[et_pb_section fb_built=”1″ _builder_version=”3.18.9″][et_pb_row _builder_version=”3.18.9″][et_pb_column type=”4_4″ _builder_version=”3.18.9″ parallax=”off” parallax_method=”on”][et_pb_text _builder_version=”3.18.9″]<\/p>\n
In these confusing times there\u2019s a certain sense of power that comes with understanding, or at least trying to understand, the dynamics of disease spread and epidemiology. I certainly felt that as I\u2019ve looked into the mathematics disease modeling over the course of this quarantine\u2013\u2013a field that is absolutely fascinating, empowering, and daunting all at once. I recommend checking out <\/span>Julian Lee\u2019s article<\/span><\/a> on his original disease modeling application, which describes the effects of visiting friends in a quarantine (his application is a randomized agent-based model as opposed to the more top-down mathematical models you\u2019ll see here).<\/span><\/p>\n In this article, I present three epidemiology thinking problems, in ascending orders of difficulty, meant to put you in the position of the disease modeler. Have fun!<\/span><\/p>\n [\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section][et_pb_section fb_built=”1″ _builder_version=”3.18.9″][et_pb_row _builder_version=”3.18.9″][et_pb_column type=”4_4″ _builder_version=”3.18.9″ parallax=”off” parallax_method=”on”][et_pb_image max_width=”50%” src=”https:\/\/students.pingry.org\/record\/wp-content\/uploads\/sites\/3\/2020\/04\/MathProblem.png” _builder_version=”3.18.9″ module_alignment=”center”][\/et_pb_image][et_pb_text text_line_height=”1.3em” _builder_version=”3.18.9″ text_font=”||||||||” inline_fonts=”Inconsolata”]<\/p>\n Fig: <\/b>A graphical representation of an SIR (Susceptible-Infected-Recovered) Disease Model. The green curve is the curve that our social distancing efforts are \u201cflattening.\u201d This is the classic, top-down disease modeling approach<\/span><\/p>\n [\/et_pb_text][et_pb_text text_line_height=”1.3em” _builder_version=”3.18.9″ text_font=”Inconsolata||||||||” header_font=”||||||||” inline_fonts=”Inconsolata”]<\/p>\n 1) In epidemiology, R0 (\u201cthe basic reproductive number\u201d or \u201cr-naught\u201d) is defined as the maximum number of new cases expected per infected person. The R0 of COVID-19 has been estimated to be 2.28 (Zhang, et al). An infected individual is expected to cause \u00df new cases per day. This is essentially the \u201cbirth rate.\u201d Meanwhile, \u03b4 is the expected proportion of cases dying on a given day. This is essentially the \u201cdeath rate.\u201d Describe R0 in terms of \u00df and \u03b4.<\/span><\/p>\n 2) Does R0 tend to decrease, increase, or remain the same as a virus grows in an isolated population? Why or why not?<\/span><\/p>\n 3) Consider the following differential equation to describe the spread of COVID-19,\u00a0where \u00df and \u03b4 have the same values defined in problem 1.\u00a0<\/span><\/span><\/p>\n [\/et_pb_text][et_pb_image max_width=”23%” src=”https:\/\/students.pingry.org\/record\/wp-content\/uploads\/sites\/3\/2020\/04\/mathEquation2-1.png” _builder_version=”3.18.9″ module_alignment=”left”][\/et_pb_image][et_pb_text text_line_height=”1.3em” _builder_version=”3.18.9″ text_font=”Inconsolata||||||||” header_font=”||||||||” inline_fonts=”Inconsolata”]<\/p>\n