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Â In this session on mathematical modeling of communicable disease,

Â I will not pretend to give you many details on mathematics here.

Â Don't worry too much.

Â It will not be something where I can assume or

Â foresee that you will become mathematicians.

Â You will not develop mathematical modeling just after this session for sure.

Â I just wanna give you some clues to really realize that the mathematical modeling

Â of communicable disease is very important today when controlling infectious disease,

Â in particular outbreak of emerging infectious disease.

Â 1:15

And the line of this model was to say that peoples were divided in three sections.

Â You were the susceptible when you did not have any contact with the virus.

Â You were an infected people when you had a contact with the virus or

Â you were immunized or removed from the chain of transmissions when

Â you were either recovered or died because of the virus infection.

Â 1:44

So in the three compartments there are some interactions,

Â interaction between susceptible and infected people.

Â Of course when you have sufficient contact between a susceptible and

Â an infected people, the susceptible may get the infection and catch the disease.

Â And also the interaction which immunized people because when you are immunized,

Â you protect the other people from infection.

Â You are acting as a bacteria for an infection.

Â You can be immunized today, either because you have already catch the disease and

Â you have recovered, or maybe immunized because you have been vaccinated.

Â This kinda mathematical modeling is applied now for

Â many other disease, even for mosquito disease.

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And how does it work and how can it help?

Â It can help in better understanding this communicable disease.

Â For instance, there is a parameter which is named the reproductive rate are not.

Â The reproductive rate can be defined

Â as the number of secondary cases due to one index case.

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If I take the measles, so measles is a child disease.

Â If a child has the measles,

Â he can transmit the disease to 20 other children.

Â Of course, non-immunized children.

Â That means that is 20.

Â So hopefully to avoid is 20.

Â 3:50

Meaning that this tool, the mathematical modelling of communicable disease may be

Â used as an early warning system.

Â If for instance, we can define, we can estimate for

Â epidemiological records that there are not the reproductive right is above one,

Â you can trigger the epidemic layout of the country and that is used as that.

Â When there was an outbreak of any disease, of influenza in Mexico,

Â of Ebola in West Africa, in the recent years it was used for

Â assessing what was not [INAUDIBLE] above one and

Â there was a risk of epidemic at an international level or at a local level.

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And it can be also used as a tool for

Â assessing the control measures against this disease,

Â until the reproductive rate is both one.

Â You have to control the disease, you have not succeeded to control it effectively.

Â But when you can really be sure that is below one,

Â after you have implemented all the control measures you may wanna implement,

Â control of the borders, screenings of patients, treating the patients,

Â insulating by quarantines and so on or maybe vaccinating the people.

Â You are below one, you have succeeded, it is the end of the process.

Â The end of the outbreak.

Â But when it is still above 1, you can say it's not enough.

Â We need to continue the effort.

Â So it is a tool which is very useful for driving,

Â steering the management of communicable disease and

Â particularly of emerging infectious disease.

Â But this tool can also be used for

Â simulating various scenarios on a computer.

Â It's not easy to propose to the policy makers the appropriate

Â measures to take for controlling an outbreak of infectious disease.

Â But thanks to the mathematical modeling tools we can simulate

Â what will be the actions of quarantine,

Â what would be actions of controlling the borders by stopping any flights.

Â It is very costly, economically to stop all the planes in an airport.

Â But if it is effective.

Â If it proven as effective under computer simulations,

Â you may give these results to the policy makers,

Â and they may take the appropriate actions they wanna take for that.

Â But if you see that there is not an effective action by doing that,

Â you may say to the policymakers that it is not effective.

Â You can also simulate values, policies, regarding vaccinations.

Â If you have certain amount, constrained amount of vaccines available for

Â your population.

Â You may say that if you vaccinate this class of ages or

Â this part of the population that will be effective or not.

Â So you can give some insight to the policy makers with a rational tool.

Â 7:11

And last, but not least,

Â is the use of these mathematical tools for predictions, for forecasting.

Â Okay, you can use these tools for assessing scenarios on the computer.

Â So it is easy to understand that you can also use that

Â tool to forecast the future of the epidemic.

Â But be cautious regarding this forecasting, these predictions.

Â Of course, in imaginary fictitious disease, one never knows what will happen.

Â So the forecasting maybe prone to wrong predictions.

Â I would suggest, I would recommend not to use any predictions after one month.

Â Within one month of an epidemic particularly the start of the epidemic is

Â of exponential in nature you have a very high risk of providing wrong predictions.

Â After one month.

Â Because it goes very, very fast.

Â And sometimes it ends very, very quickly.

Â So you cannot really forecast the future today, even with these tools.

Â So we can forecast within the delay, the period of one month, not after.

Â So the predictions are prone to be wrong, as I said.

Â But you can view that as something which may be useful for

Â the policy maker to forecast a choice,

Â very useful even with some caution, but maybe also the people and

Â the journalists may be very interested by some predictions of what can happen.

Â And you can give some wrongs of what could happen with these epidemics.

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Â