence in drug-resistant strains may face different selective pressures than in drug-sensitive strains and hence proceed at different rates. Hence, treatment itself modulates evolution of virulence. As one of the reviewers emphasizes, the present manuscript offers a mathematical view on why the resistant and more virulent strains can be selected in epidemics. Also, we both find important that the author highlights that the topic and results of this study can be attributed to public health policies and development of optimal treatment protocols .
Mathematical models are simplified representations of reality, created with a particular purpose. It can be simple as well as complex, but even simple models can produce relatively complex and knitted results. The art of modelling thus lies not only in developing a model, but also in interpreting and unknitting the results. And this is what Alizon  indeed does carefully and exhaustively. Using two contrasting theoretical approaches to study co-evolution, the Price equation approach to study short-term evolution and the adaptive dynamics approach to study long-term evolution, Alizon  shows that a positive correlation between the rate of treatment and infection severity causes virulence in drug-sensitive strains to decrease. Clearly, no single model can describe and explain an examined system in its entirety, and even this aspect of the work is taken seriously. Many possible extensions of the study are laid out, providing a wide opportunity to pursue this topic even further. Personally, I have had an opportunity to read many Alizon’s papers and use, teach or discuss many of his models and results. All, including the current one, keep high standard and pursue the field of theoretical (evolutionary) epidemiology.
 Gandon S, Day T, Metcalf JE, Grenfell BT (2016) Forecasting epidemiological and evolutionary dynamics of infectious diseases. Trends Ecol Evol 31: 776-788. doi: https://doi.org/10.1016/j.tree.2016.07.010
 Berngruber TW, Froissart R, Choisy M, Gandon S (2013) Evolution of virulence in emerging epidemics. PLoS Pathog 9(3): e1003209. doi: https://doi.org/10.1371/journal.ppat.1003209
 Spicknall IH, Foxman B, Marrs CF, Eisenberg JNS (2013) A modeling framework for the evolution and spread of antibiotic resistance: literature review and model categorization. Am J Epidemiol 178: 508-520. doi: https://doi.org/10.1093/aje/kwt017
 Alizon S (2020) Treating symptomatic infections and the co-evolution of virulence and drug resistance. bioRxiv, 2020.02.29.970905, ver. 3 peer-reviewed and recommended by PCI Evol Biol. doi: https://doi.org/10.1101/2020.02.29.970905
 Carval D, Ferriere R (2010) A unified model for the coevolution of resistance, tolerance, and virulence. Evolution 64: 2988–3009. doi: https://doi.org/10.1111/j.1558-5646.2010.01035.x
 Read AF, T Day, and S Huijben (2011). The evolution of drug resistance and the curious orthodoxy of aggressive chemotherapy. Proc Natl Acad Sci USA 108 Suppl 2, 10871–7. doi: https://doi.org/10.1073/pnas.1100299108
DOI or URL of the preprint: 10.1101/2020.02.29.970905
Version of the preprint:
Three reviewers evaluated the manuscript and all agree that the study is interesting. On the other hand, all raise a number of comments that require a revision of the manuscript. These comments vary and include a request to (1) provide a more detailed biological ground for the model, (2) perform some sensitivity analysis with respect to model parameters as well as to motivate the selected parameter values, (3) provide a deeper justification of the modelling choices. I agree with all these comments.
The central aspect of the study appears to be that more virulent infections are treated more. However, I miss any consistent part of the manuscript, such a subsection, that would discuss this issue at a reasonable depth. Information is provided here and there, but I cannot see any formula that would model this. Moreover, Figure S3A that appears to describe this is given only in the appendix, and its legend is quite poor; How the points are obtained? Is the dashed line a fit? I think a deeper discussion of this has to precede model formulation. I admit I do not fully agree with the general idea that more treatment of more virulent individuals generally means faster recovery. I can imagine that severely symptomatic individuals, despite receiving more treatment, may recover much later than individuals with mild symptoms and less treatment.
Furthermore, it seems the parameter rho is constant in simulations and does not depend on treatment level and symptoms severity. Is this realistic? Is not more likely that when more treatment is provided then there is more likely that treatment fails (or vice versa), so that rho cannot be considered constant?
Is seems the only result that is reflected in the abstract comes from Figure 3B. Honestly, I do not see the shown difference worth the merit given in the abstract and am curious how small changes in model parameters may change the curves. On the other hand, why results from adaptive dynamics are not reflected in the abstract?
Regarding adaptive dynamics, I am curious why calculations conserving evolutionary and convergence stability are not provided and a typical pairwise invasibility plot is not shown.
My final remark concerns the use of Price equation technique. As Figure 2 suggests, even at quite short temporal scale the approximation power of the Price equation system is quite poor, as the author himself admits, so I really do not see utility of it. Why the author keeps it here? I can imagine moving everything of it to an appendix and say it does not work well, but I regret not providing it in any form, but as it is now I doubt it is useful.
In summary, I also find the study interesting and useful, but at the same time think the author should revise the manuscript in order to present motivation, model formulation and results presentation in a more balanced way.