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ParametersDescription
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SProportion of susceptible individualsFunction of time 
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IProportion of infective individualsFunction of time  
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RProportion of removed (recovered or deceased) individuals Function of time
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transTransmission rateAssume constant. Transmission rate (is the average number of contacts per person per time, multiplied by the probability of disease transmission in a contact between a susceptible and an infectious subject)
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remove Removal rateEither dead or recovered. Recovery rate (If an individual is infectious for an average time period D, then γ = 1/D.)
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tTime (days)
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dtSmall change in time (1 day)
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S’Rate of change of S (per day)S′(t,S,I,R)= -trans∗S∗I
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I’Rate of change of I (per day)I′(t,S,I,R)=trans∗S∗I- remove∗I
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R’Rate of change of R (per day)R′(t,S,I,R)=remove∗I
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R_0Basic reproduction number (the number of new cases from a single infectious individual in entirely susceptible population).R_0 = transmissibility of pathogen x contact rate of hosts x duration of infection.
R_0 > 1: successful outbreak,
R_0 = 1 :endemic,
R_0<1 :outbreak will die out
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Assumptions
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•Total population remains constant
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•Each individual has an equal likelihood of infection
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•Recovered individuals will not get re-infected
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•When a susceptible and an infectious individual come into "infectious contact", the susceptible individual contracts the disease and transitions to the infectious compartment.
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•Constant rate of transmission (proportional to number of contacts)
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•Constant rate of removal
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equations/models
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1) S'(t,S,I,R)=ds/dt= -trans*S*I
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2) I'(t,S,I,R)=trans*S*I- remove*I
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3) R'(t,S,I,R)=remove*I
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References
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https://www.youtube.com/watch?v=TdFmy-MeJ4s
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https://www.youtube.com/watch?v=1nKQ-EiJKfE
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https://youtu.be/k6nLfCbAzgo
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https://youtu.be/NKMHhm2Zbkw
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