Curso de dinámica de sistemas

7/24/2019 Curso de dinmica de sistemas

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SIR and SIRS ModelsCindy Wu, Hyesu Kim, Michelle Zajac, Amanda Clemm

SPWM 2011


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Cindy Wu Gonzaga

ni!e"si#y

$"% &u"'e

Our group!

Hyesu Kim Manha##an

College $"% (yle"

MichelleZajac

Al)"edni!e"si#y

$"% Pe#"illo

AmandaClemm

Sc"i**sCollege $"% +u


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Cindy Wu

Why Ma#h -"iends

Cooles# #hing you

lea"ned .um/e"(heo"y

Why SPWM $CS*o'ane +#he"ise,

un*"oduc#i!e


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Why ma#h Common language

Challenging

Cooles# #hing youlea"ned Ma#h is e!e"yhe"e

Any#hing is *ossi/le

Why SPWM Wo"' o" g"ad school

Possi/le ca"ee"s

Hyesu Kim


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Why ma#h n#e"es#ing

Challenging

Cooles# (hing you3ea"ned 4SA C"y*#osys#em

Why SPWM

G"ad school 3ea"n some#hing ne

Michelle Zajac


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Why Ma#h A**lica#ions

Challenge

Cooles# (hing you3ea"ned n5ni#ude o) #he

*"imes

Why SPWM 3i)e a)#e" college

$C

Amanda Clemm


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S#udy o) disease occu""ence Ac#ual e6*e"imen#s !s Models P"e!en#ion and con#"ol *"ocedu"es

Epidemiology


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Epidemic7 nusually la"ge, shor ermou#/"ea' o) a disease

Endemic7 (he disease persiss

ial "ynamics7 &i"#hs and na#u"al dea#hsaccoun#ed )o"

8i#al $ynamics *lay a /igge" *a"# in anendemic

Epidemic #s Endemic


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(o#al *o*ula#ion9. : a cons#an#; Po*ula#ion )"ac#ions

S:#;9susce*#i/le *o*% )"ac#ion

:#;9in)ec#ed *o*% )"ac#ion

4:#;9"emo!ed *o*% )"ac#ion

$opulaions


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&o#h a"e e*idemiological models #ha#com*u#e #he num/e" o) *eo*le in)ec#edi#h a con#agious illness in a *o*ula#iono!e" #ime

S47 (hose in)ec#ed #ha# "eco!e" gainpermanent immuni#y :+$


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$AR% O&E' SIR Models usingO"ES


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Model )o" in)ec#ion #ha#con)e"s *e"manen#immuni#y

Com*a"#men#al diag"am

:.S:#;;9B=S. :.:#;;9 =S.B >. :.4:#;;9 >.

%he SIR Model *ihou ial"ynamics

&SSuscepi(les

&IIn)eci#es

&RRemo#eds

+S&I ,&I

S-./01+SII-./0+SI1,I


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S-./01+SI I-./0+SI1,I 3e# S:#; and :#; /e solu#ions o) #his sys#em% CAS< +.


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MA%4A5 Epidemic


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$AR% %WO' SIRS Models using""ES


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dS3d06781S./91:I./S./;r< < e16=

I.1=/ dI3d0:I./S./1.6;


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-ocus on #he endemic s#eady s#a#e :R?S08;

4e*"oduc#i!e num/e"7

R?0:3.6;


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d3d01y1B.a;(y/;ry.1=/ dy3d0.8;y/

he"e 9:IJ;@>21

and r0.e16=

ruaions


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r0.e16= r


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+;Ba+;81re1+=0?

.o#e7 When "90, #he delay #e"m is "emo!edlea!ing a scaled S4 model such #ha# #heendemic s#eady s#a#e is s#a/le )o" 401

Characerisic E>uaion


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When does he Hop) (i)urcaionoccurD


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In erms o) he original#aria(les


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r0?F??G


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r0?F??G .Zoomed in/


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r0?F?


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r0?F? .Zoomed in/


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r0?F?


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r0?F? .Zoomed in/


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r0?F


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n ou" +$< e "e*"esen#ed an e*idemic $$< case mo"e accu"a#ely "e*"esen#s

longe" #e"m *o*ula#ion /eha!io" Changing #he delay and "esusce*#i/le !alue

changes #he models /eha!io" &e##e" *"e!en#ion and con#"ol s#"a#egies

Conclusion

Curso de dinámica de sistemas

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