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23, 23, 23, 23, 23, 24, 24, 24, 25, 27, 31, 37, 46, 59, 77, 100, 127, 155, 179, 198, 213, 224, 229, 231, 230, 224, 214, 200, 181, 158, 131, 106, 85, 69, 58, 51, 47, 46, 46, 46, 47, 47, 47, 47, 47, 47, 47, 47, 47}};\)\)], "InputOnly", FontSize->6, FontWeight->"Plain", FontVariations->{"CompatibilityType"->0}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Epidemics", "Section"], Cell[CellGroupData[{ Cell["\<\ The Kermack-McKendrick model (Susceptibles \[Rule] Infectives \[Rule] \ Removals)\ \>", "Subsection", CellDingbat->None], Cell[CellGroupData[{ Cell["Code", "Subsubsection"], Cell["Initial conditions", "Text"], Cell[BoxData[{ \(\(L00Suscept\ = Reverse[NorthAmericaPopulationData];\)\), "\[IndentingNewLine]", \(\(L01Infectd\ = \ Table[0, {421}, {681}];\)\), "\[IndentingNewLine]", \(\(L02Removed = \ Table[0, {421}, {681}];\)\), "\[IndentingNewLine]", \(\(L03Picture\ = \ Map[2\ Round[4\ Log[# + 1]] &, L00Suscept, {2}];\)\), "\[IndentingNewLine]", \(\(L04Outbreak\ = \ Table[0, {421}, {681}];\)\), "\[IndentingNewLine]", \(\(L01Infectd[\([210, 340]\)]\ = \ 5;\)\ (*Initial\ location\ for\ outbreak*) \), \ "\[IndentingNewLine]", \(\(L04Outbreak[\([210, 340]\)]\ = \ 1;\)\), "\[IndentingNewLine]", \(\(Airports\ = \ 0;\)\)}], "Input"], Cell[BoxData[ \(\(Show[ApplyColorScheme[L03Picture]];\)\)], "Input"], Cell["\<\ From here on out, it's the same code, repeated. Takes about 2 minutes to \ run.\ \>", "Text"], Cell[BoxData[ \(Do[\[IndentingNewLine]L04Outbreak\ = \ Last[CellularAutomaton[{1022, {2, 1}, {1, 1}}, L04Outbreak, 1]]\ * Sign[L03Picture\ - \ Map[Min, Transpose[{L03Picture, Table[Random[Integer, {0, 200}], {421}, {681}]}, {3, 1, 2}], {2}]]; \[IndentingNewLine]L01Infectd\ = \ Map[Max, Transpose[{L04Outbreak, L01Infectd}, {3, 1, 2}], {2}]; \[IndentingNewLine]L01Infectd\ \ = \ Map[Min, Transpose[{L00Suscept, 3\ L01Infectd}, {3, 1, 2}], {2}]\ + \ L01Infectd; \[IndentingNewLine]L04Outbreak\ = \ Sign[L01Infectd\ + \ If[Airports \[Equal] 1, Map[If[# > 86, If[Random[] < .02, 1, 0], 0]\ &, L03Picture, {2}], 0]]; \[IndentingNewLine]If[ Airports\ \[Equal] \ 0, If[Max[L04Outbreak\ L03Picture] > 86, Airports = 1]]; \[IndentingNewLine]L00Suscept\ = \ Map[Max[#, 0] &, L00Suscept\ - \ L01Infectd, {2}]; \[IndentingNewLine]L03Picture\ = \ \ Map[ If[Last[#] \[Equal] 0, 2\ Round[4\ Log[First[#] + 1]], 2\ Round[4\ Log[Last[#] + 1]] - 1]\ &, Transpose[{L00Suscept, L01Infectd}, {3, 1, 2}], {2}];\[IndentingNewLine], {4}]\)], "Input"], Cell[BoxData[ \(\(Show[ApplyColorScheme[L03Picture]];\)\)], "Input"], Cell[BoxData[ \(Do[\[IndentingNewLine]L04Outbreak\ = \ Last[CellularAutomaton[{1022, {2, 1}, {1, 1}}, L04Outbreak, 1]]\ * Sign[L03Picture\ - \ Map[Min, Transpose[{L03Picture, Table[Random[Integer, {0, 200}], {421}, {681}]}, {3, 1, 2}], {2}]]; \[IndentingNewLine]L01Infectd\ = \ Map[Max, Transpose[{L04Outbreak, L01Infectd}, {3, 1, 2}], {2}]; \[IndentingNewLine]L01Infectd\ \ = \ Map[Min, Transpose[{L00Suscept, 3\ L01Infectd}, {3, 1, 2}], {2}]\ + \ L01Infectd; \[IndentingNewLine]L04Outbreak\ = \ Sign[L01Infectd\ + \ If[Airports \[Equal] 1, Map[If[# > 86, If[Random[] < .02, 1, 0], 0]\ &, L03Picture, {2}], 0]]; \[IndentingNewLine]If[ Airports\ \[Equal] \ 0, If[Max[L04Outbreak\ L03Picture] > 86, Airports = 1]]; \[IndentingNewLine]L00Suscept\ = \ Map[Max[#, 0] &, L00Suscept\ - \ L01Infectd, {2}]; \[IndentingNewLine]L03Picture\ = \ \ Map[ If[Last[#] \[Equal] 0, 2\ Round[4\ Log[First[#] + 1]], 2\ Round[4\ Log[Last[#] + 1]] - 1]\ &, Transpose[{L00Suscept, L01Infectd}, {3, 1, 2}], {2}];\[IndentingNewLine], {4}]\)], "Input"], Cell[BoxData[ \(\(Show[ApplyColorScheme[L03Picture]];\)\)], "Input"], Cell[BoxData[ \(Do[\[IndentingNewLine]L04Outbreak\ = \ Last[CellularAutomaton[{1022, {2, 1}, {1, 1}}, L04Outbreak, 1]]\ * Sign[L03Picture\ - \ Map[Min, Transpose[{L03Picture, Table[Random[Integer, {0, 200}], {421}, {681}]}, {3, 1, 2}], {2}]]; \[IndentingNewLine]L01Infectd\ = \ Map[Max, Transpose[{L04Outbreak, L01Infectd}, {3, 1, 2}], {2}]; \[IndentingNewLine]L01Infectd\ \ = \ Map[Min, Transpose[{L00Suscept, 3\ L01Infectd}, {3, 1, 2}], {2}]\ + \ L01Infectd; \[IndentingNewLine]L04Outbreak\ = \ Sign[L01Infectd\ + \ If[Airports \[Equal] 1, Map[If[# > 86, If[Random[] < .02, 1, 0], 0]\ &, L03Picture, {2}], 0]]; \[IndentingNewLine]If[ Airports\ \[Equal] \ 0, If[Max[L04Outbreak\ L03Picture] > 86, Airports = 1]]; \[IndentingNewLine]L00Suscept\ = \ Map[Max[#, 0] &, L00Suscept\ - \ L01Infectd, {2}]; \[IndentingNewLine]L03Picture\ = \ \ Map[ If[Last[#] \[Equal] 0, 2\ Round[4\ Log[First[#] + 1]], 2\ Round[4\ Log[Last[#] + 1]] - 1]\ &, Transpose[{L00Suscept, L01Infectd}, {3, 1, 2}], {2}];\[IndentingNewLine], {4}]\)], "Input"], Cell[BoxData[ \(\(Show[ApplyColorScheme[L03Picture]];\)\)], "Input"], Cell[BoxData[ \(Do[\[IndentingNewLine]L04Outbreak\ = \ Last[CellularAutomaton[{1022, {2, 1}, {1, 1}}, L04Outbreak, 1]]\ * Sign[L03Picture\ - \ Map[Min, Transpose[{L03Picture, Table[Random[Integer, {0, 200}], {421}, {681}]}, {3, 1, 2}], {2}]]; \[IndentingNewLine]L01Infectd\ = \ Map[Max, Transpose[{L04Outbreak, L01Infectd}, {3, 1, 2}], {2}]; \[IndentingNewLine]L01Infectd\ \ = \ Map[Min, Transpose[{L00Suscept, 3\ L01Infectd}, {3, 1, 2}], {2}]\ + \ L01Infectd; \[IndentingNewLine]L04Outbreak\ = \ Sign[L01Infectd\ + \ If[Airports \[Equal] 1, Map[If[# > 86, If[Random[] < .02, 1, 0], 0]\ &, L03Picture, {2}], 0]]; \[IndentingNewLine]If[ Airports\ \[Equal] \ 0, If[Max[L04Outbreak\ L03Picture] > 86, Airports = 1]]; \[IndentingNewLine]L00Suscept\ = \ Map[Max[#, 0] &, L00Suscept\ - \ L01Infectd, {2}]; \[IndentingNewLine]L03Picture\ = \ \ Map[ If[Last[#] \[Equal] 0, 2\ Round[4\ Log[First[#] + 1]], 2\ Round[4\ Log[Last[#] + 1]] - 1]\ &, Transpose[{L00Suscept, L01Infectd}, {3, 1, 2}], {2}];\[IndentingNewLine], {4}]\)], "Input"], Cell[BoxData[ \(\(Show[ApplyColorScheme[L03Picture]];\)\)], "Input"], Cell[BoxData[ \(Do[\[IndentingNewLine]L04Outbreak\ = \ Last[CellularAutomaton[{1022, {2, 1}, {1, 1}}, L04Outbreak, 1]]\ * Sign[L03Picture\ - \ Map[Min, Transpose[{L03Picture, Table[Random[Integer, {0, 200}], {421}, {681}]}, {3, 1, 2}], {2}]]; \[IndentingNewLine]L01Infectd\ = \ Map[Max, Transpose[{L04Outbreak, L01Infectd}, {3, 1, 2}], {2}]; \[IndentingNewLine]L01Infectd\ \ = \ Map[Min, Transpose[{L00Suscept, 3\ L01Infectd}, {3, 1, 2}], {2}]\ + \ L01Infectd; \[IndentingNewLine]L04Outbreak\ = \ Sign[L01Infectd\ + \ If[Airports \[Equal] 1, Map[If[# > 86, If[Random[] < .02, 1, 0], 0]\ &, L03Picture, {2}], 0]]; \[IndentingNewLine]If[ Airports\ \[Equal] \ 0, If[Max[L04Outbreak\ L03Picture] > 86, Airports = 1]]; \[IndentingNewLine]L00Suscept\ = \ Map[Max[#, 0] &, L00Suscept\ - \ L01Infectd, {2}]; \[IndentingNewLine]L03Picture\ = \ \ Map[ If[Last[#] \[Equal] 0, 2\ Round[4\ Log[First[#] + 1]], 2\ Round[4\ Log[Last[#] + 1]] - 1]\ &, Transpose[{L00Suscept, L01Infectd}, {3, 1, 2}], {2}];\[IndentingNewLine], {4}]\)], "Input"], Cell[BoxData[ \(\(Show[ApplyColorScheme[L03Picture]];\)\)], "Input"], Cell[BoxData[ \(Do[\[IndentingNewLine]L04Outbreak\ = \ Last[CellularAutomaton[{1022, {2, 1}, {1, 1}}, L04Outbreak, 1]]\ * Sign[L03Picture\ - \ Map[Min, Transpose[{L03Picture, Table[Random[Integer, {0, 200}], {421}, {681}]}, {3, 1, 2}], {2}]]; \[IndentingNewLine]L01Infectd\ = \ Map[Max, Transpose[{L04Outbreak, L01Infectd}, {3, 1, 2}], {2}]; \[IndentingNewLine]L01Infectd\ \ = \ Map[Min, Transpose[{L00Suscept, 3\ L01Infectd}, {3, 1, 2}], {2}]\ + \ L01Infectd; \[IndentingNewLine]L04Outbreak\ = \ Sign[L01Infectd\ + \ If[Airports \[Equal] 1, Map[If[# > 86, If[Random[] < .02, 1, 0], 0]\ &, L03Picture, {2}], 0]]; \[IndentingNewLine]If[ Airports\ \[Equal] \ 0, If[Max[L04Outbreak\ L03Picture] > 86, Airports = 1]]; \[IndentingNewLine]L00Suscept\ = \ Map[Max[#, 0] &, L00Suscept\ - \ L01Infectd, {2}]; \[IndentingNewLine]L03Picture\ = \ \ Map[ If[Last[#] \[Equal] 0, 2\ Round[4\ Log[First[#] + 1]], 2\ Round[4\ Log[Last[#] + 1]] - 1]\ &, Transpose[{L00Suscept, L01Infectd}, {3, 1, 2}], {2}];\[IndentingNewLine], {4}]\)], "Input"], Cell[BoxData[ \(\(Show[ApplyColorScheme[L03Picture]];\)\)], "Input"] }, Open ]] }, Open ]] }, Open ]] }, Open ]] }, FrontEndVersion->"5.0 for Microsoft Windows", ScreenRectangle->{{0, 1280}, {0, 979}}, WindowSize->{1004, 716}, WindowMargins->{{134, Automatic}, {Automatic, 12}} ] (******************************************************************* Cached data follows. 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