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Update About.mdx
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Edits for clarification on lines 29, 68, and 105-107
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samanthahamilton committed Jul 27, 2020
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The model works as follows:
* Susceptible individuals are exposed/infected through contact with infectious individuals. Each infectious individual causes on average $R_0$ secondary infections while they are infectious.
- Transmissibility of the virus could have seasonal variation which is parameterized with the parameter "seasonal forcing" (amplitude) and "peak month" (month of most efficient transmission).
* Exposed individuals progress to a symptomatic/infectious state after an average latency. This progression happens in three stages to ensure the distribution of times spent in the exposed compartment is more realistic than a simple exponential model.
* Exposed individuals progress to a symptomatic/infectious state after a latency period. This progression happens in three stages to ensure the distribution of times spent in the exposed compartment is more realistic than a simple exponential model.
* Infectious individuals recover or progress to severe disease. The ratio of recovery to severe progression depends on age.
* Severely sick individuals either recover or deteriorate and turn critical. Again, this depends on the age.
* Critically ill individuals either get admitted to ICU (if space is available) or are placed in an overflow compartment. Younger age-groups are given preferential access to ICU.
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## Transmission reduction

The tool allows one to explore temporal variation in the reduction of transmission by infection control measures.
This is implemented as a curve through time that can be dragged by the mouse to modify the assumed transmission. The curve is read out and used to change the transmission relative to the base line parameters for $R_0$ and seasonality.
The tool allows one to explore temporal variation in the reduction of transmission by infection control measures.
Control measures can be specified as time intervals with start and end dates, during which transmission is reduced by a certain amount.

Several studies attempt to estimate the effect of different aspects of social distancing and infection control on the rate of transmission.
A report by [Wang et al.](https://www.medrxiv.org/content/10.1101/2020.03.03.20030593v1) estimates a step-wise reduction of $R_0$ from above 3 to around 1 and then to around 0.3 due to successive measures implemented in Wuhan.
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</div>

The parameters of this model fall into three categories: (1) A time dependent infection rate $\beta(t)$ time scales of transition to a different subpopulation $t_l$, $t_i$, $t_h$, $t_c$, and age specific parameters $m_a$, $c_a$ and $f_a$ that determine relative rates of different outcomes;
(2) The latency time from infection to infectiousness is $t_l$, the time an individual is infectious after which he/she either recovers or falls severely ill is $t_i$, the time a sick person recovers or deteriorates into a critical state is $t_h$, and the time a person remains critical before dying or stabilizing is $t_c$;
(3) The fraction of infectious that are asymptomatic or mild is $m_a$, the fraction of severe cases that turn critical is $c_a$, and the fraction of critical cases that are fatal is $f_a$.
The parameters of this model fall into three categories, which determine the relative rates of different outcomes: (1) A time-dependent infection rate $\beta(t)$; (2) Time scales of transition to a different subpopulation $t_l$, $t_i$, $t_h$, $t_c$; and (3) Age-specific parameters $m_a$, $c_a$ and $f_a$.
Here the latency time from infection to infectiousness is $t_l$, the time an individual is infectious after which he/she either recovers or falls severely ill is $t_i$, the time a sick person recovers or deteriorates into a critical state is $t_h$, and the time a person remains critical before dying or stabilizing is $t_c$.
While the fraction of infectious that are asymptomatic or mild is $m_a$, the fraction of severe cases that turn critical is $c_a$, and the fraction of critical cases that are fatal is $f_a$.

One aspect of the model is not reflected in the above system of equations: If the number of critically ill patients exceeds the capacity of ICU, they are placed in an overflow category $O$.
Individuals in this category die at a higher rate.
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