APPENDIX: SEIR MODEL
In these equations, π + πΈ + πΌ + π
= π is the total population, with rate of spread, Ξ² >
0, incubation rate Ο > 0, and recovery rate Ξ³ > 0. The value of
represents the rate of change π
with respect to time π‘. Same as
,
,
.
The rate of spread, Ξ² is the rate of infection from an infected individual to one of their
susceptible contacts on the unitary time step dt. For example, given two people A (infectious) and
B (susceptible), the probability of B becoming infected after contacting A during the unitary time
step is Ξ². The term
βt is the difference between two observation points. Thus, number of
individuals transferred from Susceptible state to Exposed state is
π₯π‘, (14)
where is the
is the Force of Infection in the SEIR model. Similarly, on the unitary time step,
there are ΟEβt number of cases transferred from Exposed state to Infectious, and Ξ³I (t)βt number
of cases transferred from Infectious to Removed.
Let
S(t) ,
E(t),
I(t) and
R(t) be the number of susceptible, exposed, infectious and
removed individuals at time t, then
π(π‘ + βπ‘) = π(π‘) β ()()
βπ‘, (15)
πΈ(π‘ + βπ‘) = πΈ(π‘) + ()()β
β ππΈ(π‘)βπ‘, (16)
πΌ(π‘ + βπ‘) = πΌ(π‘) + ππΈ(π‘)βπ‘ β πΎπΌ(π‘)βπ‘, (17)
π
(π‘ + βπ‘) = π
(π‘) + πΎπΌ(π‘)βπ‘, (18)
Based on the definition of the first-order derivative,
=
(β)() β
, as βπ‘ β 0 + . Thus
equation (15) β (18) can be rewritten as equation (10) β (13).
Assumptions of SEIR model [24] are as follows.
i. The SEIR model assumes a closed population, which means that the total number of
populations is fixed, no births, no death, or introduction new individuals. From equation
(10) β (13), we see that
[π(π‘) + πΈ(π‘) + πΌ(π‘) + π
(π‘)] = 0, where the population N is
constant in any time π‘:π(π‘) + πΈ(π‘) + πΌ(π‘) + π
(π‘) = π for any π‘ β₯ 0.
ii. The individuals in the Exposed state are infected but not yet infectious.
iii. Well-mixed population.
iv. SEIR model assumes that the latent and infectious times of the pathogen are exponentially
distributed.
In general, the dynamic SEIR is summarized as below [24].
a) Start the epidemic with a group of Susceptible individuals and at least one Infectious
individual.
b) The Infectious individuals mix with the Susceptible class and create Exposed individuals
following a probabilistic process.
c) Exposed individuals spend some days without spreading the virus and based on another
probabilistic process become additional Infectious class.
d) Newly Infectious class repeat #2 and create more Exposed class.
Infectious individuals based on a probabilistic process either recover or die and become Removed
class.
CoronaTracker: World-wide COVID-19 Outbreak Data Analysis and Prediction
When police, law makers, judges, government departments break and ignore the law they have sworn to uphold, then there isn't any law - just a fight for survival.
These days so many governments around the planet seem to be having a lot of trouble following their own rules, and seem to believe in selective enforcement, this section is here to try to help people find ways (preferably non-violent ways) to survive the tyranny.
Note: Anyone can read this forum, only registered users may post or reply to messages.
These days so many governments around the planet seem to be having a lot of trouble following their own rules, and seem to believe in selective enforcement, this section is here to try to help people find ways (preferably non-violent ways) to survive the tyranny.
Note: Anyone can read this forum, only registered users may post or reply to messages.
Return to βSurvival Ideasβ
Jump to
- Test Category
- ↳ test forum
- System FAQs, issues, etc.
- ↳ Local FAQs
- ↳ System updates, changes, issues, etc.
- ↳ General System Questions
- Polls
- ↳ General Topic Polls
- ↳ Christian Bible Polls
- General Discussions
- ↳ General Discussion Topics
- ↳ e-books & documment posts
- ↳ Jury Nullification / Jury Responsibility
- ↳ Survival Ideas
- ↳ Unknowns / Possible Solutions
- ↳ Government Topics
- ↳ Politics
- ↳ Science and Technology
- Discussions about Religion
- ↳ Christianity
- ↳ General Religion Discussions
- ↳ General Discussion about other religions
- ↳ Rituals and Spells
- ↳ List of demons and information
- ↳ Islam Terms
- ↳ Islam Discussions
- movies and videos
- ↳ Animation/Cartoons
- ↳ general movies
- ↳ self defense
- ↳ religious videos
- Old reference notes.
- ↳ General Info
- ↳ BitCoin
- ↳ undefined topic 1
- ↳ undefined topic 2
- ↳ undefined topic 3
- ↳ undefined topic 4