with force of infection
and total population along the road
Event | Date | Location | Disease | Death toll (estimate) |
---|---|---|---|---|
Plague of Megiddo | 1350 BCE | Megiddo, land of Canaan | Unknown | Unknown |
Plague of Athens | 429–426 BCE | Greece, Libya, Egypt, Ethiopia | Possibly typhus, typhoid fever or VHF | 75,000–100,000 |
412 BCE epidemic | 412 BCE | Greece, Roman Republic | Possibly influenza | Unknown |
Antonine Plague | 165–180 CE (possibly up to 190 CE) | Roman Empire | Possibly smallpox | 5–10 million |
Jian'an Plague | 217 CE | Han dynasty | Possibly typhoid fever or VHF | Unknown |
Plague of Cyprian | 250–266 CE | Europe | Possibly smallpox | Unknown |
Plague of Justinian (1st plague pandemic) | 541–549 CE | Europe and West Asia | Bubonic plague | 15–100 million (25–60% of population of Europe) |
Roman Plague of 590 (1st plague pandemic) | 590 CE | Rome, Byzantine Empire | Bubonic plague | Unknown |
Plague of Sheroe (1st plague pandemic) | 627–628 CE | Bilad al-Sham | Bubonic plague | 25,000+ |
Plague of Amwas (1st plague pandemic) | 638–639 CE | Byzantine Empire, West Asia, Africa | Bubonic plague | 25,000+ |
Plague of 664 (1st plague pandemic) | 664–689 CE | British Isles | Bubonic plague | Unknown |
Plague of 698–701 (1st plague pandemic) | 698–701 CE | Byzantine Empire, West Asia, Syria, Mesopotamia | Bubonic plague | Unknown |
735–737 Japanese smallpox epidemic | 735–737 CE | Japan | Smallpox | 2 million (approx. 1/3 of Japanese population) |
Plague of 746–747 (1st plague pandemic) | 746–747 CE | Byzantine Empire, West Asia, Africa | Bubonic plague | Unknown |
= various levels or scales of the functional or spatial aspects of a diffusion process. Scale (cone of resolution) takes on two dimensions: functional (decisions made by different groups of individuals) and spatial (manifestations of these decisions as observed in a spatial context)
or
In each patch, put a system describing the evolution of the number of individuals in each compartment present
Assume uninfected (s) and infected (i) compartments U and I. For all j∈U, k∈I and ℓ∈L
f and g describe interactions between compartments in a given location. Might involve more than Sℓ,Iℓ, but always local (ℓ)
Sums describe movement of (individuals from) compartments between locations
Movement from location q∈L to location p∈L occurs at rate mXpq for individuals in compartment X
Movement matrix for compartment X:
Date | Location | Note |
---|---|---|
13 Jan. | Thailand | Arrived 8 Jan. |
16 Jan. | Japan | Arrived 6 Jan. |
20 Jan. | Republic of Korea | Airport detected on 19 Jan. |
20 Jan. | USA | Arrived Jan. 15 |
23 Jan. | Nepal | Arrived 13 Jan. |
23 Jan. | Singapore | Arrived 20 Jan. |
24 Jan. | France | Arrived 22 Jan. |
24 Jan. | Vietnam | Arrived 13 Jan. |
25 Jan. | Australia | Arrived 19 Jan. |
25 Jan. | Malaysia | Arrived 24 Jan. |
J. Arino, N. Bajeux, S. Portet & J. Watmough. Quarantine and the risk of COVID-19 importation. Epidemiology & Infection, 2020
In Ecology, importations are called introductions and have been studied for a while, because they are one of the drivers of evolution and, more recently, because of invasive species
An importation occurs when an individual who acquired the infection in a jurisdiction makes their way to another jurisdiction while still infected with the disease
Geographies greatly influence reasoning
Modify the usual S (susceptible), L (latent), I (infectious with symptoms), A (infectious without symptoms) and R (recovered)
p fraction of cases detected a posteriori (stricto sensu)
Q:
S.P Otto, T. Day, J. Arino, C. Colijn et al. The origins and potential future of SARS-CoV-2 variants of concern in the evolving COVID-19 pandemic. Current Biology, 2021
Country | Travel suspension | First_case |
---|---|---|
Seychelles | 2020-03-03 | 2020-03-14 |
El Salvador | 2020-03-17 | 2020-03-18 |
Cape Verde | 2020-03-17 | 2020-03-20 |
Sudan | 2020-03-17 | 2020-04-05 |
Marshall Islands | 2020-04-22 | 2020-10-29 |
Vanuatu | 2020-03-20 | 2020-11-11 |
North Korea | 2020-01-21 | Unreported |
Turkmenistan | 2020-03-20 | Unreported |
Tuvalu | 2020-03-26 |
1/λ the mean time between case importations, 1/λq the mean quarantine-regulated time between case importations, c the efficacy of quarantine (in %). Then
Suppose 1/λ= 5 days and efficacy of quarantine is 90% at 7 days and 98% at 14 days, respectively
Then 1/λq= 50 and 250 days, respectively
Left hand side
Right hand side