{"id":1436,"date":"2020-04-08T20:17:50","date_gmt":"2020-04-08T20:17:50","guid":{"rendered":"http:\/\/www.briansutton.uk\/?p=1436"},"modified":"2020-05-07T13:55:53","modified_gmt":"2020-05-07T13:55:53","slug":"the-sir-model-and-importance-of-the-ro-reproductive-number","status":"publish","type":"post","link":"https:\/\/www.briansutton.uk\/?p=1436","title":{"rendered":"The SIR model and importance of the R0 Reproductive Number"},"content":{"rendered":"<div class=\"\" data-block=\"true\" data-editor=\"2k0m0\" data-offset-key=\"b024f-0-0\">\n<div class=\"_1mf _1mj\" data-offset-key=\"b024f-0-0\">\n<p><span style=\"font-weight: 400;\">In the recent daily UK Government presentations, the R<\/span><span style=\"font-weight: 400;\">0<\/span><span style=\"font-weight: 400;\"> Reproductive Number has been mentioned a few times, and with good reason. Its value is as a commonly accepted measure of the propensity of an infectious disease outbreak to become an epidemic.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">It turns out to be a relatively simple number to define, although working back from current data to calculate it is awkward if you don&#8217;t have the data. That\u2019s my next task, from public data.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">If <\/span><span style=\"font-weight: 400;\">R<\/span><span style=\"font-weight: 400;\">0 <\/span><span style=\"font-weight: 400;\">is below 1, then the epidemic will reduce and disappear. If it is greater than 1, then the epidemic grows.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The UK Government and its health advisers have made a few statements about it, and I covered these in an earlier post. <\/span><\/p>\n<p><span style=\"font-weight: 400;\">This is a more technical post, just to present a derivation of R<\/span><span style=\"font-weight: 400;\">0<\/span><span style=\"font-weight: 400;\">, and its consequences. I have used a few research papers to help with this, but the focus, brevity(!) and mistakes are mine (although I have corrected some in the sources).<\/span><\/p>\n<\/div>\n<\/div>\n<div class=\"\" data-block=\"true\" data-editor=\"2k0m0\" data-offset-key=\"8k9dn-0-0\">\n<div class=\"_1mf _1mj\" data-offset-key=\"8k9dn-0-0\"><span data-offset-key=\"8k9dn-0-0\">\u00a0<\/span><\/div>\n<\/div>\n<div class=\"\" data-block=\"true\" data-editor=\"2k0m0\" data-offset-key=\"ass0c-0-0\">\n<div class=\"_1mf _1mj\" data-offset-key=\"ass0c-0-0\"><span data-offset-key=\"ass0c-0-0\">See it at <a title=\"The SIR model and R0\" href=\"https:\/\/docs.google.com\/document\/d\/1b9lB4RszIHJipS27raXxN6ECTFbihJ_fQFhdy5oCEwA\/edit?usp=sharing\" target=\"_blank\" rel=\"noopener noreferrer\">The SIR model and R0<\/a><\/span><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>In the recent daily UK Government presentations, the R0 Reproductive Number has been mentioned a few times, and with good reason. Its value is as a commonly accepted measure of the propensity of an infectious disease outbreak to become an epidemic. It turns out to be a relatively simple number to define, although working back [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":1438,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":"","jetpack_publicize_message":"","jetpack_is_tweetstorm":false},"categories":[103,104,105],"tags":[94,95,97,96],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/www.briansutton.uk\/wp-content\/uploads\/2020\/04\/Solving-logx-Rx-1-for-a-family-of-R-values.png?fit=600%2C371&ssl=1","jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/paDNTg-na","jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.briansutton.uk\/index.php?rest_route=\/wp\/v2\/posts\/1436"}],"collection":[{"href":"https:\/\/www.briansutton.uk\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.briansutton.uk\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.briansutton.uk\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.briansutton.uk\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1436"}],"version-history":[{"count":7,"href":"https:\/\/www.briansutton.uk\/index.php?rest_route=\/wp\/v2\/posts\/1436\/revisions"}],"predecessor-version":[{"id":1716,"href":"https:\/\/www.briansutton.uk\/index.php?rest_route=\/wp\/v2\/posts\/1436\/revisions\/1716"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.briansutton.uk\/index.php?rest_route=\/wp\/v2\/media\/1438"}],"wp:attachment":[{"href":"https:\/\/www.briansutton.uk\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1436"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.briansutton.uk\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1436"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.briansutton.uk\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1436"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}