<div dir="ltr"><div>Thanks Will, Thanks Robin,</div><div><br></div><div>This communication between us took a few weeks and has now become public in the integration subgroup and in the Model Reproducibility, Credibility & Standardization subgroup. </div><div><br></div><div>For the sake of new readers, it shows the difficulties of integrating a model into another model, even after publication. The interested readers are welcome to read the correspondence in chronological order - meaning starting from the end of this forwarded email and going up to see obstacles in integrating a model even after publication.</div><div><br></div><div>For those interested only is a summary, here are highlights of the effort.</div><div>I was looking for an infectiousness model to plug into my ensemble model. Will and Robin created such a model and published it as a pre-print:</div><div> <a href="https://www.medrxiv.org/content/10.1101/2020.11.20.20235754v1">https://www.medrxiv.org/content/10.1101/2020.11.20.20235754v1</a> </div><div>and made code and data available:</div><div> <a href="https://github.com/will-s-hart/COVID-19-Infectiousness-Profile">https://github.com/will-s-hart/COVID-19-Infectiousness-Profile</a><br></div><div><br></div><div>Despite the good work, there are still difficulties in integration that I summarize below:</div><div><br></div><div>1. Licensing / legal issues - even with the good will and permission of the authors to reuse results, it was still unclear how the code is allowed to be reused. This problem is typical in many situations. Each jurisdiction has its own regulations on how to release results and under what conditions and in many cases. Release conditions are unclear even to the creators of the work who wish to make the results available for reuse. This problem is deeper than suspected and this small example is far from representative and should be discussed in the working group.</div><div><br></div><div>2. Code transfer - Even when code is available with results in matlab, it was not easy to transfer the data/code to python. The reimplementation I chose eventually was hand digitizing the plots by hand rather than using the function or numerical form already computed - mostly to preserve time in attempts to convert data from a system I do not own. This is a good point for discussion since there are many systems constructed to help reuse and it would be helpful if researchers are familiar with them. </div><div><br></div><div>3. Adaptation of scale. The authors published the infectiousness model as a density function. I needed to transfer it to a curve that shows a value of 1 at max infectiousness to integrate it with multiple other infectiousness models I was integrating into the ensemble. Such typical adjustments of scale are regular in any integration adh should not be forgotten. Therefore it is important that model units and outputs are made clear.In this situation this was easy, yet it is an important element that researchers should be attentive to when publishing and integrating models. </div><div><br></div><div><br></div><div>This model was successfully integrated into the ensemble and initial simulations show the model has influence on the ensemble. There are more simulations needed to confirm this and work is on the way towards publication, yet for the sake of discussion it was important to show this effort to the working group in the most authentic way possible. I thank Will and Robin for allowing the release of our private communications. </div><div><br></div><div>This conversation adds information to another example with Filippo Castiglione summarized here:</div><div><a href="https://lists.simtk.org/pipermail/vp-integration-subgroup/2021-January/000011.html">https://lists.simtk.org/pipermail/vp-integration-subgroup/2021-January/000011.html</a><br></div><div><br></div><div>I call upon other members of the working group to continue the discussion and raise other issues they had with reproducing models or integrating them. If we collect enough examples, we will have a good picture of difficulties and perhaps make some recommendations that can help us all in the future.</div><div><br></div><div> Jacob</div><div><br></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Mon, Jan 11, 2021 at 4:39 AM William Hart <<a href="mailto:william.hart@keble.ox.ac.uk">william.hart@keble.ox.ac.uk</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div dir="ltr">
<div style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">
Hi both,</div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">
<br>
</div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">
This is fine with me.</div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">
<br>
</div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">
Best,</div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">
Will</div>
<div id="gmail-m_8347977369011973893appendonsend"></div>
<hr style="display:inline-block;width:98%">
<div id="gmail-m_8347977369011973893divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> Robin Thompson <<a href="mailto:robin.thompson1988@gmail.com" target="_blank">robin.thompson1988@gmail.com</a>><br>
<b>Sent:</b> 11 January 2021 10:03<br>
<b>To:</b> Jacob Barhak <<a href="mailto:jacob.barhak@gmail.com" target="_blank">jacob.barhak@gmail.com</a>><br>
<b>Cc:</b> William Hart <<a href="mailto:william.hart@keble.ox.ac.uk" target="_blank">william.hart@keble.ox.ac.uk</a>><br>
<b>Subject:</b> </font>
<div> </div>
</div>
<div style="overflow-wrap: break-word;">Hi Jacob,
<div><br>
</div>
<div>If it is ok with Will, please feel free to post the text below to the mailing list, if you think this is useful (including this email).</div>
<div><br>
</div>
<div>I guess it might be worth highlighting in addition the fact that we were unsure, from the university’s perspective, whether there would be any issues regarding commercial use of IP. None of the coauthors of the preprint had any *personal* issues
with the results being used (instead we were grateful that someone else was interested in our research!)</div>
<div><br>
</div>
<div>As you mentioned, please also feel free to summarise any other things we discussed in a summary paragraph, if this is helpful.</div>
<div><br>
</div>
<div>Thanks, and best wishes,</div>
<div>Robin<br>
<div>
<div>
<div dir="auto" style="color:rgb(0,0,0);letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none">
<div dir="auto" style="color:rgb(0,0,0);letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none">
<div>----------------------------------------------------------------------<br>
Dr Robin Thompson<br>
Assistant Professor of Mathematical Epidemiology<br>
Mathematics Institute<br>
University of Warwick, UK<br>
<a href="http://www.robin-thompson.co.uk" target="_blank">www.robin-thompson.co.uk</a><br>
----------------------------------------------------------------------</div>
</div>
</div>
</div>
<div><br>
</div>
<div>
<blockquote type="cite">
<div>
<blockquote style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div>
<blockquote style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div>
<blockquote style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div>
<div>
<div>
<blockquote type="cite">
<div>On 21 Dec 2020, at 00:45, Jacob Barhak <<a href="mailto:jacob.barhak@gmail.com" rel="noreferrer" target="_blank">jacob.barhak@gmail.com</a>> wrote:</div>
<br>
<div>
<div dir="ltr">Hi Will, Hi Robin,
<div><br>
</div>
<div>Would you be ok if this entire private conversation we have becomes public on the integration working group mailing list?</div>
<div><br>
</div>
<div>I am trying to start activities there and it seems some of the discussion here are relevant to the group activities. I already posted one, and hope to get a few more going to be posted here: </div>
<div><a href="https://lists.simtk.org/pipermail/vp-integration-subgroup/" rel="noreferrer" target="_blank">https://lists.simtk.org/pipermail/vp-integration-subgroup/</a><br>
</div>
<div><br>
</div>
<div>I started looking at your code and saw that you extract the data for the plots from the results that are saved in matlab format. </div>
<div>I do not have matlab so I tried to load your data into python and it seems I cannot load it. Here is what I did within python:</div>
<div><br>
</div>
<div>>>> import <a href="http://scipy.io/" rel="noreferrer" target="_blank">scipy.io</a><br>
</div>
<div>>>> a=scipy.io.loadmat('gen_tost_serial_varinf.mat')<br>
>>> a<br>
{'__function_workspace__': array([[ 0, 1, 73, ..., 0, 0, 0]], dtype=uint8), 'None': MatlabOpaque([('f_tost_varinf', 'MCOS', 'chebfun', array([[3707764736],<br>
[ 2],<br>
[ 1],<br>
[ 1],<br>
[ 351],<br>
[ 5]], dtype=uint32))],<br>
dtype=[('s0', 'O'), ('s1', 'O'), ('s2', 'O'), ('arr', 'O')]), '__version__': '1.0', '__header__': 'MATLAB 5.0 MAT-file, Platform: MACI64, Created on: Wed Nov 25 15:32:08 2020', '__globals__': []}<br>
>>> b=a['__function_workspace__']<br>
>>> b.shape<br>
(1L, 328760L)<br>
>>> b[:,0:60]<br>
array([[ 0, 1, 73, 77, 0, 0, 0, 0, 14, 0, 0, 0, 152,<br>
3, 5, 0, 6, 0, 0, 0, 8, 0, 0, 0, 2, 0,<br>
0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 8, 0, 0,<br>
0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0,<br>
0, 0, 0, 0, 5, 0, 4, 0]], dtype=uint8)<br>
</div>
<div><br>
</div>
<div>This data does not look the same shape and size that you are plotting, so I assume I cannot read it from python directly. To the record, I also tried importing with <span style="font-family:inherit;font-size:13px;font-style:inherit;font-variant-ligatures:inherit;font-variant-caps:inherit;white-space:inherit">mat4py
and with </span>h5py assuming you are using matlab of at least version 7.3. Yet all those attempts were unsuccessful so I am going to use other - more manual techniques. Currently it seems that the fastest way for me to integrate your model into mine is
by using hand digitization of your plot - not a very advanced way, yet more practical timewise.</div>
<div><br>
</div>
<div>I am showing this example so people will be aware that when models are integrated they may arrive from different systems and bridging this gap is something the group will have to think about. This also relates to the reproducibility working group
- so I would like you permission post this example there as well if you allow.</div>
<div><br>
</div>
<div>Please note that you did a lot by making the code available, yet we need to figure out ways to help integration. </div>
<div><br>
</div>
<div>Hopefully you will allow me to post this exchange of words publicly for the working group to learn from.</div>
<div><br>
</div>
<div> Jacob</div>
</div>
<br>
<div>
<div dir="ltr">On Thu, Dec 17, 2020 at 12:11 AM Jacob Barhak <<a href="mailto:jacob.barhak@gmail.com" rel="noreferrer" target="_blank">jacob.barhak@gmail.com</a>> wrote:<br>
</div>
<blockquote style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div dir="ltr">Thanks Will,
<div><br>
</div>
<div>This is a great response. </div>
<div><br>
</div>
<div>By the way, you forgot to put a license on Github. However, the plot there is good enough for me to use - I will figure out how. </div>
<div><br>
</div>
<div>No need for you to do anything more about this for now - I think I have enough information to plug this into my model.</div>
<div><br>
</div>
<div>And yes, this can surely be an activity of the working group since it has to do with model integration. </div>
<div><br>
</div>
<div>Also the discussion we had about legalities is a discussion that we need to have within the working group - those are important issues so we can integrate models in the future - there are legal and reproducibility issues on top of technical issues
- we will for sure visit those in the working group. </div>
<div><br>
</div>
<div>And believe me, I understand having little time - you already contributed more than many others and I will make sure to mention this contribution and you and Robin will know when it gets published.</div>
<div><br>
</div>
<div>Many thanks.</div>
<div><br>
</div>
<div> Jacob</div>
<div><br>
</div>
<div><br>
</div>
</div>
<br>
<div>
<div dir="ltr">On Wed, Dec 16, 2020 at 6:19 AM William Hart <<a href="mailto:william.hart@keble.ox.ac.uk" rel="noreferrer" target="_blank">william.hart@keble.ox.ac.uk</a>> wrote:<br>
</div>
<blockquote style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div dir="ltr">
<div style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:12pt">
Dear Jacob,</div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:12pt">
<br>
</div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:12pt">
Please see replies inline below.</div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:12pt">
<br>
</div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:12pt">
Best,</div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:12pt">
Will</div>
<div id="gmail-m_8347977369011973893x_gmail-m_-5131238465839367626gmail-m_-4983041146313843276m_-2632048584263934382gmail-m_-3942947124605790361gmail-m_-1706512601079854910appendonsend">
</div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:12pt">
<br>
</div>
<hr style="display:inline-block;width:945.297px">
<div id="gmail-m_8347977369011973893x_gmail-m_-5131238465839367626gmail-m_-4983041146313843276m_-2632048584263934382gmail-m_-3942947124605790361gmail-m_-1706512601079854910divRplyFwdMsg" dir="ltr">
<font face="Calibri, sans-serif" style="font-size:11pt"><b>From:</b> Jacob Barhak <<a href="mailto:jacob.barhak@gmail.com" rel="noreferrer" target="_blank">jacob.barhak@gmail.com</a>><br>
<b>Sent:</b> 14 December 2020 06:15<br>
<b>To:</b> William Hart <<a href="mailto:william.hart@keble.ox.ac.uk" rel="noreferrer" target="_blank">william.hart@keble.ox.ac.uk</a>><br>
<b>Cc:</b> robin_thompson1988_gmail_com <<a href="mailto:robin.thompson1988@gmail.com" rel="noreferrer" target="_blank">robin.thompson1988@gmail.com</a>><br>
<b>Subject:</b> Re: Interface article</font>
<div> </div>
</div>
<div>
<div dir="ltr">
<div dir="ltr">Ok William,
<div><br>
</div>
<div>Your paper has the elements I need to plug into my ensamble. In fact perhaps several of them. However, I cannot easily extract those since the paper is written from a theoretical point of view and I need actual numbers. </div>
<div><br>
</div>
<div>What I need is the function you show in figure 2A. Yet I need it as a function. f(t) where f is relative infectiousness and t is time from infection. </div>
<div><br>
</div>
<div>This relative infectiousness will later be multiplied by a transmission probability that I calculate another way.</div>
<div><br>
</div>
<div>My questions to you are:</div>
<div>1. Is the generation function you show in 2A a density function such that Int(f(t))=1? Since the title is density I assume the answer is yes.</div>
</div>
</div>
</div>
<blockquote style="margin:0px 0px 0px 40px;border:none;padding:0px">
<div>
<div dir="ltr">
<div dir="ltr">
<div><span style="color:rgb(200,38,19)">Yes</span></div>
</div>
</div>
</div>
</blockquote>
<div>
<div dir="ltr">
<div dir="ltr">
<div>2. Are the functions shown in figure 2A the curves that best fit your data and do those optimize all parameters or did you make some assumptions on some of the parameters - basically I am asking if those curves are one example of a family of curves,
or are those the optimal curve. I assume it is the optimal one.</div>
</div>
</div>
</div>
<blockquote style="margin:0px 0px 0px 40px;border:none;padding:0px">
<div>
<div dir="ltr">
<div dir="ltr">
<div><span style="color:rgb(200,38,19)"><i>This is slightly different for each different model, but in general 2 or 3 parameters are fitted in each case, whereas some others may be assumed (this is fully detailed in the methods section).</i></span></div>
</div>
</div>
</div>
</blockquote>
<div>
<div dir="ltr">
<div dir="ltr">
<div>3. Do you have the function form of the curves im 2A or are those numerically solved - I assume those are numerically solved - I saw you use MCMC. Yet I may be mistaken.</div>
</div>
</div>
</div>
<blockquote style="margin:0px 0px 0px 40px;border:none;padding:0px">
<div>
<div dir="ltr">
<div dir="ltr">
<div><span style="color:rgb(200,38,19)"><i>Again, this differs between models, but in most cases there is no closed form for the generation time distribution, so some numerics are necessary. </i></span></div>
</div>
</div>
</div>
</blockquote>
<div>
<div dir="ltr">
<div dir="ltr">
<div>4. Is it possible to get the numbers that generated plot 2A in spreadsheet / table form rather than extracting them by manual digitization from the figure?</div>
</div>
</div>
</div>
<blockquote style="margin:0px 0px 0px 40px;border:none;padding:0px">
<div>
<div dir="ltr">
<div dir="ltr">
<div><span style="color:rgb(200,38,19)"><i>MATLAB code from the preprint is publicly available; in particular, please find the code to generate Fig. 2 here (<a href="https://github.com/will-s-hart/COVID-19-Infectiousness-Profile/tree/main/Plotting%20code" id="gmail-m_8347977369011973893x_gmail-m_-5131238465839367626gmail-m_-4983041146313843276m_-2632048584263934382gmail-m_-3942947124605790361gmail-m_-1706512601079854910LPlnk" rel="noreferrer" target="_blank">https://github.com/will-s-hart/COVID-19-Infectiousness-Profile/tree/main/Plotting%20code</a>).
If you have no access to MATLAB (the code may work on Octave etc, but I'm not sure), I may be able to send you a spreadsheet of values.</i></span></div>
</div>
</div>
</div>
</blockquote>
<div>
<div dir="ltr">
<div dir="ltr">
<div></div>
<div>5. Can this information be used for commercial purposes and what terms of use are affiliated with this information? I need to ask since I am a sole proprietor - a company of one person. If I invest the time to hand digitize the functions in
2A and plug them into my ensemble, I need to know I will not have to remove them in the future because of some legal limitation or a scientist that misbehaves - this happened in the past and cost me a lot of work and it is not worth for me using if the model
is somehow restricted. Basically I am asking you what the usage term for your are?</div>
</div>
</div>
</div>
<blockquote style="margin:0px 0px 0px 40px;border:none;padding:0px">
<div>
<div dir="ltr">
<div dir="ltr">
<div><span style="color:rgb(200,38,19)"><i>Please see Robin's reply (I have no personal issue with you using our results).</i></span></div>
</div>
</div>
</div>
</blockquote>
<div>
<div dir="ltr">
<div dir="ltr">
<div><br>
</div>
<div>Also, are you aware of this publication:</div>
<div><a href="https://doi.org/10.1101/2020.09.25.20201772" rel="noreferrer" target="_blank">https://doi.org/10.1101/2020.09.25.20201772</a><br>
</div>
<div><br>
</div>
<div>It has an infectiousness model and Alan Perelson talked about it here:</div>
<div><a href="https://www.youtube.com/watch?v=RXY8EoChWU4" rel="noreferrer" target="_blank">https://www.youtube.com/watch?v=RXY8EoChWU4</a><br>
</div>
<div><br>
</div>
</div>
</div>
</div>
<blockquote style="margin:0px 0px 0px 40px;border:none;padding:0px">
<div>
<div dir="ltr">
<div dir="ltr">
<div><span style="color:rgb(200,38,19)"><i>Looks very interesting!</i></span><br>
</div>
</div>
</div>
</div>
</blockquote>
<div>
<div dir="ltr">
<div dir="ltr">
<div><br>
</div>
<div>The video is part of the Viral pandemic working group. I saw that you are part of the integration working group - so if we reach an agreement I will be happy to add this as an official activity of the subgroup. </div>
<div><br>
</div>
</div>
</div>
</div>
<blockquote style="margin:0px 0px 0px 40px;border:none;padding:0px">
<div>
<div dir="ltr">
<div dir="ltr">
<div><span style="color:rgb(200,38,19)"><i>Up to you - unfortunately, I don't think I would have time to contribute to this if it became a subgroup activity, but I would be interested to see the results.</i></span><br>
</div>
</div>
</div>
</div>
</blockquote>
<div>
<div dir="ltr">
<div dir="ltr">
<div><br>
</div>
<div> Jacob</div>
<div><br>
</div>
<div>--<br>
Jacob Barhak Ph.D.<br>
<a href="https://sites.google.com/view/jacob-barhak/home" rel="noreferrer" target="_blank">https://sites.google.com/view/jacob-barhak/home</a><br>
<br>
</div>
<div><br>
</div>
</div>
</div>
<br>
<div>
<div dir="ltr">On Thu, Dec 10, 2020 at 12:57 AM Jacob Barhak <<a href="mailto:jacob.barhak@gmail.com" rel="noreferrer" target="_blank">jacob.barhak@gmail.com</a>> wrote:<br>
</div>
<blockquote style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div dir="ltr">Great William,
<div><br>
</div>
<div>You may be right, at first glance this seems like what I am looking for - yet I need to read the details and can do this only during the weekend - so I will come back with questions after I read this and see if I can plug your model into the ensemble.</div>
<div><br>
</div>
<div>I look forward to more communications.</div>
<div><br>
</div>
<div> Jacob</div>
</div>
<br>
<div>
<div dir="ltr">On Wed, Dec 9, 2020 at 9:44 AM William Hart <<a href="mailto:william.hart@keble.ox.ac.uk" rel="noreferrer" target="_blank">william.hart@keble.ox.ac.uk</a>> wrote:<br>
</div>
<blockquote style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div dir="ltr">
<div style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:12pt">
Hi Jacob,</div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:12pt">
<br>
</div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:12pt">
Looks interesting!</div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:12pt">
<br>
</div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:12pt">
Yes, we have actually recently released a pre-print in which we do (I think) exactly what you're looking for (<a href="https://www.medrxiv.org/content/10.1101/2020.11.20.20235754v1" id="gmail-m_8347977369011973893x_gmail-m_-5131238465839367626gmail-m_-4983041146313843276m_-2632048584263934382gmail-m_-3942947124605790361gmail-m_-1706512601079854910x_gmail-m_-5673067390408668895gmail-m_-5902831182261359202gmail-m_7619410952582035214LPlnk" rel="noreferrer" target="_blank">https://www.medrxiv.org/content/10.1101/2020.11.20.20235754v1</a>).
In particular, Figure 2A of the pre-print shows the (expected) infectiousness as a function of time since infection (we considered fitting several different models of infectiousness to data; the blue curve corresponds to our best model).</div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:12pt">
<br>
</div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:12pt">
Please do let me know if you have any questions about what we did.</div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:12pt">
<br>
</div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:12pt">
Best,</div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:12pt">
Will</div>
<div>
<div id="gmail-m_8347977369011973893x_gmail-m_-5131238465839367626gmail-m_-4983041146313843276m_-2632048584263934382gmail-m_-3942947124605790361gmail-m_-1706512601079854910x_gmail-m_-5673067390408668895gmail-m_-5902831182261359202gmail-m_7619410952582035214LPBorder_GTaHR0cHM6Ly93d3cubWVkcnhpdi5vcmcvY29udGVudC8xMC4xMTAxLzIwMjAuMTEuMjAuMjAyMzU3NTR2MQ.." style="width:800px;margin-top:16px;margin-bottom:16px;max-width:800px;min-width:424px">
<table id="gmail-m_8347977369011973893x_gmail-m_-5131238465839367626gmail-m_-4983041146313843276m_-2632048584263934382gmail-m_-3942947124605790361gmail-m_-1706512601079854910x_gmail-m_-5673067390408668895gmail-m_-5902831182261359202gmail-m_7619410952582035214LPContainer580217" style="padding:12px 36px 12px 12px;width:750px;border:1px solid rgb(200,200,200);border-radius:2px">
<tbody>
<tr valign="top" style="border-spacing:0px">
<td style="width:744px">
<div id="gmail-m_8347977369011973893x_gmail-m_-5131238465839367626gmail-m_-4983041146313843276m_-2632048584263934382gmail-m_-3942947124605790361gmail-m_-1706512601079854910x_gmail-m_-5673067390408668895gmail-m_-5902831182261359202gmail-m_7619410952582035214LPTitle580217" style="font-size:21px;margin-right:8px;font-family:wf_segoe-ui_light,"Segoe UI Light","Segoe WP Light","Segoe UI","Segoe WP",Tahoma,Arial,sans-serif;margin-bottom:12px">
<a id="gmail-m_8347977369011973893x_gmail-m_-5131238465839367626gmail-m_-4983041146313843276m_-2632048584263934382gmail-m_-3942947124605790361gmail-m_-1706512601079854910x_gmail-m_-5673067390408668895gmail-m_-5902831182261359202gmail-m_7619410952582035214LPUrlAnchor580217" href="https://www.medrxiv.org/content/10.1101/2020.11.20.20235754v1" rel="noreferrer" style="text-decoration:none" target="_blank">High
infectiousness immediately before COVID-19 symptom onset highlights the importance of contact tracing | medRxiv</a></div>
<div id="gmail-m_8347977369011973893x_gmail-m_-5131238465839367626gmail-m_-4983041146313843276m_-2632048584263934382gmail-m_-3942947124605790361gmail-m_-1706512601079854910x_gmail-m_-5673067390408668895gmail-m_-5902831182261359202gmail-m_7619410952582035214LPDescription580217" style="font-size:14px;max-height:100px;color:rgb(102,102,102);font-family:wf_segoe-ui_normal,"Segoe UI","Segoe WP",Tahoma,Arial,sans-serif;margin-bottom:12px;margin-right:8px;overflow:hidden">
Understanding changes in infectiousness during COVID-19 infections is critical to assess the effectiveness of public health measures such as contact tracing. Data from known source-recipient pairs can be used to estimate the average infectiousness profile of
infected individuals, and to evaluate the proportion of presymptomatic transmissions.</div>
<div id="gmail-m_8347977369011973893x_gmail-m_-5131238465839367626gmail-m_-4983041146313843276m_-2632048584263934382gmail-m_-3942947124605790361gmail-m_-1706512601079854910x_gmail-m_-5673067390408668895gmail-m_-5902831182261359202gmail-m_7619410952582035214LPMetadata580217" style="font-size:14px;color:rgb(166,166,166);font-family:wf_segoe-ui_normal,"Segoe UI","Segoe WP",Tahoma,Arial,sans-serif">
<a href="http://www.medrxiv.org/" rel="noreferrer" target="_blank">www.medrxiv.org</a></div>
</td>
</tr>
</tbody>
</table>
</div>
</div>
<br>
<div id="gmail-m_8347977369011973893x_gmail-m_-5131238465839367626gmail-m_-4983041146313843276m_-2632048584263934382gmail-m_-3942947124605790361gmail-m_-1706512601079854910x_gmail-m_-5673067390408668895gmail-m_-5902831182261359202gmail-m_7619410952582035214appendonsend">
</div>
<hr style="display:inline-block;width:921.219px">
<div id="gmail-m_8347977369011973893x_gmail-m_-5131238465839367626gmail-m_-4983041146313843276m_-2632048584263934382gmail-m_-3942947124605790361gmail-m_-1706512601079854910x_gmail-m_-5673067390408668895gmail-m_-5902831182261359202gmail-m_7619410952582035214divRplyFwdMsg" dir="ltr">
<font face="Calibri, sans-serif" style="font-size:11pt"><b>From:</b> Jacob Barhak <<a href="mailto:jacob.barhak@gmail.com" rel="noreferrer" target="_blank">jacob.barhak@gmail.com</a>><br>
<b>Sent:</b> 09 December 2020 14:30<br>
<b>To:</b> robin_thompson1988_gmail_com <<a href="mailto:robin.thompson1988@gmail.com" rel="noreferrer" target="_blank">robin.thompson1988@gmail.com</a>><br>
<b>Cc:</b> William Hart <<a href="mailto:william.hart@keble.ox.ac.uk" rel="noreferrer" target="_blank">william.hart@keble.ox.ac.uk</a>><br>
<b>Subject:</b> Re: Interface article</font>
<div> </div>
</div>
<div>
<div dir="ltr">Hi William,
<div><br>
</div>
<div>Robin communicated to me that you may have some answers regarding COVID-19 infectiousness. I am modeling COVID-19 as you can see from this article:</div>
<div>
<ul>
<li>
<p style="margin-bottom:0in;line-height:14.6667px;font-family:Calibri,serif;font-size:11pt;direction:ltr;color:rgb(0,0,10)">
<font face="Times New Roman, serif">Barhak J , The Reference Model Initial Use Case for COVID-19. Cureus. </font><font color="#0000ff"><u><a href="http://dx.doi.org/10.7759/cureus.9455" rel="noreferrer" style="color:rgb(0,0,255)" target="_blank"><font face="Times New Roman, serif">http://dx.doi.org/10.7759/cureus.9455</font></a></u></font><font face="Times New Roman, serif"> ,
Online: </font><font color="#0000ff"><u><a href="https://www.cureus.com/articles/36677-the-reference-model-an-initial-use-case-for-covid-19" rel="noreferrer" style="color:rgb(0,0,255)" target="_blank"><font face="Times New Roman, serif">https://www.cureus.com/articles/36677-the-reference-model-an-initial-use-case-for-covid-19</font></a></u></font><font face="Times New Roman, serif"> .
PMCID: </font><font color="#0000ff"><u><a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7392354/" rel="noreferrer" style="color:rgb(0,0,255)" target="_blank"><font face="Times New Roman, serif">PMC7392354</font></a></u></font><font face="Times New Roman, serif"> ,
PMID: 32760637 , Interactive Results: </font><font color="#0000ff"><u><a href="https://jacob-barhak.netlify.app/thereferencemodel/results_covid19_2020_06_27/combinedplot" rel="noreferrer" style="color:rgb(0,0,255)" target="_blank"><font face="Times New Roman, serif">https://jacob-barhak.netlify.app/thereferencemodel/results_covid19_2020_06_27/combinedplot</font></a></u></font><font face="Times New Roman, serif"></font></p>
</li></ul>
</div>
<div><br>
</div>
<div>I am expanding this work to include multiple infectioneness models and have preliminary results already, yet I am looking for more infectiousness models to plug into the model.</div>
<div><br>
</div>
<div>Specifically I am looking for a function that will communicate how infectious is an individual as a function of time since their infection.</div>
<div><br>
</div>
<div>Hopefully you have something like this and will be happy to communicate.</div>
<div><br>
</div>
<div> Jacob</div>
<div><br>
</div>
<div><br>
</div>
<div><br>
</div>
<div><br>
</div>
<div><br>
</div>
</div>
<br>
<div>
<div dir="ltr">On Wed, Dec 9, 2020 at 5:34 AM Robin Thompson <<a href="mailto:robin.thompson1988@gmail.com" rel="noreferrer" target="_blank">robin.thompson1988@gmail.com</a>> wrote:<br>
</div>
<blockquote style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
Hi Will,<br>
<br>
Jacob Barhak (cc’d) contacted me because he is interested in your within-host -> between-host manuscript. I thought you might be in a better position to answer any questions he might have, so this email is to connect him to you.<br>
<br>
Thanks, and best wishes,<br>
Robin<br>
--------------------------------------------------------------------------<br>
Dr Robin Thompson<br>
Junior Research Fellow in Mathematical Epidemiology<br>
Christ Church<br>
University of Oxford, UK<br>
<a href="http://www.robin-thompson.co.uk/" rel="noreferrer noreferrer" target="_blank">www.robin-thompson.co.uk</a><br>
--------------------------------------------------------------------------<br>
<br>
</blockquote>
</div>
</div>
</div>
</blockquote>
</div>
</blockquote>
</div>
</div>
</div>
</blockquote>
</div>
</blockquote>
</div>
</div>
</blockquote>
</div>
<br>
</div>
</div>
</blockquote>
</div>
</blockquote>
</div>
</blockquote>
</div>
</blockquote>
</div>
</div>
</div>
</div>
</div>
</blockquote></div></div>