Table 2. Parameter combinations for the 10 best-fit simulations for the Great Lakes region as validated with Illinois P&I mortality data.

Rank	RMS Error	Correlation Coefficient (r)	L (years)	D (days)		*
1	0.0049	0.93	5.74	4.58	5.11	2.35
2	0.0061	0.87	3.81	2.08	3.33	2.84
3	0.0062	0.84	9.78	2.68	4.92	1.90
4	0.0062	0.86	3.54	3.60	2.85	3.18
5	0.0064	0.86	3.66	3.29	3.67	2.29
6	0.0064	0.88	4.39	6.47	7.13	2.69
7	0.0065	0.83	7.65	2.42	2.79	3.69
8	0.0066	0.82	4.59	2.71	3.30	2.34
9	0.0069	0.82	4.81	6.53	3.15	3.32
10	0.0069	0.91	7.41	5.80	7.71	2.14

3000 simulations were performed at each site with the parameters L (mean duration of immunity), D (mean infectious period), ϕ (vitamin D scaling), and R ₀ ^* (the basic reproduction number if γ_i,t = 1) randomly chosen from within specified ranges. Parameters λ (inflection point) and η (inflection point slope) were fixed at and . Best-fit simulations were selected based on RMS error after scaling the 31-year mean daily infection number to the 31-year mean observed daily excess P&I mortality rate.