Some Special Cases and Some Numerical Examples

Abstract

In the preceding section a model was proposed which essentially involved the following three equations in T(t), I(t) and S(t) for large t,

$$\int\limits_{\tau (t)}^t {[\rho _1 (x) + \rho _2 (x)I(x)]dx = m,\,\,\tau (t) \equiv 0,\,\,\,\,\,0 \leqslant t \leqslant t_0 < \sigma ,}$$

(5.1)

$$S(t) = I_1 (t) + S_0 - \int\limits_{\tau (t - \sigma - \omega )}^\tau {r(x)S(x)I(x)dx,}$$

(5.2)

$$I(t) = I_0 (t) + \int\limits_{\tau (t - \sigma )}^{\tau (t)} {r(x)} S(x)I(x)dx.$$

(5.3)