{"id":5305,"date":"2021-12-30T06:00:00","date_gmt":"2021-12-29T21:00:00","guid":{"rendered":"https:\/\/skimura.com\/?p=5305"},"modified":"2022-02-03T07:27:39","modified_gmt":"2022-02-02T22:27:39","slug":"mathematical-prediction-of-covid19-spread-and-convergence","status":"publish","type":"post","link":"https:\/\/skimura.com\/en\/mathematical-prediction-of-covid19-spread-and-convergence\/","title":{"rendered":"Mathematical prediction of COVID-19 spread and convergence"},"content":{"rendered":"\n

The number of people infected with COVID-19 is predicted by the multiple synthetic waves analyzed in the blogs “Will restraint in going out speed up the convergence of COVID-19 infection?<\/a><\/em><\/span>” and “Why the number of COVID-19 infections is surging<\/a><\/em><\/span>” dated November 22, 2020. The blue dots<\/em> are the weekly total of the number of infected people in Japan as published on the website of the Ministry of Health, Labor and Welfare. The solid blue line<\/em> is the synthetic wave for each variant until December 2021.<\/p>\n

In the second half of December 2021, the number of infected people, which had been on a gradual downward trend, seems to have started to increase. The number of people infected with the Omicron variant<\/em> is rapidly increasing overseas and the effect is spreading to Japan. Let us consider the following two scenarios for the near future prediction.\u00a0<\/p>\n

Scenario a: Assuming the average infectiousness of the variants so far \u2192 Orange <\/em>dashed line<\/em><\/p>\n

Scenario b: Assuming the same level of infectivity as Type 11<\/em>, the most infectious species to date \u2192 gray <\/em><\/span>dashed line<\/em><\/p>\n

Number of people infected by COVID-19 (in thousands)<\/strong><\/em><\/h5>\n
The blue dots are the weekly total number of infected people in Japan.<\/em><\/strong><\/h5>\n
The dashed line is the number of infected people for each variant, and the solid blue line is the synthetic wave.<\/strong><\/em><\/h5>\n
The orange and gray dashed lines are the prediction.<\/strong><\/em><\/h5>\n

\"\"<\/p>\n

As of December 26 2021<\/em><\/strong><\/h5>\n

\u00a0<\/p>\n

If the number of people who may be infected is $x$ (hereafter, “uninfected”) and the number of people who are infected and may pass it on to others is $y$ (hereafter, “infected”), the rate of change of each is predicted to follow the following differential equation. (Note: The term “uninfected” does not include people who are avoiding contact with infected people or are taking precautions to avoid infection.\u00a0<\/p>\n

$$\\frac{dx}{dt}=-bxy\\tag{1}$$<\/p>\n

$$\\frac{dy}{dt}=bxy-cy\\tag{2}$$<\/p>\n

Equation $(1)$ shows that the number of uninfected people decreases as they come into contact with infected people, while equation $(2)$ shows that the number of infected people increases as a result, but they are cured or die and are no longer infected. The coefficient $B$ is the “infection coefficient” and $C$ is the “cure coefficient”. The coefficients for each wave (dashed line) that makes up the synthetic wave (solid blue line) are as follows.<\/p>\n

\"\"<\/p>\n

\u00a0<\/p>\n

For your reference (compiled from the MHLW website and press-related materials)<\/p>\n

\u00a0<\/p>\n

Cumulative total number of PCR tests (blue dots<\/span>), positive cases (green line<\/span>), and deaths (gray line<\/span>) on logarithmic axis<\/em><\/strong><\/h5>\n

\u00a0<\/p>\n

\"\"<\/p>\n

As of December 26 2021<\/em><\/strong><\/h5>\n

\u00a0<\/p>\n

PCR test positive rate (green line<\/span>), mortality rate of positive patients (gray line<\/span>) and cumulative total number of PCR tests (blue dots<\/span>)\u00a0 by week<\/em><\/strong><\/h5>\n

\"\"<\/p>\n

As of December 26 2021<\/em><\/strong><\/h5>\n

\u00a0<\/p>\n

Monthly trends in the number of PCR tests and deaths due to COVID-19<\/em><\/strong><\/h5>\n

\"\"<\/p>\n

Since 2020 up to date<\/em><\/strong><\/h5>\n

\u00a0<\/p>\n

Compared to the Spanish flu that was prevalent 100 years ago, the number of variants is larger and the interval between their appearance is shorter.<\/p>\n

\u00a0<\/p>\n

Monthly death toll from the Spanish flu epidemic of 1918-1921<\/em><\/strong><\/h5>\n

\"\"<\/p>\n

Tokyo Metropolitan Institute of Health and Safety Annual Report 56, 2005<\/em><\/strong><\/h5>\n

\u00a0<\/p>\n

The end<\/p>\n

\u00a0<\/p>\n

\u00a0<\/h5>\n","protected":false},"excerpt":{"rendered":"

The number of people infected with COVID-19 is predicted by the multiple synthetic waves analyzed in the blogs … Continued<\/a><\/p>\n","protected":false},"author":3,"featured_media":5174,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_locale":"en_US","_original_post":"https:\/\/skimura.com\/?p=5173","footnotes":""},"categories":[13],"tags":[29,30,31],"class_list":["post-5305","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-13","tag-prediction","tag-differential-equation","tag-covid-19-2","en-US"],"acf":[],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\t\n\t\t