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

`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. $ `Source input:`

`Source output:`

`Follow-up input:`

`Follow-up output:`

`Input relation:`

`Output relation:`

`Pattern:`

`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. $ `Source input:`

`Source output:`

`Follow-up input:`

`Follow-up output:`

`Input relation:`

`Output relation:`

`Pattern:`

`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. `Source input:`

`Source output:`

`Follow-up input:`

`Follow-up output:`

`Input relation:`

`Output relation:`

`Pattern:`

`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). `Source input:`

`Source output:`

`Follow-up input:`

`Follow-up output:`

`Input relation:`

`Output relation:`

`Pattern:`

`Description:`

`Property:`

$x'=x*n,n<1.0 \Rightarrow$
Decreases the number of people infected, which in turn influences the number of Deceased (decreases) `Source input:`

`Source output:`

`Follow-up input:`

`Follow-up output:`

`Input relation:`

`Output relation:`

`Pattern:`

`Description:`

`Property:`

$x'=x*n,n>1.0 \Rightarrow$
Increases the number of people infected, which in turn influences the number of Deceased (increases) `Source input:`

`Source output:`

`Follow-up input:`

`Follow-up output:`

`Input relation:`

`Output relation:`

`Pattern:`

`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 `Source input:`

`Source output:`

`Follow-up input:`

`Follow-up output:`

`Input relation:`

`Output relation:`

`Pattern:`

`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 `Source input:`

`Source output:`

`Follow-up input:`

`Follow-up output:`

`Input relation:`

`Output relation:`

`Pattern:`

`Description:`

`Property:`

$x'=x*n,n<1.0 \Rightarrow$
Compresses the model timeline, with related changes in other parameters `Source input:`

`Source output:`

`Follow-up input:`

`Follow-up output:`

`Input relation:`

`Output relation:`

`Pattern:`

`Description:`

`Property:`

$x'=x*n,n>1.0 \Rightarrow$
Stretches out model timeline, with related changes in other parameters `Source input:`

`Source output:`

`Follow-up input:`

`Follow-up output:`

`Input relation:`

`Output relation:`

`Pattern:`

`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)`Source input:`

`Source output:`

`Follow-up input:`

`Follow-up output:`

`Input relation:`

`Output relation:`

`Pattern:`

`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)`Source input:`

`Source output:`

`Follow-up input:`

`Follow-up output:`

`Input relation:`

`Output relation:`

`Pattern:`

`Description:`

`Property:`

$x'=x*n,n<1.0 \Rightarrow$
Decreases the number of cases, which in turn influences the rate of Deceased (decreases)`Source input:`

`Source output:`

`Follow-up input:`

`Follow-up output:`

`Input relation:`

`Output relation:`

`Pattern:`

`Description:`

`Property:`

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

`Source output:`

`Follow-up input:`

`Follow-up output:`

`Input relation:`

`Output relation:`

`Pattern:`