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#|
This is the basic model of 

Periodic and Chaotic Host-Parasite Interactios in Human Malaria
Dominic Kwiatkowski, Martin Nowak
Proceedings of the National Academy of Sciences of the United States of
America, Vol. 88, No. 12 (Jun. 15, 1991), pp. 5111-5113

My expected equilibria aren't coming out right: don't know why....

		yt = (* d1 xt (f xt))
		xt = (* r d2 yt (g xt)))
Therefore
		xt = (* r d2 (* d1 xt (f xt)) (g xt)))
		1  = (* r d2 d1 (f xt) (g xt))
		1  = (* r d2 d1 (exp (- (+ s p) (trans xt))))
		(exp (* (+ s p) (trans xt)))  = (* r d2 d1)
		(* (+ s p) (trans xt))  = (ln (* r d2 d1))
		(trans xt)  = (ln (* r d2 d1))/(+ s p)
		xt  = (arctrans (ln (* r d2 d1))/(+ s p))
|#
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(defun run(r &key
	     (p .00001)
	     (s .001)
	     (d1 1)
	     (d2 1)
	     (n 50)
	     (x 1)
	     (y 1)
	     (trans (lambda(x) x))
	     (arctrans (lambda(x) x))
	     )
  "
;; Example
 (run 2 :n 150)
 (run 2 :n 500 :x .001 :y .001)
 (run 24 :n 150)
 (run 32 :n 1000)
 (run 32 :p .001 :s .001 :n 1000)
 (run 12 :p .001 :s .001 :n 1000)
 (run 2 :n 150 
   :trans (lambda(x) (square x))
   :arctrans (lambda(x) (sqrt x))
   )
 (run 2 :n 300 :trans (lambda(x) (exp (* .001 x)))
   :arctrans (lambda(x) (* 1000 (ln x)))
   )
"
  (flet (
	 (f(x)
	   (exp (* -1 p (funcall trans x)))
	   )
	 (g(x)
	   (exp (* -1 s (funcall trans x)))
	   )
	 )
	(setq y 
	      (if y (list y) (let ((val (final x))) (list (* val d1 (f val)))))
	      )
	(dotimes
	    (i n)
	  (let (
		(xt (final x))
		(yt (final y))
		)
	    (setq
	     y (combine y (* d1 xt (f xt)))
	     x (combine x (* r d2 yt (g xt)))
	     )
	    )
	  )
	(title
	 (format
	  nil
	  "young parasites: r=~d; d1=~,2f; d2=~,2f; p=~,2e; s=~,2e" r d1 d2 p s)
	 )
	(send (plotter x) :size 600 300)
	(send my-plot :add-plot-item
	      (list
	       'lines
	       (list 0 (length x))
	       (let ((val (funcall arctrans (/ (ln (* r d1 d2)) (+ s p)))))
		 (list val val)
		 )
	       'black
	       )
	      )
	(title 
	 (format
	  nil
	  "old parasites: r=~d; d1=~,2f; d2=~,2f; p=~,2e; s=~,2e" r d1 d2 p s
	  )
	 )
	(send (plotter y) :size 600 300)
	(send my-plot :add-plot-item
	      (list
	       'lines
	       (list 0 (length x))
	       (let* (
		      (val (funcall arctrans (/ (ln (* r d1 d2)) (+ s p))))
		      (yend (* d1 val (f val)))
		      )
		 (list yend yend)
		 )
	       'black
	       )
	      )

	(title 
	 (format
	  nil
	  "combined parasites: r=~d; d1=~,2f; d2=~,2f; p=~,2e; s=~,2e" r d1 d2 p s
	  )
	 )
	(send (plotter (log (+ x y) 10)) :size 600 300)
	(send my-plot :add-plot-item
	      (list
	       'lines
	       (list 0 (length x))
	       (let* (
		      (val (funcall arctrans (/ (ln (* r d1 d2)) (+ s p))))
		      (yend (* d1 val (f val)))
		      )
		 (log (list (+ val yend)  (+ val yend)) 10)
		 )
	       'black
	       )
	      )

	(title 
	 (format
	  nil
	  "young against old parasites: r=~d; d1=~,2f; d2=~,2f; p=~,2e; s=~,2e" r d1 d2 p s
	  )
	 )
	(plotter x y)
	(send my-plot :add-plot-item
	      (list
	       'points
	       (let* (
		      (val (funcall arctrans (/ (ln (* r d1 d2)) (+ s p))))
		      )
		 (list val)
		 )
	       (let* (
		      (val (funcall arctrans (/ (ln (* r d1 d2)) (+ s p))))
		      (yend (* d1 val (f val)))
		      )
		 (format t "~,2f young~%~,2f old~%" val yend)
		 (list yend)
		 )
	       'black
	       )
	      )
	)
  )