Friday, March 1, 2019

Illustration of how infection spreads with and without social distanceing and travel restrictions

In this post, we use a cellular automata model of infection to illustrate the effects of social distancing and travel restrictions.

DISCLAIMER:  THIS IS AN UNREALISTIC MODEL, FOR TEACHING PURPOSES ONLY.  IN PARTICULAR THE INFECTION RATIOS ARE PROBABLY TOO SMALL.

The images below are from a cellular automata model of the spread of a disease on a 100x100 grid.  White dots represent uninfected; red dots, infected; green dots, survivors; black dots, deaths.  The key parameters are:
  • death rate=1%, given that a person has been infected.  
  • r0 = 2 is the basic reproduction number, the number of people infected by each infected person, e.g., here are estimates for corona virus.   We model social distancing as reducing this number.  
  • mean distance of infection = 5.0 cells away from an infected cell, modeled as a standard normal distribution over unit distance.  We model travel restrictions as reducing this number


In the video above, the infected cells (red) spread slowly out from the center, where the outbreak began.  Most infections are on the "border" of the infected area because that is where infected cells are more likely to come in contact with uninfected ones.

Infections eventually die out because many of the people who come in contact with the infection have already developed an immunity (green) or are dead (black).  This is referred to as "Herd Immunity."

We graph the spread of the infection below.  The vertical axis represents people on the grid (10,000=100x100) and the horizontal axis represents time, denoted in periods (the life span of an infection virus).   The blue line represents the uninfected population, the green line the infected population, and the orange line, the infection rate.


In the simulation and graph below, we increase r0 (the infection ratio) from 2 to 3, and mean travel distance from 5 to 25.   We see that more people get infected (higher green line), and much more quickly (peak infections occur at period 11, instead of period 15).


What policy makers mean by "flattening the curve" is flattening the orange infection curve (compare the smaller, flatter orange peak in first graph to the  graph to the sharper, higher peak in the second) with social distancing and travel restrictions so that our hospital system does not get overwhelmed by infected patients.

From estimates I have seen, the basic infection ratios for old covid is thought to be around 2.5, but the infection ratio for the new Delta variant is about 3 times as big.  

HT:  Colleague Steven Tschantz designed and wrote the code.

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    Replies
    1. My name Clinton joy Am given out this review about a good and powerful hacker called Wizard Brixton who have helped me . I have been deceived by serval Hacker of helping me to spy or clone my Husband mobile phone but they end up demanding a lot of money without giving me proof. I saw a post about Wizard Brixton and I contacted him ( wizardbrixton at gmail dot com ) to spy on my husband and to Clone his phone he ask for few details in less than 3 hours he got me serval proof showing his cheating Ass on me. Everyone contact him he is the best hacker Contact: wizardbrixton at gmail dot com WhatsApp MR Wizard Brixton (+1- /807-23 ) 4-0428 )

      Delete
  18. My name Clinton joy Am given out this review about a good and powerful hacker called Wizard Brixton who have helped me . I have been deceived by serval Hacker of helping me to spy or clone my Husband mobile phone but they end up demanding a lot of money without giving me proof. I saw a post about Wizard Brixton and I contacted him ( wizardbrixton at gmail dot com ) to spy on my husband and to Clone his phone he ask for few details in less than 3 hours he got me serval proof showing his cheating Ass on me. Everyone contact him he is the best hacker Contact: wizardbrixton at gmail dot com WhatsApp MR Wizard Brixton (+1- /807-23 ) 4-0428 )

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  29. Recovery Lost Funds From Online Scammer's/ Cryptocurrency/ Recovery of Stolen bitcoin / Bitcoin Mining/ Increase your Credit score/ MOBILE SPY REMOTECONTROL ACCESS AUTHORIZATION. Removing Bad Records from Both Public and Private database via Email: schwartzsoftwarehackins@gmail.com and WhatsApp contact : ‪+16076220782

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  33. Hello everyone, I’m Hans Brunman. I’m recommending AstraWeb Cyber security service for all your cryptocurrency and digital assets recovery. I was one of their clients and I was able to recover my funds with their help. Truly, they are the best when it comes to cryptocurrency recovery. I had invested my money into a cryptocurrency trading platform that crashed earlier this month, I contacted Astraweb Cyber Security after coming across their website, and they were able to recover my funds from the crashed platform. If you wish to contact them, you can reach them via the following information.

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  34. Hello, everyone I'm giving out this testimonial on what the Wizard hacker did for me I never know that I could get a mirror phone I was in a long-distance relationship but was scared about my girlfriend because she doesn't show me the love I ever wanted so I have this doubt that she is cheating on me to my greater surprise I have to contact: WIZARDBRIXTON(AT) GMAIL (DOT) COM he asked me a few information about her so I shared it with him to my great surprise my girlfriend is cheating on me I was able to see her call record Snapchat message, Instagram message, the Facebook message most of it all she sends her nude pictures to this other guy thanks to Wizard Brixton who help me out in this services and he collected a low services fee on like others who charge so high everyone should be aware and contact him on WIZARDBRIXTON(AT) GMAIL (DOT) COM

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