Mathematical/Numerical Solution
We now consider the analytical solution of equations (A1.4)-(A1.6). By eliminating I from equations (A1.4) and (A1.6), we have:
Integration yields:
Which can be expressed as:
When t = 0:
And thus,S=So=A
Since I=n−S−R, equation (A1.6) becomes:
As:
The right-hand side of the equation above can be expanded as far as the term in R squared to give:
Stay tuned for Part 4
Please Note: This model is inspired by a paper co-authored by Jim Caldwell and Kei Shing Ng, titled: Deterministic Model in Contagious Disease, and is going through a continual overhaul to make it more robust. So far I've had this model critiqued by Rick Bookstaber, author of A Demon Of Our Own Design: Markets, Hedge Funds And The Perils of Financial Innovation, and he highlighted a lot of flaws, in the model and its presentation, that I'm currently addressing. Dr. Ernest Chan, the author of a quantitative text titled Quantitative Trading: How to Build Your Own Algorithmic Trading Business is also in the process of critiquing the model, and I'll also take his opinions on board. Furthermore, Dr. Jim Caldwell, the originator of the model I drew analogies from, also gave me a few pointers on how to make the model more realistic, and I'll also be taking his pointers on board. I also benefited from Eric Falkenstein's critique of the model, and I will be taking his suggestions on board as well. Please stay tuned!
