{"id":10264,"date":"2018-11-02T09:05:56","date_gmt":"2018-11-02T13:05:56","guid":{"rendered":"https:\/\/blogs.mathworks.com\/pick\/?p=10264"},"modified":"2018-11-02T09:05:56","modified_gmt":"2018-11-02T13:05:56","slug":"zombie-outbreak","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/pick\/2018\/11\/02\/zombie-outbreak\/","title":{"rendered":"Zombie Outbreak"},"content":{"rendered":"
\n <\/p>\n

Sean<\/a>‘s pick this week is Mathematical modelling of an outbreak of zombie infection<\/a> by E. Cheynet<\/a>.\n <\/p>\n

<\/introduction><\/p>\n

In honor of Halloween, E. has provided us with a way to simulate zombie outbreaks! Do you have what it takes to save humanity?<\/p>\n

Npop = 500; % population<\/span>\r\nalpha = 7.5e-3 ; %  \"zombie destruction\" rate.<\/span>\r\nbeta = 5e-3; % \"zombie creation\" rate.<\/span>\r\nzeta = 9.2e-2; % zombie resurrection rate<\/span>\r\ndelta = 1.2e-4; % susceptibles death rate<\/span>\r\ntmax = 100; % max duration of the simulation (non-dimensional)<\/span>\r\ndt = 0.005; % time step<\/span>\r\n\r\n[SRZ, t] = zombies(Npop, alpha, beta, zeta, delta, tmax, dt, 0);\r\nplotPopulations(t, SRZ, Npop)\r\nsnapnow<\/pre>\n
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Hmm, what if we work on our sharp shooter skills and eat healthy?<\/p>\n
alpha = 1e-2; % Go to the range<\/span>\r\ndelta = 9e-5; % Add broccoli<\/span>\r\n[SRZ, t] = zombies(Npop, alpha, beta, zeta, delta, tmax, dt, 0);\r\nplotPopulations(t, SRZ, Npop)\r\nsnapnow<\/pre>\n
 <\/p>\n
That only delays the inevitable; skip the broccoli, we need to execute a mass extermination of zombies.  The erad<\/tt> function gives us the ability to raid them.\n   <\/p>\n
delta = 1.2e-4; % Back to pizza<\/span>\r\nk = 0.65;\r\nNraid = 4;\r\n[SRZ, t] = erad(Npop, alpha, beta, zeta, delta, k, Nraid, tmax, dt,0);\r\nplotPopulations(t, SRZ, Npop)<\/pre>\n
Zombies have been eradicated (until now...). \r\n<\/pre>\n
 <\/p>\n
Unfortunately, the model doesn’t seem to account for new humans being born, so I think any simulation eventually ends with us all dead…  Have a great weekend!\n   <\/p>\n
Comments<\/a><\/h3>\n
Give it a try and let us know what you think here<\/a> or leave a comment<\/a> for E.\n   <\/p>\n
\r\nfunction<\/span> plotPopulations(t, SRZ, Npop)\r\nfigure\r\nplot(t, SRZ);\r\nylim([0, 1.1*Npop])\r\nlegend('Susceptibles'<\/span>, 'Deads'<\/span>, 'Zombies'<\/span>, 'location'<\/span>, 'west'<\/span>)\r\nylabel('Population'<\/span>)\r\nxlabel('Non-dimensional Time'<\/span>)\r\nend<\/span>\r\n<\/pre>\n