Appendix A — Dictionary
Ad hoc: (literally Latin for “for this”) means built for a particular purpose, usually quickly and temporarily, generally signifies a solution designed for a specific problem or task, non-generalizable, and not intended to be able to be adapted to other purposes, source.
Definition A.1 Case fatality rate (CFR): the number of deaths divided by the number of confirmed cases (Meyerowitz-Katz & Merone, 2020).
Definition A.2 Infection fatality rate (IFR): the number of deaths divided by the number of infected individuals (Meyerowitz-Katz & Merone, 2020).
Definition A.3 Forecast: predictions about what will happen, helpful for situation awareness.
Definition A.4 Projection: estimates about what could happen, considering multiple possible outcomes, helpful for intervention planning when faced with uncertainty.
Definition A.5 Epidemic is “the occurrence of more cases of disease than expected in a given area or among a specific group of people over a particular period of time” (US-CDC) (Texier et al., 2016). Epidemic is derived from the Greek epi and demos meaning “that which is upon the people”, to describe the burden of some phenomenon on “the people” (Nelson & Williams, 2014).
Definition A.6 Tractable: can be solved (source)
Definition A.7 Microsimulation: an analysis in which individual instantiations of a system - such as a patient’s lifetime or the course of an epidemic - are generated using a random process to ‘draw’ from probability distributions a large number of times, in order to examine the central tendency and possibly the distribution of outcomes (Kim & Goldie, 2008).
Definition A.8 iid (independent and identically distributed random variables): each random variable has the same probability distribution as the others and all are mutually independent.
Definition A.9 Closed-form solution (or closed form expression) is any formula that can be evaluated in a finite number of standard operations (source).
infection fatality ratio (IFR) and case fatality ratio (CFR) and serology data.
Definition A.10 Residual: is the difference between the observed value and the estimated value.
Definition A.11 Error: is the deviation of the observed value from the true value.
Matrix and linear transformation:
- Linear transformation is a function (transformation = function) that take in a vector and spit out a vector.
- Lines remain lines, and origin remains fixed.
Eigenvector (\(\vec{v}\)):
Eigenvalue (\(\lambda\)):
Definition A.12 Inverse matrix:
\[\begin{bmatrix} a & b \\ c & d \end{bmatrix}^{-1} = \frac{1}{ad - bc} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix}\]
Definition A.13 Monte Carlo methods or Monte Carlo experiments: using repeated random sampling simulation to obtain numerical results.
Transpose: flips a matrix/vector such that row become column and column become row. Notation: \(A^\intercal\)
\[\begin{align} A &= \begin{bmatrix} a & b & c \\ d & e & f \end{bmatrix} \\ A^\intercal &= \begin{bmatrix} a & d \\ b & e \\ c & f \end{bmatrix} \end{align}\]
\[\begin{align} A &= \begin{bmatrix} a & b & c \end{bmatrix} \\ A^\intercal &= \begin{bmatrix} a \\ b \\ c \end{bmatrix} \end{align}\]
Tensor: an object with > 1 dimension
Matrix: an object with 2 dimensions
A probability is between 0 and 1 and is the chance (or risk) that an event (death, infection, etc…) happens. In general this probability is defined over a period of time and will necessarily increase as the duration of this period of time increases.
Definition A.14 A rate is the number of new events that occur during specified time period (Selvin, 2004). It is thus always positive (because both the number of events and time period are positive) and always expressed per unit of time (like speed km/h or m/s). Rate can be > 1. Mathematically, it is the limit of the above-mentioned probability when the duration of the period of time tends towards zero (i.e. very small, i.e. instantaneous measure).
A proportion is the ratio of a numerator and a denominator and by definition is between 0 and 1.
What is the difference between proportion and probability? Consider this example:
A bag is filled with 100 balls, of which 30 are blue and 70 are green. Without looking, you pull out a ball, write down the color, then put it back to the bag. You repeat the action 10,000 times. The number of times you pulled out a blue ball is 3011.
- The proportion of blue balls in the bag is 30/100 = 0.3
- A Frequentist say: The probability of pulling out a blue ball is 3011/10,000 = 0.3011 because you did experiment in long-run (10,000 times).
- A Bayesian say: The probability of pulling out a blue ball is 0.3 because you know that you have a proportion of 0.3 blue balls in the bag.
Definition A.15 Hazard: is the probability an event occurs at time \(t\), conditionally on being at risk.
\[h(t) = \mathbb{P}(T = t|Survive = 1)\]
In infectious disease modelling, hazard is the force of infection (Hay et al., 2024).
Definition A.16 Cumulative incidence or cumulative distribution function: is the probability an event occurs at anytime before time \(t\).
\[I(t) = \mathbb{P}(T \leq t)\]