Evaluation of real time methods for epidemic forecasting 3

❈❤❛♣t❡r ✸ ❘❡s✉❧ts ■♥ t❤✐s s❡❝t✐♦♥ ✇❡ ❞✐s♣❧❛② t❤❡ ♦✉t♣✉t ♦❢ ♣r❡❞✐❝t✐♦♥s ❢♦r t❤❡ ❛✈❡r❛❣❡ ♥✉♠❜❡r ♦❢ ■▲■s ♣❡r ●P ❢♦r t❤❡ ♣❛♥❞❡♠✐❝ ❛♥❞ t❤❡ ♣❛r❛♠❡t❡rs ❛ss♦❝✐❛t❡❞ ✇✐t❤ ❡❛❝❤ ♠♦❞❡❧ ✉s❡❞✳ ❲❡ ❤❛✈❡ ♣❡r❢♦r♠❡❞ t❤❡ ♣❛rt✐❝❧❡ ✜❧t❡r r♦✉t✐♥❡ ♦♥ ❞❡t❡r♠✐♥✐st✐❝ ❙■❘ ♠♦❞❡❧ ❛♥❞ st♦❝❤❛st✐❝ ❙■❘ ♠♦❞❡❧ r❡s♣❡❝t✐✈❡❧②✳ ❍♦✇❡✈❡r✱ t❤❡ ❡st✐♠❛t❡ ♦❢ t❤❡ ♣♦s✲ t❡r✐♦r ❞✐str✐❜✉t✐♦♥ ❢♦r t❤❡ st❛t❡s ✐s ✉♥s❛t✐s❢❛❝t♦r② ❢♦r t❤❡ ❞❡t❡r♠✐♥✐st✐❝ ❙■❘ ♠♦❞❡❧ ❛s s❤♦✇♥ ✐♥ ❋✐❣✉r❡ ✸✳✶✱ ❛s t❤❡ ♣❡❛❦ ♦❢ t❤❡ ♣❛♥❞❡♠✐❝ ✐s ♥♦t ❝❛♣t✉r❡❞✳ ❈♦♥s❡q✉❡♥t❧②✱ t❤❡ ♣r❡❞✐❝t✐♦♥s ❢♦r t❤❡ ❞❡t❡r♠✐♥✐st✐❝ ❙■❘ ♠♦❞❡❧ ♣r❡s❡♥t❡❞ ✐♥ t❤✐s s❡❝t✐♦♥ ✐s ❢♦r♠❡❞ ❜② ✉s✐♥❣ t❤r❡❡ ✐t❡r❛t✐♦♥s ♦❢ ▼❈▼❈ ❢♦❧❧♦✇❡❞ ❜② t❤r❡❡ ✐t❡r❛t✐♦♥s ♦❢ ✐♠♣♦rt❛♥❝❡ s❛♠♣❧✐♥❣✳ ❲❡ ✉s❡ ✐♠♣♦rt❛♥❝❡ s❛♠♣❧✐♥❣ ♦♥ ❘✐❝❤❛r❞s ♠♦❞❡❧ t♦ ♦❜t❛✐♥ ♣r❡❞✐❝t✐♦♥s✳ ✹✻ ✹✼ ❋✐❣✉r❡ ✸✳✶✿ Pr❡❞✐❝t✐♦♥s ♦❢ t❤❡ ♥✉♠❜❡r ♦❢ ✐♥❢❡❝t❡❞ s✉❜❥❡❝ts ✐♥ t❤❡ ♣♦♣✉❧❛t✐♦♥ ♣❡r ❞❛② ✉s✐♥❣ t❤❡ ♣❛rt✐❝❧❡ ✜❧t❡r ♠❡t❤♦❞ ❢♦r t❤❡ ❞❡t❡r♠✐♥✐st✐❝ ❙■❘ ♠♦❞❡❧✳ ❚❤❡ s❤❛❞❡❞ ❛r❡❛ ✐♥❞✐❝❛t❡s ❛ s❡r✐❡s ♦❢ s✉❝❝❡ss✐✈❡ r❡❣✐♦♥s s♣❛♥♥❡❞ ❜② ✾✺✪✱ ✾✸✪✱ ✾✶✪✱ ✳✳✳✱ ✵✪ ❝r❡❞✐❜❧❡ ✐♥t❡r✈❛❧s ✐♥ ✐♥❝r❡❛s✐♥❣ ✐♥t❡♥s✐t②✳ Susceptible, 1000s 2500 2000 1500 1000 500 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 16 20 16 20 16 20 Oct Infected, 1000s 250 200 150 100 50 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 Oct Removed, 1000s 5000 4000 3000 2000 1000 0 26 30 Jun 4 8 12 16 Jul 20 24 28 2 6 10 14 18 Aug 22 26 30 2 6 10 14 18 Sep 22 26 30 4 8 12 Oct ✸✳✶ P❛r❛♠❡t❡rs ❛♥❞ ♣r❡❞✐❝t✐♦♥s ❢♦r ❡❛❝❤ ♠♦❞❡❧ ❚❤❡ s❝❛tt❡r♣❧♦t ❢♦r t❤❡ ♣❛r❛♠❡t❡rs ✐♥ t❤❡ ❘✐❝❤❛r❞s ♠♦❞❡❧ ✐s s❤♦✇♥ ✐♥ ❋✐❣✉r❡ ✸✳✷✱ ✇✐t❤ t❤❡ s✐③❡ ♦❢ ♣♦✐♥ts ♣r♦♣♦rt✐♦♥❛❧ t♦ t❤❡✐r r❡s♣❡❝t✐✈❡ ❧✐❦❡❧✐❤♦♦❞s✳ ❚❤❡ ♣r❡❞✐❝t✐♦♥ ♦♥ t❤❡ ♥✉♠❜❡r ♦❢ ✐♥❢❡❝t❡❞ s✉❜❥❡❝ts ♣❡r ●P ❡❛❝❤ ❞❛② t❤r♦✉❣❤♦✉t ✹✽ t❤❡ ♣❛♥❞❡♠✐❝ ✐s s❤♦✇♥ ✐♥ ❋✐❣✉r❡ ✸✳✸✱ ✉s✐♥❣ t❤❡ ❢✉❧❧ ❞❛t❛ t❤❛t ✇❡ ❤❛✈❡ ❝♦❧✲ ❧❡❝t❡❞ ❢r♦♠ ✷✺t❤ ❏✉♥❡ ✷✵✵✾ t♦ ✷✹t❤ ❙❡♣t❡♠❜❡r ✷✵✵✾✳ ❚❤❡ s❤❛❞❡❞ ❛r❡❛ ✐♥ r❡❞ ✐♥❞✐❝❛t❡s ❛ s❡r✐❡s ♦❢ s✉❝❝❡ss✐✈❡ r❡❣✐♦♥s s♣❛♥♥❡❞ ❜② ✾✺✪✱ ✾✸✪✱ ✾✶✪✱ ✳✳✳✱ ✵✪ ❝r❡❞✐❜❧❡ ✐♥t❡r✈❛❧s ♦❢ t❤❡ ♣r❡❞✐❝t❡❞ ♥✉♠❜❡r ♦❢ ✐♥❢❡❝t❡❞ s✉❜❥❡❝ts ♣❡r ●P ❡❛❝❤ ❞❛② ✐♥ ✐♥❝r❡❛s✐♥❣ ✐♥t❡♥s✐t②✱ ❛♥❞ t❤❡ ❡♠♣✐r✐❝❛❧ ♥✉♠❜❡r ♦❢ ✐♥❢❡❝t❡❞ s✉❜❥❡❝ts ♣❡r ●P ❢r♦♠ t❤❡ ❞❛t❛ ✐s ♣❧♦tt❡❞ ✐♥ ❜❧❛❝❦✳ ❚❤❡ ❝♦rr❡s♣♦♥❞✐♥❣ s❝❛tt❡r♣❧♦t ❢♦r ♣❛r❛♠❡t❡rs ❛♥❞ ♣❧♦t ♦❢ ♣r❡❞✐❝t❡❞ ♥✉♠✲ ❜❡r ♦❢ ✐♥❢❡❝t❡❞ s✉❜❥❡❝ts ♣❡r ●P ❛r❡ ❛❧s♦ s❤♦✇♥ ❢♦r ❞❡t❡r♠✐♥✐st✐❝ ❙■❘ ♠♦❞❡❧ ✭❋✐❣✉r❡ ✸✳✹ ❛♥❞ ❋✐❣✉r❡ ✸✳✺✮ ❛♥❞ st♦❝❤❛st✐❝ ❙■❘ ♠♦❞❡❧ ✭❋✐❣✉r❡ ✸✳✻ ❛♥❞ ❋✐❣✉r❡ ✸✳✼✮✳ ✹✾ ❋✐❣✉r❡ ✸✳✷✿ ❙❝❛tt❡r♣❧♦t ♦❢ ♣❛r❛♠❡t❡rs ❢♦r ❘✐❝❤❛r❞s ♠♦❞❡❧✱ ♣♦✐♥ts ❛r❡ ♣r♦♣♦rt✐♦♥❛❧ t♦ t❤❡✐r ❝♦rr❡s♣♦♥❞✐♥❣ ✇❡✐❣❤t✳ t❤❡ ❛r❡❛ ♦❢ t❤❡ ✺✵ ❋✐❣✉r❡ ✸✳✸✿ Pr❡❞✐❝t✐♦♥s ♦❢ t❤❡ ♥✉♠❜❡r ♦❢ ✐♥❢❡❝t❡❞ s✉❜❥❡❝ts ♣❡r ●P ♣❡r ❞❛② ✉s✐♥❣ t❤❡ ❘✐❝❤❛r❞s ♠♦❞❡❧ ✇✐t❤ ❝r❡❞✐❜❧❡ ✐♥t❡r✈❛❧s s❤♦✇♥ ✐♥ r❡❞✳ ❇❧❛❝❦ ❧✐♥❡ ✐♥❞✐❝❛t❡s ♦❜s❡r✈❡❞ ❞❛t❛✳ 5 Avr ILIs per GP 4 3 2 1 0 26 Jun 2 6 12 18 Jul 24 30 4 8 14 20 Aug 26 2 6 12 18 Sep 24 30 6 12 Oct 18 ✺✶ ❋✐❣✉r❡ ✸✳✹✿ ❙❝❛tt❡r♣❧♦t ♦❢ ♣❛r❛♠❡t❡rs ❢♦r ❞❡t❡r♠✐♥✐st✐❝ ❙■❘ ♠♦❞❡❧✱ ❛r❡❛ ♦❢ t❤❡ ♣♦✐♥ts ❛r❡ ♣r♦♣♦rt✐♦♥❛❧ t♦ t❤❡✐r ❝♦rr❡s♣♦♥❞✐♥❣ ✇❡✐❣❤t✳ t❤❡ ✺✷ ❋✐❣✉r❡ ✸✳✺✿ Pr❡❞✐❝t✐♦♥s ♦❢ t❤❡ ♥✉♠❜❡r ♦❢ ✐♥❢❡❝t❡❞ s✉❜❥❡❝ts ♣❡r ●P ♣❡r ❞❛② ✉s✐♥❣ t❤❡ ❞❡t❡r♠✐♥✐st✐❝ ❙■❘ ♠♦❞❡❧ ✇✐t❤ ❝r❡❞✐❜❧❡ ✐♥t❡r✈❛❧s s❤♦✇♥ ✐♥ r❡❞✳ ❇❧❛❝❦ ❧✐♥❡ ✐♥❞✐❝❛t❡s ♦❜s❡r✈❡❞ ❞❛t❛✳ 5 Avr ILIs per GP 4 3 2 1 0 26 Jun 2 6 12 18 Jul 24 30 4 8 14 20 Aug 26 2 6 12 18 Sep 24 30 6 12 Oct 18 ✺✸ ❋✐❣✉r❡ ✸✳✻✿ ❙❝❛tt❡r♣❧♦t ♦❢ ♣❛r❛♠❡t❡rs ❢♦r st♦❝❤❛st✐❝ ❙■❘ ♠♦❞❡❧✱ ♦❢ t❤❡ ♣♦✐♥ts ❛r❡ ♣r♦♣♦rt✐♦♥❛❧ t♦ t❤❡✐r ❝♦rr❡s♣♦♥❞✐♥❣ ✇❡✐❣❤t✳ t❤❡ ❛r❡❛ ✺✹ ❋✐❣✉r❡ ✸✳✼✿ Pr❡❞✐❝t✐♦♥s ♦❢ t❤❡ ♥✉♠❜❡r ♦❢ ✐♥❢❡❝t❡❞ s✉❜❥❡❝ts ♣❡r ●P ♣❡r ❞❛② ✉s✐♥❣ t❤❡ st♦❝❤❛st✐❝ ❙■❘ ♠♦❞❡❧ ✇✐t❤ ❝r❡❞✐❜❧❡ ✐♥t❡r✈❛❧s s❤♦✇♥ ✐♥ r❡❞✳ ❇❧❛❝❦ ❧✐♥❡ ✐♥❞✐❝❛t❡s ♦❜s❡r✈❡❞ ❞❛t❛✳ 5 Avr ILIs per GP 4 3 2 1 0 26 Jun 2 6 12 18 Jul 24 30 4 8 14 20 Aug 26 2 6 12 18 Sep 24 30 6 12 18 Oct ■♥ ♦r❞❡r t♦ ❛ss❡ss t❤❡ ♣r❡❞✐❝t✐✈❡ ❛❜✐❧✐t② ♦❢ t❤❡ ♠♦❞❡❧s✱ ✇❡ ❛❧s♦ ❣❡♥❡r❛t❡ ♣r❡❞✐❝t✐♦♥s ♦♥ ♥✉♠❜❡r ♦❢ ✐♥❢❡❝t❡❞ s✉❜❥❡❝ts ♣❡r ●P ❢♦r t❤❡ ❢✉t✉r❡ ❢♦r ❡❛❝❤ ♠♦❞❡❧ ❛ss✉♠✐♥❣ t❤❛t ✇❡ ❦♥♦✇ ♦♥❧② ❛ s✉❜s❡t ♦❢ t❤❡ ❞❛t❛✳ ❯s✐♥❣ ❞❛t❛ ❢r♦♠ ✺✺ ❞❛②s ✶✕✶✹ ✭✽t❤ ❏✉❧②✮✱ ❞❛②s ✶✕✷✶ ✭✶✺t❤ ❏✉❧②✮✱ ❞❛②s ✶✕✷✽ ✭✷✷t❤ ❏✉❧②✮✱ ❞❛②s ✶✕✸✺ ✭✷✾t❤ ❏✉❧②✮✱ ❞❛②s ✶✕✹✷ ✭✺t❤ ❆✉❣✉st✮✱ ❞❛②s ✶✕✺✻ ✭✶✾t❤ ❆✉❣✉st✮✱ ❞❛②s ✶✕✼✵ ✭✷♥❞ ◆♦✈❡♠❜❡r✮ ❛♥❞ ❞❛②s ✶✕✽✹ ✭✶✻t❤ ◆♦✈❡♠❜❡r✮✱ ✇❡ ❣❡♥❡r❛t❡ ❛ ♣r❡✲ ❞✐❝t✐♦♥ ✉♣ t♦ ❞❛② ✶✷✵ ✭✷✷♥❞ ❖❝t♦❜❡r✮✳ ❋✐❣✉r❡s ✸✳✽✱ ✸✳✾ ❛♥❞ ✸✳✶✵ s❤♦✇s t❤❡ ♣r❡❞✐❝t✐♦♥s ❢♦r ❘✐❝❤❛r❞s ♠♦❞❡❧✱ ❞❡t❡r♠✐♥✐st✐❝ ❙■❘ ♠♦❞❡❧ ❛♥❞ st♦❝❤❛st✐❝ ❙■❘ ♠♦❞❡❧ r❡s♣❡❝t✐✈❡❧②✳ ✺✻ ❋✐❣✉r❡ ✸✳✽✿ Pr❡❞✐❝t✐♦♥s ✉s✐♥❣ ❞❛t❛ s✉❜s❡t ✭❜❧❛❝❦ s♦❧✐❞ ❧✐♥❡✮ ♦♥ ♥✉♠❜❡r ♦❢ ❘✐❝❤❛r❞s ♠♦❞❡❧ s❤♦✇♥ ✐♥ ✾✺✪ ❝r❡❞✐❜❧❡ ✐♥t❡r✈❛❧ ■♥❢❡❝t❡❞ s✉❜❥❡❝ts ♣❡r ●P ❜② ✭r❡❞✮✳ ❋✉t✉r❡ ❞❛t❛ ✭❜❧❛❝❦ ❞♦tt❡❞ ❧✐♥❡✮ s❤♦✇♥ ❞♦❡s ♥♦t ❝♦♥tr✐❜✉t❡ t♦ t❤❡ ♣♦st❡r✐♦r ❞✐str✐❜✉t✐♦♥✳ Days 1−14 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 16 20 16 20 16 20 16 20 Oct Days 1−21 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 Oct Days 1−28 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 Oct Days 1−35 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 Jun 4 8 12 16 Jul 20 24 28 2 6 10 14 18 Aug 22 26 30 2 6 10 14 18 Sep 22 26 30 4 8 12 Oct ✺✼ Days 1−42 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 16 20 16 20 16 20 16 20 Oct Days 1−56 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 Oct Days 1−70 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 Oct Days 1−84 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 Jun 4 8 12 16 Jul 20 24 28 2 6 10 14 18 Aug 22 26 30 2 6 10 14 18 Sep 22 26 30 4 8 12 Oct ✺✽ ❋✐❣✉r❡ ✸✳✾✿ Pr❡❞✐❝t✐♦♥s ✉s✐♥❣ ❞❛t❛ s✉❜s❡t ✭❜❧❛❝❦ s♦❧✐❞ ❧✐♥❡✮ ♦♥ ♥✉♠❜❡r ♦❢ ■♥✲ ❢❡❝t❡❞ s✉❜❥❡❝ts ♣❡r ●P ❜② ❞❡t❡r♠✐♥✐st✐❝ ❙■❘ ♠♦❞❡❧ s❤♦✇♥ ✐♥ ✾✺✪ ❝r❡❞✐❜❧❡ ✐♥t❡r✈❛❧ ✭r❡❞✮✳ ❋✉t✉r❡ ❞❛t❛ ✭❜❧❛❝❦ ❞♦tt❡❞ ❧✐♥❡✮ s❤♦✇♥ ❞♦❡s ♥♦t ❝♦♥tr✐❜✉t❡ t♦ t❤❡ ♣♦st❡r✐♦r ❞✐str✐❜✉t✐♦♥✳ Days 1−14 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 16 20 16 20 16 20 16 20 Oct Days 1−21 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 Oct Days 1−28 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 Oct Days 1−35 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 Jun 4 8 12 16 Jul 20 24 28 2 6 10 14 18 Aug 22 26 30 2 6 10 14 18 Sep 22 26 30 4 8 12 Oct ✺✾ Days 1−42 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 16 20 16 20 16 20 16 20 Oct Days 1−56 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 Oct Days 1−70 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 Oct Days 1−84 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 Jun 4 8 12 16 Jul 20 24 28 2 6 10 14 18 Aug 22 26 30 2 6 10 14 18 Sep 22 26 30 4 8 12 Oct ✻✵ ❋✐❣✉r❡ ✸✳✶✵✿ Pr❡❞✐❝t✐♦♥s ✉s✐♥❣ ❞❛t❛ s✉❜s❡t ✭❜❧❛❝❦ s♦❧✐❞ ❧✐♥❡✮ ♦♥ ♥✉♠❜❡r ♦❢ ■♥❢❡❝t❡❞ s✉❜❥❡❝ts ♣❡r ●P ❜② st♦❝❤❛st✐❝ ❙■❘ ♠♦❞❡❧ s❤♦✇♥ ✐♥ ✾✺✪ ❝r❡❞✐❜❧❡ ✐♥t❡r✈❛❧ ✭r❡❞✮✳ ❋✉t✉r❡ ❞❛t❛ ✭❜❧❛❝❦ ❞♦tt❡❞ ❧✐♥❡✮ s❤♦✇♥ ❞♦❡s ♥♦t ❝♦♥tr✐❜✉t❡ t♦ t❤❡ ♣♦st❡r✐♦r ❞✐str✐❜✉t✐♦♥✳ Days 1−14 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 16 20 16 20 16 20 16 20 Oct Days 1−21 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 Oct Days 1−28 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 Oct Days 1−35 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 Jun 4 8 12 16 Jul 20 24 28 2 6 10 14 18 Aug 22 26 30 2 6 10 14 18 Sep 22 26 30 4 8 12 Oct ✻✶ Days 1−42 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 16 20 16 20 16 20 16 20 Oct Days 1−56 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 Oct Days 1−70 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 Oct Days 1−84 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 Jun 4 8 12 16 Jul 20 24 28 2 6 10 14 18 Aug 22 26 30 2 6 10 14 18 Sep 22 26 30 4 8 12 Oct ✻✷ ✸✳✷ ❊✈❛❧✉❛t✐♦♥ ♦❢ ♣r❡❞✐❝t✐✈❡ ♣❡r❢♦r♠❛♥❝❡s ❚♦ ❛ss❡ss ❤♦✇ t❤❡ ❧❡♥❣t❤ ♦❢ ❞❛t❛s❡t ❛✛❡❝ts t❤❡ ♣r❡❞✐❝t✐✈❡ ♣❡r❢♦r♠❛♥❝❡s ♦❢ t❤❡ ♠♦❞❡❧s✱ ✇❡ ❝❛❧❝✉❧❛t❡ t❤❡ ❢♦❧❧♦✇✐♥❣ ✈❛❧✉❡s ❢♦r ❡❛❝❤ ♦❢ t❤❡ ♣r❡❞✐❝t✐♦♥s ✉s✐♥❣ t❤❡ ❡✐❣❤t ❞❛t❛ s✉❜s❡ts ♠❡♥t✐♦♥❡❞ ✐♥ t❤❡ ♣r❡✈✐♦✉s s❡❝t✐♦♥ ❢♦r ❛❧❧ t❤r❡❡ ♠♦❞❡❧s t♦ t♦ ❝♦♠♣❛r❡ t❤❡ ❢♦r❡❝❛sts ✇✐t❤ t❤❡ ❛❝t✉❛❧ ♦❜s❡r✈❛t✐♦♥s✿ ▼❡❛♥ ❡rr♦r ✭▼❊✮ = 1 n−ts +1 n i=ts yˆi − yi ▼❡❛♥ ❛❜s♦❧✉t❡ ❡rr♦r ✭▼❆❊✮ = 1 n−ts +1 n i=ts |yˆi − yi | ▼❡❛♥ sq✉❛r❡❞ ❡rr♦r ✭▼❙❊✮ = 1 n−ts +1 n ˆi i=ts (y P❡r❝❡♥t❛❣❡ ❡rr♦r ✭P❊✮ = 1 n−ts +1 n i=ts ✇❤❡r❡ yˆ − yi )2 100 × yi −yˆi yi ✐s t❤❡ ♣r❡❞✐❝t❡❞ ❛✈❡r❛❣❡ ♥✉♠❜❡r ♦❢ ■▲■s ♣❡r ●P r❡t✉r♥❡❞ ❜② ♦✉r ❛❧❣♦r✐t❤♠s✱ y ✐s t❤❡ ♦❜s❡r✈❡❞ ❛✈❡r❛❣❡ ♥✉♠❜❡r ♦❢ ■▲■s ♣❡r ●P✱ ❛♥❞ t❤❡ ❞❛② ♦♥ ✇❤✐❝❤ ✇❡ ❤❛✈❡ ♦✉r ❧❛st ❛✈❛✐❧❛❜❧❡ ♦❜s❡r✈❡❞ ❞❛t❛ n = 92 ✐s y✳ ❚❤❡ ▼❊ ❛♥❞ P❊ ❛r❡ s✐❣♥❡❞ ♠❡❛s✉r❡s ♦❢ ❡rr♦r ✇❤✐❝❤ ✐♥❞✐❝❛t❡ ✇❤❡t❤❡r t❤❡ ❢♦r❡❝❛sts ❛r❡ ❜✐❛s❡❞✱ s♣❡❝✐✜❝❛❧❧②✱ ✇❤❡t❤❡r t❤❡② ❛r❡ ❞✐s♣r♦♣♦rt✐♦♥❛t❡❧② ♣♦s✐t✐✈❡ ♦r ♥❡❣❛t✐✈❡✳ ❈♦♥✈❡rs❡❧②✱ t❤❡ ▼❆❊ ❛♥❞ ▼❙❊ ❞✐sr❡❣❛r❞ t❤❡ ❞✐r❡❝t✐♦♥ ♦❢ t❤❡ ❜✐❛s✱ t❤❡② ♠❡❛s✉r❡ t❤❡ ❛✈❡r❛❣❡ ♠❛❣♥✐t✉❞❡ ♦❢ ❢✉♥❝t✐♦♥s t❤❡ ❡rr♦rs ✐♥ t❤❡ ❢♦r❡❝❛sts✳ ❚❤❡ ▼❙❊ ❞❡t❡r♠✐♥❡s t❤❡ q✉❛❧✐t② ♦❢ ❢♦r❡❝❛sts ❜❛s❡❞ ♦♥ t❤❡✐r ✈❛r✐❛♥❝❡ ❛♥❞ ❜✐❛s✳ ❚❤❡ ♦✉t♣✉t ✐s ♣❧♦tt❡❞ ✐♥ ❋✐❣✉r❡ ✸✳✶✶ ❜❡❧♦✇✱ ✇✐t❤ ♣r❡❞✐❝t✐✈❡ ♣❡r❢♦r♠❛♥❝❡s ❢♦r ❘✐❝❤❛r❞s ♠♦❞❡❧✱ ❞❡t❡r♠✐♥✐st✐❝ ❙■❘ ♠♦❞❡❧ ❛♥❞ st♦❝❤❛st✐❝ ❙■❘ ♠♦❞❡❧ ✐♥❞✐✲ ❝❛t❡❞ ✐♥ ❜❧✉❡✱ r❡❞ ❛♥❞ ♠❛❣❡♥t❛✳ ❚❤❡ ✈❛❧✉❡s ❛r❡ ❝❛❧❝✉❧❛t❡❞ ❜② ❡①❝❧✉❞✐♥❣ t❤❡ ✻✸ ♣❡r✐♦❞ ✉s❡❞ t♦ ♠❛❦❡ t❤❡ ♣r❡❞✐❝t✐♦♥s✱ t❤❡r❡❢♦r❡ ❝❛❧❝✉❧❛t✐♦♥s st❛rts ❢r♦♠ t✐♠❡ ts ✱ ✇❤❡r❡ ts = 15, 22, 29, 36, 43, 57, 71, ❛♥❞ 85 ❢♦r ♣r❡❞✐❝t✐♦♥ ❜② ✉s✐♥❣ ❞❛t❛ ❢r♦♠ ❞❛②s ✶✕✶✹✱ ❞❛②s ✶✕✷✶✱ ❞❛②s ✶✕✷✽✱ ❞❛②s ✶✕✸✺✱ ❞❛②s ✶✕✹✷✱ ❞❛②s ✶✕✺✻✱ ❞❛②s ✶✕✼✵ ❛♥❞ ❞❛②s ✶✕✽✹ r❡s♣❡❝t✐✈❡❧②✳ ❋✐❣✉r❡ ✸✳✶✶✿ Pr❡❞✐❝t✐✈❡ ♣❡r❢♦r♠❛♥❝❡s ❢♦r ❘✐❝❤❛r❞s ♠♦❞❡❧✱ ❞❡t❡r♠✐♥✐st✐❝ ❙■❘ ♠♦❞❡❧ ❛♥❞ st♦❝❤❛st✐❝ ❙■❘ ♠♦❞❡❧ 30 ME 20 10 0 ● ● ● ● ● ● ● ● −10 ● −20 −30 1−14 1−21 1−28 1−35 1−56 1−70 ● ● ● 1−84 ● MAE 20 15 1−42 Richards Det. SIR Stoc. SIR Richards Det. SIR Stoc. SIR ● ● 10 ● ● 5 ● 0 1−14 1−21 1−28 1−35 2500 1−42 1−56 1−70 ● MSE 2000 1−84 Richards Det. SIR Stoc. SIR 1500 1000 500 ● ● ● ● ● 0 1−14 1−21 1−28 1−35 1−42 ● ● ● 1−56 1−70 1−84 PE 50 ● ● ● ● ● ● 0 ● ● ● −50 1−14 1−21 1−28 1−35 1−42 1−56 1−70 Richards Det. SIR Stoc. SIR 1−84 ✻✹ ✸✳✸ ❊✛❡❝ts ♦❢ ♣r✐♦r ❲❡ ❡①❛♠✐♥❡ t❤❡ ❡✛❡❝ts ♦❢ ♣r✐♦r ✐♥ t❤✐s s❡❝t✐♦♥✱ ❜② ❝♦♠♣❛r✐♥❣ t❤❡ ♦✉t♣✉t ♦❜t❛✐♥❡❞ ✉s✐♥❣ ✐♥❢♦r♠❛t✐✈❡ ❛♥❞ ♥♦♥✲✐♥❢♦r♠❛t✐✈❡ ♣r✐♦rs r❡s♣❡❝t✐✈❡❧②✳ ❆❧❧ ♦✉r ♦✉t♣✉t ✐♥ t❤❡ ♣r❡✈✐♦✉s s❡❝t✐♦♥ ✐s ❣❡♥❡r❛t❡❞ ✉s✐♥❣ ✐♥❢♦r♠❛t✐✈❡ ♣r✐♦r✱ ❛s ❧✐st❡❞ ✐♥ t❤❡ ✜rst ❝♦❧✉♠♥ ♦❢ ❚❛❜❧❡ ✸✳✶✳ ❲❡ ❣❡♥❡r❛t❡❞ ♦✉t♣✉t ❜❛s❡❞ ♦♥ ♥♦♥✲✐♥❢♦r♠❛t✐✈❡ ♣r✐♦r s❤♦✇♥ ✐♥ t❤❡ s❡❝♦♥❞ ❝♦❧✉♠♥ ♦❢ ❚❛❜❧❡ ✸✳✶ ❢♦r ❘✐❝❤❛r❞s ♠♦❞❡❧ ✭❋✐❣✉r❡ ✸✳✶✷✮✱ ❞❡t❡r♠✐♥✐st✐❝ ❙■❘ ♠♦❞❡❧ ✭❋✐❣✉r❡ ✸✳✶✸✮ ❛♥❞ st♦❝❤❛st✐❝ ❙■❘ ♠♦❞❡❧ ✭❋✐❣✲ ✉r❡ ✸✳✶✹✮✳ ✻✺ ❚❛❜❧❡ ✸✳✶✿ ■♥❢♦r♠❛t✐✈❡ ❛♥❞ ♥♦♥✲✐♥❢♦r♠❛t✐✈❡ ♣r✐♦rs ❢♦r ❡❛❝❤ ❢♦r ❘✐❝❤❛r❞s ♠♦❞❡❧✱ ❞❡t❡r♠✐♥✐st✐❝ ❙■❘ ♠♦❞❡❧ ❛♥❞ st♦❝❤❛st✐❝ ❙■❘ ♠♦❞❡❧✳ ■♥❢♦r♠❛t✐✈❡ ♣r✐♦r ❘✐❝❤❛r❞s ♠♦❞❡❧ ❉❡t❡r♠✐♥✐st✐❝ ❙■❘ ♠♦❞❡❧ ❙t♦❝❤❛st✐❝ ❙■❘ ♠♦❞❡❧ K ∼ ◆✭200, 100✮ r ∼ ◆✭0.06, 0.002✮ tm ∼ ❊①♣✭1/8✮ a ∼ ◆✭5.5, 1✮ δsph ∼ ❯❬0, 0.8❪ β ∼ ◆✭1.1, 3✮ γ ∼ ◆✭0.9, 3✮ δwds ∼ ◆✭0.2, 0.5✮ δsph ∼ ◆✭0.5, 0.5✮ φ ∼ ◆✭0.8, 0.2✮ S0 ∼ ◆✭4790000, 2000✮ R0 ∼ ◆(10000, 200) β ∼ ◆✭1, 1✮ γ ∼ ◆✭2, 0.5✮ δwds ∼ ◆✭0.4, 0.2✮ δsph ∼ ◆✭0.5, 0.1✮ φ ∼ ◆✭0.5, 0.25✮ S0 ∼ ◆✭4560000, 2500✮ R0 ∼ ◆(24000, 1200) ◆♦♥✲✐♥❢♦r♠❛t✐✈❡ ♣r✐♦r β γ δwds δsph φ S0 R0 β γ δwds δsph φ S0 R0 K r tm a δsph ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ❯❬0, 10000❪ ∼ ❯❬0, 15❪ ∼ ❯❬0, 90❪ ∼ ❯❬0, 15❪ ∼ ❯❬0, 1❪ ❯❬0, 100❪ ❯❬0, 100❪ ❯❬0, 1❪ ❯❬0, 1❪ ❯❬0, 50❪ ❯❬3000000, 4800000❪ ❯❬0, 100000❪ ❯❬0, 100❪ ❯❬0, 100❪ ❯❬0, 1❪ ❯❬0, 1❪ ❯❬0, 50❪ ❯[3000000, 4800000] ❯❬0, 100000❪ ✻✻ ❋✐❣✉r❡ ✸✳✶✷✿ Pr❡❞✐❝t✐✈❡ ♣❡r❢♦r♠❛♥❝❡s ❢♦r ❘✐❝❤❛r❞s ♠♦❞❡❧ ✐♥❢♦r♠❛t✐✈❡ ♣r✐♦rs s❤♦✇♥ ✇✐t❤ ✾✺✪ ❝r❡❞✐❜❧❡ ✐♥t❡r✈❛❧ ✭r❡❞✮✳ ✉s✐♥❣ ♥♦♥✲ ❇❧❛❝❦ ❧✐♥❡ ✐♥✲ ❞✐❝❛t❡s ♦❜s❡r✈❡❞ ❞❛t❛✳ 5 Avr ILIs per GP 4 3 2 1 0 26 Jun 2 6 12 18 Jul 24 30 4 8 14 20 Aug 26 2 6 12 18 Sep 24 30 6 12 Oct 18 ✻✼ ❋✐❣✉r❡ ✸✳✶✸✿ Pr❡❞✐❝t✐✈❡ ♣❡r❢♦r♠❛♥❝❡s ❢♦r ❞❡t❡r♠✐♥✐st✐❝ ❙■❘ ♠♦❞❡❧ ♥♦♥✲✐♥❢♦r♠❛t✐✈❡ ♣r✐♦rs s❤♦✇♥ ✇✐t❤ ✾✺✪ ❝r❡❞✐❜❧❡ ✐♥t❡r✈❛❧ ✭r❡❞✮✳ ❇❧❛❝❦ ❧✐♥❡ ✐♥❞✐❝❛t❡s ♦❜s❡r✈❡❞ ❞❛t❛✳ 5 Avr ILIs per GP 4 3 2 1 0 26 Jun 2 6 12 18 Jul 24 30 4 8 14 20 Aug 26 2 6 12 18 Sep 24 30 6 ✉s✐♥❣ 12 Oct 18 ✻✽ ❋✐❣✉r❡ ✸✳✶✹✿ Pr❡❞✐❝t✐✈❡ ♣❡r❢♦r♠❛♥❝❡s ❢♦r st♦❝❤❛st✐❝ ❙■❘ ♠♦❞❡❧ ✉s✐♥❣ ♥♦♥✲ ✐♥❢♦r♠❛t✐✈❡ ♣r✐♦rs s❤♦✇♥ ✇✐t❤ ✾✺✪ ❝r❡❞✐❜❧❡ ✐♥t❡r✈❛❧ ✭r❡❞✮✳ ❇❧❛❝❦ ❧✐♥❡ ✐♥❞✐✲ ❝❛t❡s ♦❜s❡r✈❡❞ ❞❛t❛✳ 5 Avr ILIs per GP 4 3 2 1 0 26 Jun 2 6 12 18 Jul 24 30 4 8 14 20 Aug 26 2 6 12 18 Sep 24 30 6 12 Oct 18 [...]... per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 16 20 16 20 16 20 16 20 Oct Days 1−21 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 Oct Days 1−28 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep... Oct Days 1 35 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 Jun 4 8 12 16 Jul 20 24 28 2 6 10 14 18 Aug 22 26 30 2 6 10 14 18 Sep 22 26 30 4 8 12 Oct ✺✼ Days 1−42 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 16 20 16 20 16 20 16 20 Oct Days 1−56 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10... per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 16 20 16 20 16 20 16 20 Oct Days 1−21 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 Oct Days 1−28 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep... Oct Days 1 35 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 Jun 4 8 12 16 Jul 20 24 28 2 6 10 14 18 Aug 22 26 30 2 6 10 14 18 Sep 22 26 30 4 8 12 Oct ✺✾ Days 1−42 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 16 20 16 20 16 20 16 20 Oct Days 1−56 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10... per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 16 20 16 20 16 20 16 20 Oct Days 1−21 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 Oct Days 1−28 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep... Oct Days 1 35 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 Jun 4 8 12 16 Jul 20 24 28 2 6 10 14 18 Aug 22 26 30 2 6 10 14 18 Sep 22 26 30 4 8 12 Oct ✻✶ Days 1−42 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 16 20 16 20 16 20 16 20 Oct Days 1−56 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10... Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 Oct Days 1−70 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 Oct Days 1−84 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 Jun 4 8 12 16 Jul 20 24 28 2 6 10 14 18 Aug 22 26 30 2 6 10 14 18 Sep 22 26 30 4 8 12 Oct ✺✽ ❋✐❣✉r❡ ✸✳✾✿ Pr❡❞✐❝t✐♦♥s ✉s✐♥❣ ❞❛t❛ s✉❜s❡t ✭❜❧❛❝❦... Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 Oct Days 1−70 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 Oct Days 1−84 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 Jun 4 8 12 16 Jul 20 24 28 2 6 10 14 18 Aug 22 26 30 2 6 10 14 18 Sep 22 26 30 4 8 12 Oct ✻✵ ❋✐❣✉r❡ ✸✳✶✵✿ Pr❡❞✐❝t✐♦♥s ✉s✐♥❣ ❞❛t❛ s✉❜s❡t ✭❜❧❛❝❦... Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 Oct Days 1−70 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 4 8 12 Jun 16 20 24 28 2 6 10 Jul 14 18 22 26 30 2 6 10 Aug 14 18 22 26 30 4 8 Sep 12 Oct Days 1−84 6 Avr ILIs per GP 5 4 3 2 1 0 26 30 Jun 4 8 12 16 Jul 20 24 28 2 6 10 14 18 Aug 22 26 30 2 6 10 14 18 Sep 22 26 30 4 8 12 Oct ✻✷ ✸✳✷ ❊✈❛❧✉❛t✐♦♥ ♦❢ ♣r❡❞✐❝t✐✈❡ ♣❡r❢♦r♠❛♥❝❡s ❚♦ ❛ss❡ss... ❞❛t❛✳ 5 Avr ILIs per GP 4 3 2 1 0 26 Jun 2 6 12 18 Jul 24 30 4 8 14 20 Aug 26 2 6 12 18 Sep 24 30 6 ✉s✐♥❣ 12 Oct 18 ✻✽ ❋✐❣✉r❡ ✸✳✶✹✿ Pr❡❞✐❝t✐✈❡ ♣❡r❢♦r♠❛♥❝❡s ❢♦r st♦❝❤❛st✐❝ ❙■❘ ♠♦❞❡❧ ✉s✐♥❣ ♥♦♥✲ ✐♥❢♦r♠❛t✐✈❡ ♣r✐♦rs s❤♦✇♥ ✇✐t❤ ✾✺✪ ❝r❡❞✐❜❧❡ ✐♥t❡r✈❛❧ ✭r❡❞✮✳ ❇❧❛❝❦ ❧✐♥❡ ✐♥❞✐✲ ❝❛t❡s ♦❜s❡r✈❡❞ ❞❛t❛✳ 5 Avr ILIs per GP 4 3 2 1 0 26 Jun 2 6 12 18 Jul 24 30 4 8 14 20 Aug 26 2 6 12 18 Sep 24 30 6 12 Oct 18 ... 30 10 Aug 14 18 22 26 30 Sep 12 Oct Days 1−28 Avr ILIs per GP 26 30 12 Jun 16 20 24 28 10 Jul 14 18 22 26 30 10 Aug 14 18 22 26 30 Sep 12 Oct Days 1 35 Avr ILIs per GP 26 30 Jun 12 16 Jul 20 24... ILIs per GP 26 30 12 Jun 16 20 24 28 10 Jul 14 18 22 26 30 10 Aug 14 18 22 26 30 Sep 12 Oct Days 1−70 Avr ILIs per GP 26 30 12 Jun 16 20 24 28 10 Jul 14 18 22 26 30 10 Aug 14 18 22 26 30 Sep 12 Oct... 30 10 Aug 14 18 22 26 30 Sep 12 Oct Days 1−28 Avr ILIs per GP 26 30 12 Jun 16 20 24 28 10 Jul 14 18 22 26 30 10 Aug 14 18 22 26 30 Sep 12 Oct Days 1 35 Avr ILIs per GP 26 30 Jun 12 16 Jul 20 24