FIG. 14.2 Results of the deterministic simple epidemic model. a) Plot of I, the number of infectives as a function of S, the number of susceptibles, for the same parameters as used for Fig. 14.1 , as given by ( 14.10 ). The progression in time is as indicated by the arrow. b) The maximum number of infectives, I_max as a function of R 0 , for a total population of 2005, including initially 5 infectives. More about this image found in Results of the deterministic simple epidemic model. a) Plot of I...

FIG. 14.4 An epidemic modeled deterministically, for different immigration scenarios, as computed from ( 14.19 )–( 14.21 ). a) No immigration, b) Immigration only of susceptibles with μ I S = 10 , μ I I = 0 , c) Immigration only of infectives with μ I S = 0... More about this image found in An epidemic modeled deterministically, for different immigration scenarios,...

FIG. 14.5 Stochastic simulation of an epidemic with the same parameters as Fig. 14.1 , augmented by the inclusion of immigration of infectives at a rate μ_II = 0.5, in the notation of ( 14.18 ). (The right-hand plot is of the same data as the left-hand plot, but on an enlarged vertical scale.) Contact tracing and a managed isolation strategy are implemented, as described in Sec. 14.2.4 c. The strategy is implemented as in ( 14.26 ) with γ_Q = 3. The quarantine is commenced at t₁, and the epidemic diminishes rapidly. The quarantine is then stopped at t₂, when there is only a very small number of infectives. After some time, the epidemic returns, but is arrested by a second implementation of the quarantine strategy at t₃. This is not subsequently lifted, and the epidemic stays under control. More about this image found in Stochastic simulation of an epidemic with the same parameters as Fig. 14.1...

FIG. 14.3 Means and standard deviations of S(t), I(t), and R(t) resulting from 100 runs of a stochastic epidemic simulation with the same parameters as in Fig. 14.1 . Note that the standard deviations are significantly larger than the square roots of the corresponding means. More about this image found in Means and standard deviations of S(t), ...

FIG. 14.1 a) A linear plot and b) a logarithmic plot of the growth and extinction of an epidemic as described by the Kermack–McKendrick model. Dashed curves represent the solutions of the deterministic Eqs. ( 14.4 )–( 14.6 ), while the solid curves represent a single run of the corresponding s... More about this image found in a) A linear plot and b) a logarithmic plot of the growth and extinction ...