Differential Equations in Java

I am trying to create a simple simulation program of SIR-epidemics model in java.

Basically, SIR is defined by a system of three differential equations:
S'(t) = - l(t) * S(t)
I'(t) = l(t) * S(t) - g(t) * I(t)
R'(t) = g(t) * I(t)

S - susceptible people, I - infected people, R - recovered people.

l(t) = [c * x * I(t)] / N(T)

c - number of contacts, x - infectiveness (probability to get sick after contact with sick person), N(t) - total population (which is constant).

How can I solve such differential equations in Java? I don't think I know any useful way to do that, so my implementation produces rubbish.

public class Main {
public static void main(String[] args) {
    int tppl = 100;
    double sppl = 1;
    double hppl = 99;
    double rppl = 0;
    int numContacts = 50;
    double infectiveness = 0.5;
    double lamda = 0;
    double duration = 0.5;
    double gamma = 1 / duration;
    for (int i = 0; i < 40; i++) {
        lamda = (numContacts * infectiveness * sppl) / tppl;
        hppl = hppl - lamda * hppl;
        sppl = sppl + lamda * hppl - gamma * sppl;
        rppl = rppl + gamma * sppl;
        System.out.println (i + " " + tppl + " " + hppl + " " + sppl + " " + rppl); 
    }
}

}

I would greatly appreciate any help, many thanks in advance!