#Deterministic model based on
#Boots, M. and Y. Haraguchi. 1999. The evolution of costly resistance in
#host-parasite systems. Am. Nat. 153: 359-370
rm(list=ls())
require(odesolve)

#Models ******************************************************************
#second ODE
linearcost=function(t,y,parms){
    #Assign values of y to state variables.
    #This order must be maintained in the inital conditions.
    X1 = y[1]
    
    #Equations for system of ODEs
      r=a*X1+b
	    xeq=g/X1
	    yeq=(r-q*g/X1)/(X1+q);
	    x1dot=sigma*(a-yeq);
   
    #The function must return a list containing the derivatives.
    xdot = c(x1dot)
    return(list(xdot))
}

#parameter values ****************************************************
a= 2
b= 0.012
q= 0.003
g= 1
sigma = 0.01
parms = numeric(5)

#initial conditions  *********************************************
x10 = 0.4
times=seq(0,3000,by=1) # time steps
x0=c(x10)

output1 = lsoda(x0,times,linearcost,parms)

#plotting *******************************************************************
tm=output1[,1]         #time
trait=output1[,2]       #susceptibility

par(mfrow=c(1,1))
plot(tm,trait,xlab="Time",ylab="Susceptibility",lwd=2,col="red",type="l")
title(main="Linear Cost no Ecology")