![\"\"](\"https:\/\/wp-media.patheos.com\/blogs\/sites\/572\/2020\/03\/CoronavirusFlatteningCurve.png\")
<\/p>\n<\/p>\n
\u00a0<\/p>\n
The following commentary comes from Dr. JD Donovan. His\u00a0 credentials follow:<\/p>\n
\nDr. JD Donovan received his BS degree in Chemistry from the University of Notre Dame and his PhD in Biophysics and Theoretical Biology from the University of Chicago.<\/div>\n<\/blockquote>\n\n\n*<\/div>\nAlways pursuing interdisciplinary topics, he has worked in university departments ranging from Physics to Physiology as well as industrial basic research developing new technologies for diagnostic testing. \u00a0As a teacher, he has served mostly in small liberal arts colleges where he presented courses that span the sciences, from evolutionary biology through chemistry to cosmology. \u00a0His special joy, though, is to lead courses that explore the interface between science and humanities. \u00a0His enthusiasm for teaching comes through to his students who voted him runner up for teacher of the year at the University of Florida, and to his college president who nominated him for the Carnegie Foundation\u2019s US Professor of the Year Award. He recently retired from academic life (in his own words, he\u2019s \u201ca recovering academic\u201d) and was appointed Professor Emeritus at North Central College in Illinois.<\/div>\n*<\/div>\nA practicing Catholic, he has served in various ministries in his parishes over the years, particularly in liturgy and in Peace and Justice committees. \u00a0He also has special devotion to St. John of the Cross, St. Theresa of Lisieux, and Servant of God Dorothy Day.<\/div>\n*<\/div>\nJD has tried to put both his faith and his analytical side to good work. \u00a0Among other things, he is a founder and Past President of his local Habitat for Humanity affiliate, Past President of HFH Illinois, founding member of the Waukegan School Board Ethics Committee, and Past President of Waukegan Main Street.<\/div>\n*<\/div>\nFinally, JD is a member of the American Physical Society, the AAAS, Institute for the Theological Encounter of Science and Technology, and the Society of Catholic Scientists.<\/div>\n<\/blockquote>\n<\/div>\nThough this email may seem critical, please consider it instead as a teacher helping his\u00a0student with his statistics homework.<\/p>\n
After reading your first post on March 24th about coronavirus deaths, I went to the\u00a0source that you linked to<\/a> (I was not aware of it, so
\nthanks) and started doing some analysis.<\/p>\nI agree that there is reason for hope, that social distancing is working, and the curve is\u00a0flattening. But it\u2019s not for the reasons you give; the growth in daily deaths does not yet\u00a0show signs of leveling off.\u00a0 I\u2019ll explain why, but first, let\u2019s talk about other hopeful hints in\u00a0the data that I see in my analysis, and then turn to the daily deaths data.<\/p>\n
As you\u2019re aware, an epidemic first has an exponential phase which can\u2019t go on forever:\u00a0all epidemics eventually peak.\u00a0 When looking at cumulative data (whether new cases or\u00a0deaths), the graph over time first curves up, then becomes straight, and eventually\u00a0levels off and stays there.\u00a0 If you go to the Johns Hopkins website, the China and S.\u00a0Korea data illustrate this very well. You can see those curves by selecting those
\ncountries and looking at the graph of confirmed cases on the lower right of the screen.\u00a0The\u00a0part of the graph on the left\u00a0that curves\u00a0up is the exponential phase, the straight\u00a0part of the graph is the linear phase, and the flattening is the final phase.<\/p>\nThat language was kind of vague so first let me clarify what \u201cexponential\u201d and \u201clinear\u201d\u00a0mean beyond the vague words \u201ccurves up\u201d and \u201clooks straight.\u201d A theologian\u00a0(you)\u00a0knows\u00a0as well as a scientist (me) that precise definition is essential.<\/p>\n
A linear graph increases by the same\u00a0amount<\/em><\/strong>\u00a0each day.\u00a0 For example, if a curve goes\u00a0up by 100 each day, it gives a straight line.\u00a0 By contrast, an exponential curve increases\u00a0by the same\u00a0percent<\/em><\/strong>\u00a0each day.\u00a0 For example, if a curve goes up by 24% each day, it\u00a0goes up more and more each day and doubles every 3 days.\u00a0 When we look at that, we\u00a0say it curves up.<\/p>\n
Now the hopeful thing for me is that in the US data, the graph of confirmed cases in the\u00a0lower right, appears to be entering the linear phase.\u00a0 It\u2019s approaching a straight line\u00a0without being upwardly curved any more.\u00a0 This jibes with the graph on the daily increase\u00a0tab of that same chart in the lower right.\u00a0 The daily increase in confirmed cases is\u00a0leveling off, giving almost the same number of new cases each day, though it has not\u00a0yet peaked.\u00a0 As I explained to my adult daughter yesterday, it isn\u2019t the beginning of the\u00a0end but it does indicate the end of the beginning.\u00a0 I suspect (but being a scientist, I will\u00a0wait for more data before saying so definitively) that the daily increase in confirmed\u00a0cases will peak this week, which will cause the cumulative confirmed cases curve* to\u00a0begin slowly leveling off.\u00a0 There is light at the end of this tunnel.<\/p>\n
Now, let\u2019s look at the deaths data. Because deaths from Covid occur about a week\u00a0after case confirmation, one would not expect deaths to enter the linear phase until\u00a0about a week after cases themselves did.\u00a0 Regrettably, the linked website does not give\u00a0a graph of the deaths, only the confirmed cases, but the data that you\u2019ve accumulated\u00a0does allow us to analyze this.<\/p>\n
If you make a graph of your data of deaths versus time (205, 260, 340. . . 1046), you\u2019ll\u00a0see that the graph curves upward.\u00a0 That indicates the exponential phase.<\/p>\n
You also calculate and report the percent increase per day and, as you point out, the\u00a0percentage looks to be trending lower or flat.\u00a0 If it is flat\u2013meaning the percent increase\u00a0is the same each day\u2013that is the precise definition of the exponential phase of the\u00a0graph.\u00a0 Deaths, alas, continue their exponential rise and show no sign of leveling off.<\/p>\n
You correctly note that there is some variation in the percent increase as it bounces\u00a0around and you report its average as 32%.\u00a0 I\u2019m sure you\u2019re aware that statistics always\u00a0show variation (that\u2019s why we need statistics) but you may not have a feel for the\u00a0expected size of the statistical fluctuations.\u00a0 Without going into the math, I\u2019ll say that the\u00a0standard deviation (the size of the fluctuation) for numbers around 200 is about 7.\u00a0 (If
\nyou want a stats lesson and an explanation of how I got that number, let me know.)<\/p>\nWith a standard deviation of 7, then any differences within 7 units of the average is\u00a0probably nothing more than random and doesn\u2019t indicate a trend.\u00a0 Since the average in\u00a0your reported data is 32, then anything between 25 to 39 would count as normal\u00a0variation.\u00a0 And that is what you\u2019ve observed.\u00a0 That means it\u2019s too early to say that the\u00a0percent increase in deaths is trending lower. It appears not to be, so we still need to\u00a0wait.<\/p>\n
Summarizing, I applaud your expressions of hope as appropriate for a Christian\u00a0Catholic.\u00a0 I applaud your initiative for trying to figure things out and uplift others.\u00a0 I thank\u00a0you\u00a0for pointing me to that data source.\u00a0 I encourage to keep tracking the percent\u00a0changes in deaths and suggest that you also watch the confirmed cases graphs and\u00a0numbers which should serve as an early warning of the approaching peak in the\u00a0number of deaths. I also caution you about expressing too much optimism. Dr. Anthony\u00a0Fauci is a great model for us to follow with his careful language and nuanced\u00a0statements.<\/p>\n
Finally, with all that you as apologist have taught me or at least made me think about in\u00a0the past couple years, I feel graced to have maybe returned the favor from over here in\u00a0my specialty.<\/p>\n
JD Donovan PhD<\/p>\n
* I claim extra points for that alliteration.<\/p>\n
***<\/p>\n
Related Reading<\/span><\/strong><\/p>\n
God Wills to Heal Everyone Through Faith or By Request? (Biblical Refutation of \u201cHyperfaith\u201d \/ \u201cName-It-Claim-It\u201d Teaching)<\/a>\u00a0[1982; revised 7-5-02]<\/p>\n
US Coronavirus Deaths: Elderly with Preconditions<\/a>\u00a0[3-13-20]<\/p>\n
The Bible on Germs, Sanitation, & Infectious Diseases<\/a>\u00a0[3-16-20]<\/p>\n
Taylor Marshall: Pachamama \u201cIdolatry\u201d Judged by Coronavirus (Yet \u201cAntichrist\u201d Pope Francis Walks the Streets of Pandemic-Ravaged Rome Free of the Virus . . .)<\/a>\u00a0[3-17-20]<\/p>\n
Alexander Tschugguel, Taylor Marshall, & God\u2019s Wrath<\/a>\u00a0[3-19-20]<\/p>\n
\u201cBlack Death\u201d Mentality On Display at\u00a0Patheos Catholic<\/em>\u00a0<\/a>[3-26-20]<\/p>\n
Dialogue: [Irrational?] Leftish Reactions to Coronavirus<\/a>\u00a0[3-27-20]<\/p>\n
Dialogue on Leftish Reactions to Coronavirus, Part II<\/a>\u00a0[3-27-20]<\/p>\n
Why Has Italy Suffered the Most from Coronavirus? (+ Reflections on the Propriety of Using the Term, \u201cChinese Flu\u201d \/ Condemnation of Anti-Chinese Prejudice)<\/a>\u00a0[3-28-20]<\/p>\n
Reply to Unfair Criticisms of Trump Re Coronavirus<\/a>\u00a0[4-4-20]<\/p>\n
Coronavirus: Chris Ferrara vs. Science & Historical Precedent (Social Distancing Was Used in the 1918 Flu Pandemic and Has Been Shown Again and Again to be Highly Effective)<\/a>\u00a0[4-7-20]<\/p>\n
Will US Coronavirus Deaths Be Far Less than Predicted?<\/a>\u00a0[4-7-20]<\/p>\n
***<\/p>\n
Photo credit:\u00a0<\/strong><\/span>Johannes Kalliauer<\/a>\u00a0(3-12-20).\u00a0Spatial\/Social distancing delays the further spread of a virus and preserves the capacity of the health system<\/span> [Wikimedia Commons<\/a> \/\u00a0Creative Commons<\/a>\u00a0Attribution-Share Alike 4.0 International<\/a>\u00a0license]<\/p>\n
***<\/p>\n<\/div>\n<\/body><\/html>\n","protected":false},"excerpt":{"rendered":"
\u00a0 The following commentary comes from Dr. JD Donovan. His\u00a0 credentials follow: Dr. JD Donovan received his BS degree in Chemistry from the University of Notre Dame and his PhD in Biophysics and Theoretical Biology from the University of Chicago. * Always pursuing interdisciplinary topics, he has worked in university departments ranging from Physics to […]<\/p>\n","protected":false},"author":2331,"featured_media":45863,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[289],"tags":[10479,10452,10655,10569,10488,10470,10455,10563,10476,10652,10461,10464,10458,10467,10473,10566],"class_list":["post-45861","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-political-ethical-moral-issues","tag-contagious-disease","tag-coronavirus","tag-coronavirus-graph-curve","tag-covid-19","tag-disease","tag-disease-control","tag-epidemic","tag-flattening-curve","tag-flu","tag-jd-donovan","tag-mass-hysteria","tag-mass-panic","tag-pandemic","tag-quarantine","tag-virus","tag-virus-trends"],"yoast_head":"\n
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Formerly a campus missionary, as a Protestant, Dave was received into the Catholic Church in February 1991, by the late, well-known catechist and theologian, Fr. John A. Hardon, S. J. Dave\u2019s articles have appeared in many influential Catholic periodicals, including \\\"This Rock\\\" (now called \\\"Catholic Answers Magazine\\\"), \\\"Envoy Magazine\\\" (Patrick Madrid), \\\"The Catholic Answer,\\\" \\\"The Coming Home Journal,\\\" \\\"Gilbert Magazine\\\" (American Chesterton Society), and \\\"The Latin Mass.\\\" He also writes a featured column for every issue of \\\"The Michigan Catholic\\\": published by the archdiocese of Detroit, and was editor for most of the apologetics tracts published by the St. Paul Street Evangelization apostolate. Dave\u2019s apologetics and writing apostolate was the subject of a feature article in the May 2002 issue of \\\"Envoy Magazine.\\\" He served as the staff moderator at the Internet discussion forum for The Coming Home Network, from 2007-2010. Dave has been interviewed on many nationally syndicated Catholic radio shows, including \\\"Catholic Answers Live\\\" (twice), \\\"Faith and Family Live\\\" (Steve Wood), \\\"Kresta in the Afternoon,\\\" \\\"Son Rise Morning Show,\\\" \\\"Catholic Connection\\\" (Teresa Tomeo), and \\\"The Catholics Next Door.\\\" His large and popular website, \\\"Biblical Evidence for Catholicism,\\\" was online from March 1997 to March 2007, and received the 1998 Catholic Website of the Year award from \\\"Envoy Magazine.\\\" His blog of the same name (now transferred to Patheos), begun in February 2004, contains more than 1,500 papers, at least 500 debates or dialogues, and over 50 distinct \\\"index\\\" web pages. Unsolicited correspondence has indicated many hundreds of conversions (or returns) to the Catholic faith as a result, by God's grace, of these writings. Dave's conversion story was published in the bestselling book \\\"Surprised by Truth\\\" (edited by Patrick Madrid; San Diego: Basilica Press, 1994). Sophia Institute Press has published six of his books: \\\"A Biblical Defense of Catholicism\\\" (Foreword by Fr. John A. Hardon, S. J., 1996 \/ 2003), \\\"The Catholic Verses\\\" (2004), \\\"The One-Minute Apologist\\\" (2007), \\\"Bible Proofs for Catholic Truths\\\" (2009), \\\"The Quotable Newman\\\" (editor: 2012), and \\\"Proving the Catholic Faith is Biblical\\\" (2015). He is co-author (with Dr. Paul Thigpen) of the inserts for \\\"The New Catholic Answer Bible\\\" (Our Sunday Visitor: 2005), and editor for \\\"The Wisdom of Mr. Chesterton: The Very Best Quotes, Quips, and Cracks from the Pen of G. K. Chesterton\\\" (Saint Benedict Press \/ TAN Books: 2009). \\\"100 Biblical Arguments Against Sola Scriptura\\\" was published by Catholic Answers in May 2012. His \\\"Quotable Wesley\\\" compilation was published by (Protestant \/ Wesleyan publisher) Beacon Hill Press in April 2014. Several of his 49 books are bestsellers in their field. Dave maintains a popular personal Facebook page, a Facebook author page, and has a Twitter account as well. He offers almost all of his books in e-book form on his own Biblical Catholicism site (http:\/\/biblicalcatholicism.com\/), at a permanent deep discount: only $2.99 for ePub, mobi, and AZW, and $1.99 for PDF. His writing has been enthusiastically endorsed or recommended by many leading Catholic apologists, authors, and priests, including Dr. Scott Hahn, Fr. Peter M. J. Stravinskas, Marcus Grodi, Patrick Madrid, Steve Ray, Tim Staples, Devin Rose, Mike Aquilina, Al Kresta, Karl Keating, Fr. Dwight Longenecker, Brandon Vogt, Marcellino D'Ambrosio, and Fr. John A. Hardon, S. J. Dave has been happily married to his wife Judy since October 1984. 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Formerly a campus missionary, as a Protestant, Dave was received into the Catholic Church in February 1991, by the late, well-known catechist and theologian, Fr. John A. Hardon, S. J. Dave\u2019s articles have appeared in many influential Catholic periodicals, including \"This Rock\" (now called \"Catholic Answers Magazine\"), \"Envoy Magazine\" (Patrick Madrid), \"The Catholic Answer,\" \"The Coming Home Journal,\" \"Gilbert Magazine\" (American Chesterton Society), and \"The Latin Mass.\" He also writes a featured column for every issue of \"The Michigan Catholic\": published by the archdiocese of Detroit, and was editor for most of the apologetics tracts published by the St. Paul Street Evangelization apostolate. Dave\u2019s apologetics and writing apostolate was the subject of a feature article in the May 2002 issue of \"Envoy Magazine.\" He served as the staff moderator at the Internet discussion forum for The Coming Home Network, from 2007-2010. Dave has been interviewed on many nationally syndicated Catholic radio shows, including \"Catholic Answers Live\" (twice), \"Faith and Family Live\" (Steve Wood), \"Kresta in the Afternoon,\" \"Son Rise Morning Show,\" \"Catholic Connection\" (Teresa Tomeo), and \"The Catholics Next Door.\" His large and popular website, \"Biblical Evidence for Catholicism,\" was online from March 1997 to March 2007, and received the 1998 Catholic Website of the Year award from \"Envoy Magazine.\" His blog of the same name (now transferred to Patheos), begun in February 2004, contains more than 1,500 papers, at least 500 debates or dialogues, and over 50 distinct \"index\" web pages. Unsolicited correspondence has indicated many hundreds of conversions (or returns) to the Catholic faith as a result, by God's grace, of these writings. Dave's conversion story was published in the bestselling book \"Surprised by Truth\" (edited by Patrick Madrid; San Diego: Basilica Press, 1994). Sophia Institute Press has published six of his books: \"A Biblical Defense of Catholicism\" (Foreword by Fr. John A. Hardon, S. J., 1996 \/ 2003), \"The Catholic Verses\" (2004), \"The One-Minute Apologist\" (2007), \"Bible Proofs for Catholic Truths\" (2009), \"The Quotable Newman\" (editor: 2012), and \"Proving the Catholic Faith is Biblical\" (2015). He is co-author (with Dr. Paul Thigpen) of the inserts for \"The New Catholic Answer Bible\" (Our Sunday Visitor: 2005), and editor for \"The Wisdom of Mr. Chesterton: The Very Best Quotes, Quips, and Cracks from the Pen of G. K. Chesterton\" (Saint Benedict Press \/ TAN Books: 2009). \"100 Biblical Arguments Against Sola Scriptura\" was published by Catholic Answers in May 2012. His \"Quotable Wesley\" compilation was published by (Protestant \/ Wesleyan publisher) Beacon Hill Press in April 2014. Several of his 49 books are bestsellers in their field. Dave maintains a popular personal Facebook page, a Facebook author page, and has a Twitter account as well. He offers almost all of his books in e-book form on his own Biblical Catholicism site (http:\/\/biblicalcatholicism.com\/), at a permanent deep discount: only $2.99 for ePub, mobi, and AZW, and $1.99 for PDF. His writing has been enthusiastically endorsed or recommended by many leading Catholic apologists, authors, and priests, including Dr. Scott Hahn, Fr. Peter M. J. Stravinskas, Marcus Grodi, Patrick Madrid, Steve Ray, Tim Staples, Devin Rose, Mike Aquilina, Al Kresta, Karl Keating, Fr. Dwight Longenecker, Brandon Vogt, Marcellino D'Ambrosio, and Fr. John A. Hardon, S. J. Dave has been happily married to his wife Judy since October 1984. They have three sons and a daughter, and reside in southeast Michigan (metro Detroit).","sameAs":["https:\/\/biblicalcatholicism.com\/","https:\/\/www.facebook.com\/dave.armstrong.798","https:\/\/www.youtube.com\/@LuxVeritatisApologetics"],"url":"https:\/\/www.patheos.com\/blogs\/davearmstrong\/author\/davearmstrong"}]}},"_links":{"self":[{"href":"https:\/\/www.patheos.com\/blogs\/davearmstrong\/wp-json\/wp\/v2\/posts\/45861","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.patheos.com\/blogs\/davearmstrong\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.patheos.com\/blogs\/davearmstrong\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.patheos.com\/blogs\/davearmstrong\/wp-json\/wp\/v2\/users\/2331"}],"replies":[{"embeddable":true,"href":"https:\/\/www.patheos.com\/blogs\/davearmstrong\/wp-json\/wp\/v2\/comments?post=45861"}],"version-history":[{"count":0,"href":"https:\/\/www.patheos.com\/blogs\/davearmstrong\/wp-json\/wp\/v2\/posts\/45861\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.patheos.com\/blogs\/davearmstrong\/wp-json\/wp\/v2\/media\/45863"}],"wp:attachment":[{"href":"https:\/\/www.patheos.com\/blogs\/davearmstrong\/wp-json\/wp\/v2\/media?parent=45861"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.patheos.com\/blogs\/davearmstrong\/wp-json\/wp\/v2\/categories?post=45861"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.patheos.com\/blogs\/davearmstrong\/wp-json\/wp\/v2\/tags?post=45861"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}