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In 2003 there is an outbreak of SARS (Severe acute respiratory syndrome) in China that spreads to Hong Kong and then to the entire world. The following map shows the number of cases in the different countries:

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If the susceptible, infected and 'recovered' (who heal or die) are observed, the typical curves of the SIR model are observed:

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If the WHO data for the SARS epidemic in 2003 in Hong Kong is studied, the current number of infected I can be estimated if the number of accumulated infected is subtracted from the accumulated numbers of recovered and dead. The result is the graph presented below:

\\n\\nEven if you do not have the beginning section, you can see the maximum typical of the number of infected when you start to control them and it is given that\\n\\n

$\displaystyle\frac{dS}{dt}=\left(\displaystyle\frac{\beta C}{N}S-\gamma\right)I=0$

\\n\\nso that those susceptible at that point reach\\n\\n

$S=\displaystyle\frac{\gamma}{\beta C}N$

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If you study the way in which the infected descend, it is seen that as time progresses, the term gamma must dominate since it is the one that reduces the total volume described by the first term. That is why it is necessary for times when the epidemic is under control\\n\\n

$\displaystyle\frac{dI}{dt}=\left(\displaystyle\frac{\beta C}{N}S-\gamma\right)I\sim-\gamma I$

\\n\\nIn that case the asymptomatic solution is of the form\\n\\n

$I(t) \propto e^{-\gamma t}$

what can be seen in the existing infected curve for the SARS 2003 case in Hong Kong. Therefore, a minimum square adjustment of the final part of the curve can be made

\\n\\nobtaining that the factor \gamma must be of the order of 0.048 1 / day. This corresponds to an average time from infection to recovery of\\n\\n

$\tau=\displaystyle\frac{1}{\gamma}\sim 20.8,dias$

If we also assume that each person meets on a daily basis with the order of 30 people, the \beta Factor would have to be estimated so that the curve generated by the simulator is similar to the curve measured by the WHO.

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World mortality is different depending on the country in the world. While in developed countries it reaches values lower than 5 deaths per 1000 inhabitants and year in underdeveloped countries it reaches more than 11:

The factor demanded by the model is the probability per day that a person dies. In other words, the number of daily deaths (cases favorable to the hypothesis) must be taken and divided by the number of people alive. In this way, if the \mu_d factor is multiplied by the population, the susceptible, latent, infected or recovered, the number of these that will probably die in one day for another cause is obtained.

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World birth is different depending on the country of the world. While in developed countries it reaches values below 15 births per 1000 inhabitants and year in underdeveloped countries it reaches 46:

The factor demanded by the model is the probability per day that a person is born. In other words, the number of daily births (cases favorable to the hypothesis) must be taken and divided by the number of people alive. In this way, if the \mu_b factor is multiplied by the population, the number of these that will probably be born in one day is obtained.

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The SIR simulator allows defining the parameters of a SIR model and observing its evolution:

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The SEIR simulator allows defining the parameters of a SEIR model and observing its evolution:

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The SEIR-long term simulator allows defining the parameters of a SEIR model and observing its evolution:

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This simulator contains the SARS epidemic data for the case of Hong Kong and allows searching the parameters of a SEIR model by adjusting the curves to the actual values:

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