COVID-19 SOUTH AFRICA

• VIDEO - SIMULATION OF VIRUS PROPAGATION

  Video made by J.E. Amaro with the Android app Pandemic

  Monte Carlo simulation in a lattice. Planck P-model

• DOWNLOAD PANDEMIC APP FOR ANDROID

  

  Click on the image above to download the PANDEMIC APP for Android

  Monte Carlo simulation in a lattice with temperature T, representing the average

  movility (or energy) of the individuals

• SOUTH AFRICA PARAMETERS AUGUST 30 - PANDEMIC APP

  Length=300, Range=2.9,

  Exposure=0.09, Mobility=20

  Recovery time = 20, Recovery interval= 4

  Probability infect = 0.15, Probab. death= 0.2

  Lockdown time = 1000 (no effective)

  Days=250

  These parameters were fitted to D model and South Africa data on July 13 2020

• SOUTH AFRICA PARAMETERS JULY 13 - PANDEMIC APP

  Length=300, Range=2.9,

  Exposure=0.09, Mobility=20

  Recovery time = 31, Recovery interval= 3.9

  Probability infect = 0.2, Probab. death= 0.08

  Lockdown time = 1000 (no effective)

  Days=250

  These parameters were fitted to D model and South Africa data on July 13 2020

• SOUTH AFRICA PARAMETERS JULY 4 - PANDEMIC APP

  Length=300, Range=2.9,

  Exposure=0.09, Mobility=20

  Recovery time = 31, Recovery interval= 3.9

  Probability infect = 0.2, Probab. death= 0.069

  Lockdown time = 1000 (no effective)

  Days=250

  These parameters were fitted to D model and South Africa data on July 4 2020

• SOUTH AFRICA PARAMETERS JUNE 22 - PANDEMIC APP

  Length=300, Range=2.9,

  Exposure=0.09, Mobility=20

  Recovery time = 31, Recovery interval= 3.9

  Probability infect = 0.2, Probab. death= 0.051

  Lockdown time = 1000 (no effective)

  Days=250

  These parameters were fitted to D model and South Africa data on June 22 2020

• SOUTH AFRICA PARAMETERS - PANDEMIC APP

  Length=300, Range=2.9,

  Exposure=0.09, Mobility=20

  Recovery time = 31, Recovery interval= 3.9

  Probability infect = 0.2, Probab. death= 0.14

  Lockdown time = 1000 (no effective)

  Days=250

  These parameters were fitted to D model and South Africa data on June 6 2020

• DOWLOAD THE ORIGINAL PAPERS ON THESE EPIDEMIC MODELS

  1.- Global analysis of the COVID-19 pandemic using simple epidemiological models

  J.E. Amaro, J. Dudouet, J.N. Orce

  2.- The D model for deaths by COVID-19

  by J.E. Amaro

• FITS OF PANDEMIC MODELS AND PREDICTIONS

  We provide here our daily fits to the current data.

  A basic function to parametrize the total deaths is

  D(t) = a exp(t/b) / ( 1 + c exp (t/b) )

  The values of the parametes a, b, c are at the top of the plots

  Click on the figures to enlarge

  WE ALSO PROVIDE PLOTS FOR THE MODELS:

  D2, is the sum of two D-functions

  D'2, is the derivative of the D2 function to fit the deaths-per-day

  Extended SIR model where the recovered function r = R/N

  is parametrized similarly as the D-function

  Monte Carlo P-model. Virus simulation propagating in a grid of cells

• P-MODEL - DAILY DEATHS IN SOUTH AFRICA OCTOBER 20 2020

  

  This Monte Carlo P-model was fitted to data on August 30 2020.

• P-MODEL - TOTAL DEATHS IN SOUTH AFRICA OCTOBER 20 2020

  

  The Monte Carlo P-model was fitted on August 30 2020.

• P-MODEL - DAILY DEATHS IN SOUTH AFRICA AUGUST 30 2020

  

  This Monte Carlo P-model was fitted to data and D model on August 30 2020.

• P-MODEL - TOTAL DEATHS IN SOUTH AFRICA AUGUST 30 2020

  

  The D-model and Monte Carlo P-model were fitted on August 30 2020.

• P-MODEL - DAILY DEATHS IN SOUTH AFRICA JULY 13 2020

  

  This Monte Carlo P-model was fitted to data and D model on JuLY 13 2020.

• P-MODEL - DAILY DEATHS IN SOUTH AFRICA JULY 4 2020

  

  This Monte Carlo P-model was fitted to data and D model on JuLY 4 2020.

• D-MODEL - TOTAL DEATHS IN SOUTH AFRICA JULY 4 2020

  

  The D-model and Monte Carlo P-model were fitted on JuLY 13 2020.

• P-MODEL - DAILY DEATHS IN SOUTH AFRICA JUNE 27 2020

  

  This Monte Carlo P-model was fitted to data and D model on June 22 2020.

• D-MODEL - TOTAL DEATHS IN SOUTH AFRICA JUNE 27 2020

  

  D-model fitted to South Africa data with three parameters.

• P-MODEL - DAILY DEATHS IN SOUTH AFRICA JUNE 22 2020

  

  This Monte Carlo P-model was fitted to data and D model on June 22 2020.

• D-MODEL - TOTAL DEATHS IN SOUTH AFRICA JUNE 22 2020

  

  D-model fitted to South Africa data with three parameters.

• P-MODEL - DAILY DEATHS IN SOUTH AFRICA JUNE 17 2020

  

  This Monte Carlo P-model was fitted to data and D model on June 6 2020.

• D-MODEL - TOTAL DEATHS IN SOUTH AFRICA JUNE 16 2020

  

  D-model fitted to South Africa data with three parameters. Up to now the data follow the expected evolution of this simple model.

• EXTENDED SIR MODEL - DAILY DEATHS IN SOUTH AFRICA JUNE 15 2020

  

  The extended SIR model has six parameters and requieres more data to be reliable. Therefore we introduced an artificial datum in accord to D model, 200 deaths on 100th day.

• P-MODEL - DAILY DEATHS IN SOUTH AFRICA JUNE 15 2020

  

  This Monte Carlo P-model was fitted to data and D model on June 6 2020.

• D-MODEL - TOTAL DEATHS IN SOUTH AFRICA JUNE 15 2020

  

  D-model fitted to South Africa data with three parameters. Up to now the data follow the expected evolution of this simple model.

• D-MODEL - TOTAL DEATHS IN SOUTH AFRICA JUNE 12 2020

  

  D-model fitted to South Africa data with three parameters. Up to now the data follow the expected evolution of this simple model.

D'-MODEL AND MONTE CARLO - DEATHS-PER-DAY IN SOUTH AFRICA JUNE 12 2020



This Monte Carlo was fitted to data and D model on June 6 2020.

• D-MODEL - TOTAL DEATHS IN SOUTH AFRICA

  

  D-model fitted to South Africa data with three parameters. Up to now the data follow the expected evolution of this simple model.

D-MODEL AND MONTE CARLO - DEATHS-PER-DAY IN SOUTH AFRICA JUNE 6 2020



This Monte Carlo was fitted to data and D model on June 7 2020.

• D-MODEL AND MONTE CARLO - TOTAL DEATHS IN SOUTH AFRICA

  

  The Monte Carlo was fitted to data and D model up to June 6 2020.

• 2. THE D MODEL OF DEATHS BY CORONAVIRUS

  This is a summary of the paper

  The D model for deaths by COVID-19

  by J.E. Amaro

  The D model (D is for deaths) derives form the SIR model

  (susceptible, infected, recovered) as a particular case with an

  analytical solution. We assume that the recoved individuals have no

  effect on the infection rate.

  The D model is based on two hypothesis:

  1. The infection rate over time is proportional to the infected and

  non-infected individuals (SI model) :

  dI(t) = lambda I(t) ( N - I(t) ) dt

  where N is the total population exposed to the virus.

  2. The number of deaths at some time t is

  proportional to the infestation at some former time T.

  Therefore we define the D-function as

  D(t) = mI(t − T )

  Where m is the mortality or death rate, and T is the mortality time.

  With this assumption we can write the D function as

  D(t) = a exp(t/b) / ( 1 + c exp (t/b) )

  The three constants a, b, c are the parameters of the model. They

  are obtained by fit to actual data for the first pandemia days and

  they can be used to make predictions for the next days.

  The D-model for COVID-19 pandemic describes well the current data

  of several countries, including China, Spain and Italy with only

  three parameters.

  The assumption made in the SI model is that the recovered

  individuals do not influence the increase of the infected ones, This

  hypothesis does not seem to be very bad since the model reproduces

  well the data up to now. This could indicate that the

  total population N is not a constant as assumed in the SIR model,

  but it increases over time as more people are exposed, for example,

  in villages that until now had been isolated from the sources of

  infection in big cities.

  The D model is simple enough to provide fast

  estimations of pandemic evolution in other countries, and could be

  useful for the control of the disease.

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