#include<stdlib.h>

#include<time.h>

using namespace std;

int H, P;

//no hosts, no parasites

int b, d, dp, e;

//birth rate hosts, death rate hosts, death rate parasites, no eggs per host

int eggs;

//eggs currently waiting to hatch

int probability;

//probability parasite and host meet

int t;

//number of time units to be executed

int k;

//randomized number

int main()

{

cin>>H>>P>>b>>d>>dp>>e>>t;

srand(time(NULL));

for(int a=1;a<=100;a++)

{

k=rand();

}

for(int i=1;i<=t;i++)

{

probability=k*H*P;

eggs=probability*e;

H=H+(b*H)-(d*H)-probability;

P=P-(dp*P)+eggs;

cout<<"\n"<<H<<" "<<P<<"\n";

}

}

k is a randomized number between 1 and 100 meant to randomize the probability of hosts and parasites meeting while keeping it proportional to the populations' number(probability=k*H*P).
I've met some difficulty with my laptop(it literally refuses to run my programs lately) and I haven't found a good online compiler so suggestions would be appreciated!! 

We have calculated the populations' evolution for a few chosen variables and tye results have been....incomprehensible and unrealistic so we gotta figure that out.

using namespace std;

int H, P;

//no hosts, no parasites

int b, d, dp;

//birth rate hosts, death rate hosts, death rate parasites; they must be between 0 and 1

int e;

//no eggs per host

int eggs;

//eggs currently waiting to hatch

int probability;

//probability parasite and host meet

int t;

//number of time units to be executed

int k;

//random number between 0 and 1

int main()

{

cin>>H>>P>>b>>d>>dp>>e>>t>>k;

for(int i=1 ; i<=t ; i++)

{

probability=k*H*P;

eggs=probability*e;

H=H+(b*H)-(d*H)-probability;

P=P-(dp*P)+eggs;

cout<<"\n"<<H<<" "<<P<<"\n";
if(P==0 || H==0)
{
    cout<<"Population reached 0";
    return 0;

}

}

}