Inference for Ecological Dynamical Systems: A Case Study of Two Endemic Diseases

Figure 2

A two-hundred-and-fifty-week time series of the number of infected cases from the SIR immigration model discussed in this paper, simulated using the stochastic simulation algorithm (SSA) defined in the supplementary material. 𝑦-axis corresponds to observed infected cases. 𝑥-axis corresponds to time in weeks. Susceptible cases exhibit a similar complex pattern of noisy oscillations but are not shown. The simulated data are weekly numbers of infected cases; Disease 1 infected cases are shown in blue; Disease 2 infected cases are shown in red. Parameter values used in the simulations: for Disease 1: 𝛼=(𝛽,𝛾,𝜎,𝜇)=(3.70,.25,.1,.001) with 𝑁=50000 and for Disease 2: 𝛼=(14.7,.5,.1,.001) with 𝑁=100000 (see Table 2).