Colloquium Biometricum

Vol: 42 Page: 95

Authors:

Title:
Some corrections to the Kermack–McKendrick model

Language: English

Keywords:

the Kermack-McKendrick model connected with epidemiological data

Summary:
In the book “Mathematical Biology” written by J.D. Murray the Kermack-McKendrick model connected with epidemiological data is presented in the form of a system of differential equations in which fractions of individuals susceptible to illness (S), infected (I) and resistant (R) appear. From the equations Murray extracts the function I(S)=1-S+1/δ⋅ln(S/S₀), treating I₀ as fraction of infected in the initial time (δ is a parameter). In fact I₀ = I(S₀), where S₀ is fraction of individuals susceptible to illness in the initial time and I(S)=-S+1/δ⋅ln(S/S₀)+I(S₀)+S₀. In the paper differences resulting from both forms of I(S) are described.