Change Language

dx_t/dt=-bx_ty_t , dy_t/dt=bx_ty_t-cy_t

This model describes an endemic model. The host population growth is not taken into consideration in this model. The number of susceptible population(X) is x, and the patient(Y)'s population is y. This is a specific version of Lotka-Volterra model with the parameter setting of a=b and r_x=0. The value r_x=0 means that the total population, the sum of {not infected (X) + patients (Y) + cured or death population} does not change. When x > c/b then endemic occur, however, when x < c/b then patient population (y) decrease monotonically. The value x_∞ means the population who have not be infected.

b : Infection Rate

c : The Cure or Death rate of patients

x₀ & y₀ : Initial Susceptibles & Initial Patients

Simulation Time