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  • Equations

    Individuals in a population are members of one of three groups:
    • Healthy but at risk of being infected (H).
    • Infected and contagious (C).
    • Rocovered and immune (R).

    Contagious persons can infect healthy persons. Recovered persons are either immune or dead and cannot be reinfected.

    The indepedent variable is time in days.

    The healthy (H), contagious (C) and recovered (R) group sizes are equal to the integral over time of their net rate of change (dH/dt, dC/dt, dR/dt).

    The rate of contagion (HtoC) is equal to a contagion factor (Contagion) multiplied by the size of the healthy (H) and contagious (C) groups.

          HtoC = Contagion * H * C

    The rate of recovery (CtoR) is equal to a recovery factor (0.1) multiplied by the size of the contagious group (C).

          CtoR = 0.1 * C

    Infection decreases the size of the healthy group. The rate of change of the healthy group (dH/dt) is minus the infection rate (HtoC).

          dH/dt = - HtoC

    Infection increases the size of the contagious group while recovery decreases the size of this group. The rate of change of the contagious group is the infection rate (HtoC) minus the recovery rate (CtoR).

          dC/dt = HtoC - CtoR

    Recovery increases the size of the recovered group. The rate of change of the recovered group is equal to the recovery rate (CtoR).

          dR/dt = CtoR