Epidemiological Models

### Program Information

Name: Epidemiological Models
Domain: Algorithm
Functionality: Models are used to study the potential behavior and impact of disease spread in populations.
Input: The base values of the model parameters are those values that enable the original ODE and ABM models to mimic the 1918 flu pandemic.($x$=Parameter) $\textbf{P(Mortality)=0.01}$ Probability of death given a person has contacted the disease.   $\textbf{T(Recovery) = 2.5 days}$ Time to recover from the disease given that the infected person will not die.  $\textbf{T(Die) = 1 day}$ Time to die from the disease given that the person with the disease will die.    $\textbf{P(Transmission) = 0.15}$ Probability of transmitting the disease to another person upon contact with that person.    $\textbf{Rate(Encounter) = 4 people per day}$ Number of persons encountered by an individual in a day. $\textbf{T(Incubate) = 3 days}$ Time for the disease to incubate.  $\textbf{N(Infectious) = 1,000}$ Number of individuals initially infectious.
Output: The result of the changed ODE and ABM models.

#### Reference

 Early Results from Metamorphic Testing of Epidemiological Modelshttps://doi.org/10.1109/BioMedCom.2012.17

### MR Information

#### MR1------ P(Mortality)

Description:
Property: $x'=x*n,n<1.0 \Rightarrow$ $\left\{ \begin{array}{l} \textrm{Decreases the number of Deceased by less than *n} \\ \textrm{Decreases the number of Recovered by more than 1/n} \end{array}\right.$
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#### MR2------ P(Mortality)

Description:
Property: $x'=x*n,n>1.0 \Rightarrow$ $\left\{ \begin{array}{l} \textrm{Increases the number of Deceased by less than *n} \\ \textrm{Increases the number of Recovered by more than 1/n} \end{array}\right.$
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#### MR3------ N(Infectious)

Description:
Property: $x'=x*n,n<1.0 \Rightarrow$ In ODE, this transformation stretches out the start time; in the agent model, the start time is moved to the right.
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#### MR4------ N(Infectious)

Description:
Property: $x'=x*n,n>1.0 \Rightarrow$ In both models, this transformation compresses the epidemic spread time (the epidemic will spread faster, more quickly).
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#### MR5------ T(Die)

Description:
Property: $x'=x*n,n<1.0 \Rightarrow$ Decreases the number of people infected, which in turn influences the number of Deceased (decreases)
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#### MR6------ T(Die)

Description:
Property: $x'=x*n,n>1.0 \Rightarrow$ Increases the number of people infected, which in turn influences the number of Deceased (increases)
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#### MR7------  P(Transmission)

Description:
Property:  $x'=x*n,n<1.0 \Rightarrow$ Decreases the number of people infected, which in turn decreases the numbers of Deceased and Recovered
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#### MR8------  P(Transmission)

Description:
Property: $x'=x*n,n>1.0 \Rightarrow$ Increases the number of people infected, which in turn increases the numbers of Deceased and Recovered
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#### MR9------  T(Incubate)

Description:
Property: $x'=x*n,n<1.0 \Rightarrow$ Compresses the model timeline, with related changes in other parameters
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#### MR10------ T(Incubate)

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Property: $x'=x*n,n>1.0 \Rightarrow$ Stretches out model timeline, with related changes in other parameters
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#### MR11------T(Recovery)

Description:
Property: $x'=x*n,n<1.0 \Rightarrow$ Decreases the number of infectious (the number of cases), which in turn influences the rate of Deceased (decreases)
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#### MR12------T(Recovery)

Description:
Property: $x'=x*n,n>1.0 \Rightarrow$ Increases the number of infectious (the number of cases), which in turn influences the rate of Deceased (increases)
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#### MR13------Rate(Encounter)

Description:
Property: $x'=x*n,n<1.0 \Rightarrow$ Decreases the number of cases, which in turn influences the rate of Deceased (decreases)
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#### MR14------Rate(Encounter)

Description:
Property: $x'=x*n,n>1.0 \Rightarrow$ Increases the number of cases, which in turn influences the rate of Deceased (increases)
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