@Carl Love uh 50 or 100 will do i guess.. thanks before!

@Carl Love now i know that the plot go from 0 to k. But i just realize that after the result of each S(1),S(2),...S(k) it should be times with t (for differential transformation method).

for example 

do you think you can change the answer code to make the answer become like this?

@Carl Love I see, okay then.. thanks again! 

Yes it's epidemic model for measles :)

@Carl Love sorry for disturbing you again, I just wanna ask something.

The plot, is it showing the sum of (ex. k=4) S(0)+S(1)+...+S(5)? or S(1)+...+S(5)?

@Carl Love yeah I'm stuck on that too but that's okay I'm still trying to solve it.

Appreciate your help though, thanks a lot!

@Rouben Rostamian  my bad, that I(t) should be J(t)

I already replace I(t) with J(t) and gamma with gamma1 

@Carl Love here it is

dS/dt = mu*N-beta*S(t)*I(t)-mu*S(t)

dE/dt = beta*S(t)*I(t)-mu*E(t)-sigma*E(t)

dJ/dt = sigma*E(t)-mu*J(t)-gamma*J(t)

dR/dt = gamma*J(t)-mu*R(t)

@vv ah you're right. I'll change it then

@Carl Love okay then. thanks a lot again! :)

@Carl Love ah okay later I'll try to change the parameter values to see how the graph will change. Thanks! 

Btw, do you think you can help me one more time plotting another system of differential equations?

@Carl Love I think this is good enough! I tried until k=1000 and it only takes less than one minute. Thanks a lot! :)

@Carl Love allright will try. thanks a lot! you're lifetime saviour

@Carl Love alright here you go:

highest value of k will be infinite if can? if not i guess 100 or some big number will do

my bad, i wrote that delta wrong. It should be gamma not delta on I(k+1)..

thank you so much! 

@Carl Love yeah you can :)

@Carl Love no, it's not the same. The value is also different. Delta(k) s actually N (total population) but transformed into delta(k) by differential transformation method and the value remains. Meanwhile delta is constant from the beginning.