Effect of Immunity and Susceptibility on Sickness or Mortality Risk
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.
Requires a Wolfram Notebook System
Edit on desktop, mobile and cloud with any Wolfram Language product.
The probability that a person becomes ill or dies of ingested biological or chemical agents is usually estimated from the agent's dose-response curve. Such estimation does not take into account the individual's immunity or susceptibility state. This state can be represented by an index, , for example, , where the lowest value represents extreme immunity and the highest extreme susceptibility. A correction function, , can be used to convert the nominal risk, , expressed as the probability of becoming sick or dying according to the agent's dose-response curve, into a more realistic individual risk. The concept is demonstrated with three hypothetical correction modes based on linear, sigmoid, and double-sigmoid models.
Snapshot 1: correction for immunity () using an asymmetric version of the linear model
Snapshot 2: correction for susceptibility () using the sigmoid model
Snapshot 3: correction for immunity () using the double sigmoid model
The health risk caused by ingesting a pathogen or toxic substance is usually expressed in terms of the probability of becoming sick or dying. This probability, , is primarily determined by the virulence of the pathogen's cells or spores, or toxicity of the chemical agent, and their number or the amount actually ingested. This probability, , can be extracted from the pathogen's or chemical agent's dose-response curve, which is often derived from data on volunteers or from animal studies. Either way, the dose-response curve rarely if ever considers the individual person's immunity state and whether it has been compromised, thus making him or her more susceptible.
This Demonstration presents a method to adjust the risk calculated on the basis of a dose-response curve to account for the individual's immunity or susceptibility. According to the proposed method, an immunity/susceptibility index, , is introduced, having the range for simplicity, where represents extreme immunity and extreme susceptibility. Where , the risk, in terms of the probability of becoming sick or dying, is that represented by .
For an immune or susceptible person, or , respectively, the corrected is allowed to follow three user-chosen patterns:
The parameters specifying these three models, namely , , , and either or , , , and in addition, are entered or modified with sliders. In all three models . In the sigmoid model, controls the steepness of the curves between the asymptotes and . In the double-sigmoid model, the 's determine the length of the flat region around and the 's the steepness of the curve's rise and fall beyond the flat region. The display includes a plot of versus for the chosen model, the numerical values of , the chosen , and the corresponding corrected probability, . Moving the slider at the bottom moves a point marker along the curve representing the changing value of the corrected risk .
The purpose of the Demonstration is not to account for the particulars of any specific toxic agent but only to explore the general principles. Consequently, not every model choice and parameter combination considered here necessarily has a real-life counterpart.