Created by Susan Stagg-Williams, Dieter Andrew Schweiss, Gavin Sy, and H. Scott Fogler, 1994
Updated by Apeksha Bandi, Gustav Sandborgh, and Arthur Shih, 2013

Case 3: Oh no! Where's the closest stock of antivenom?

You decided to explore some ancient ruins in the rainforests of Thailand and you accidentally mistook a cobra as a stick on the ground. You are a few minutes away from your car, where the antivenom and first aid kits is located. In this case, we will explore the effects of injecting a 15 minutes and 30 minutes after a cobra bite. We will also explore the effects of delayed injections of antivenom on twitch height.

Part 1: Injection 15 minutes after Cobra Bite

Suppose it takes fifteen minutes for you to reach the first aid kit in your car and administer antivenom into the victim's body. We see if we save could your friend in such a situation.

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We see that 78.9 % of sites are blocked in fifteen minutes and the twitch height drops down to 0.978. Although the victim is slightly away from the danger zone of 85-90 % site bloackage.

Now antivenom is injected into the victim's body and we observe how this saves the life of the victim just in time :

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We see that within two hours of antivenom injection,the twitch height bounces back to one and the percentage of free sites increases from 21.1 % to 73.5 %. The victim is now absolutely safe.

Part 2: Finding the Point of No Return

Since being bit by a cobra snake can be life-taking, it is important that we find a safety bound on the amount of time delay one can afford for antivenom injection into a victim's body. We define Point of No Return as the time at which more than 85% of the sites get blocked in a victim's body. This means that it is time at which the victims just touches the danger level of 85-90 % site blockage after being bit by a cobra.

What would be the point of no return for our case?

From the data generated in base case ( no antivenom injection), we see that fraction of free sites decreases below 0.15 at 22.5 minutes. Hence the point of no return is 22.5 minutes.

We model the behaviour in the first 22.5 minutes using the code below.

Download the Polymath Code Here

We see that at the end of 22.5 minutes, the fraction of free sites in 0.1509 and the twitch height drops down to 0.6414. This indicates that the victim has reached the point of no return.

On injection of antivenom at 22.5 minutes, the twitch height bounces back to one within two hours as shown below:

Download the Polymath Code Here