Disease spreading and networks Flashcards
an interconnected world:
1. what has happened to biological processes globally?
2. what is interconnected?
3. what is disease spread not confined to?
- biological spread process are increasingly global
- interconnected worlds and species
- disease spread is not confined to political borders
an interconnected world
1. what percentage of terrestrial vertebrate species are affected by wildlife trade globally?
2. wildlife trade occurs across…?
3. mixing of …?
- Wildlife trade affects ~18% of terrestrial vertebrate species (birds, mammals,
amphibians, and reptiles) globally - the tree of life, but some clades are more heavily targeted than others
- mixing of formerly distinct biological communities
(Brockman & Helbig, 2013)
pathogen spread through global networks
1. what does the global mobility network between 4069 airports worldwide as effective distances represent?
The global mobility network between 4069 airports worldwide as effective distances
represent the spatial spreading process of the 2009 H1N1 influenza pandemic and
2003 SARS epidemic – viruses with direct person-person transmission.
(Lederberg, 2000)
an interconnected world (population): syphilis
1. what is syphilis?
2. can pass from who to who also?
3. first recognised?
4. what was proposed in 1530?
5. is the detection in Europe known?
6. how many infected worldwide in 2022 as reported by WHO?
7. how much was it understood at the time it was discovered?
8. continuous disease transmission requires?
- a sexually transmitted bacterial infection caused by Treponema pallidum
- can pass from mother who is infected to unborn child
- first recognised among French soldiers and accompanying women invading Italy in 15th Century
- 1530: proposed that syphilis was spread by “seeds” after intimate contact (Italian physician Girolamo Fracastoro
- picked up from North America by Christopher Columbus or undetected origin in Europe?
- 2022: >8 million infected worldwide as reported by WHO
- little understanding at the time
- continuous disease transmission requires more than just two: the recipient host must turn into a donor host
(Leventhal et al., 2015)
An interconnected world: contact networks
1. what occurs in a population of initially susceptible individuals?
2. what happens next?
3. when is it considered an ‘endemic’?
4. what may a different or newly evolved pathogen strain impact?
- a single individual becomes infected
- the infection spreads throughout the population
- when the number of new infections is balanced by the number of recoveries
- may impact the spread of original pathogen strains
(Newman et al., 2003)
an interconnected world: contact networks
1. what visual did they make?
2. what are edge/ link?
3. what are node/ vertice?
4. what is the backbone for contagious disease spread?
5. what can be used to describe the interconnections among individuals? and what important role do they play?
6. what does the visual allow for the quantifying of?
- risk network structure in the early epidemic phase of HIV transmissions in Colorado Springs
- connection, association, transmission pathway - edges are connections between nodes
- individuals, populations, species, patches
- contact opportunities and frequencies between hosts are a backbone for contagious disease spread
- social networks can be used to describe interconnectedness among individuals, which play an important role in spread of disease
- allows to quantify relative importance of nodes and links, distribution of links, and cluster (‘network modularity’)
(Watts et al., 1998)
Study of sexual contacts
1. what do social networks have?
2. what do social networks show?
3. what can fundamentally impact disease spread?
- social networks have small average path lengths between connections
- social networks show a large degree of clustering (“six degrees of separation”)
- ‘Rewiring’ of contact networks through changes in human mobility and interactions can fundamentally impact disease spread
mastering the art of network analysis made easy
1. step by step
- simplify complex real-world problem into a representative graph (=network) object of nodes and links between them
- write graph down as an N x N matrix, where N = node and each cell indicates presence-absence or number of links between each pair of nodes
- simple graph properties such as a node’s degree (total number of links) can be computed from the table, for computing more complex network properties use the package igraph
SIR model and onwards = (Hethcote, 2000), (Blackwood & Childs, 2018)
First step into conceptualising the dynamics of disease spread
1. compartmental disease models?
2. The SIR model as a system of ordinary differential equations (ODEs)?
3. what does S, I , and R stand for?
4. susceptibility depends on, and what is the equation (dS/dt = ?) ?
5. dI/dt = ?
6. dR/dt = ?
7. population size: N = ?
- divide a (closed) population into groups (compartments) based on individual infectious status and track the corresponding group sizes through time
- compute the difference of the number of individuals in different states over time, whereby susceptible individual may become infected and infectious individuals recover
- S = susceptible
I = infected
R = recovered - susceptibility depends on size of the pool and how many are infected
dS/dt = −βSI - dI/dt = βSI − yI
- dR/dt = yI
- Population size: N = S + I +R
what is basic reproduction number R0?
average number of secondary cases arising from an average primary case in an entirely susceptible population
Basic reproduction number R0
If everyone is initially susceptible (St-0) = N), then newly infected individual can be expected to infect others at the rate…
β during the expected infectious period 1/y:
R0 = β/y (S0)
Basic reproduction number R0
pathogen can invade and spread if…
R0 > 1
Basic reproduction number R0
What have insights into disease spread led to?
control strategies of quarantine, social distancing, culling and vaccination
Basic reproduction number R0
If someone infected walks into a room, number of cases represents…
how quickly the disease will spread
(Begon et al., 2002)
Spread of diseases: density versus frequency
Density-dependent (DD) transmission?
the per capita contact rate between susceptible (S) and infected (i) individuals depends on the population density. So, transmission rates increase with density
(Begon et al., 2002)
Spread of diseases: density versus frequency
Frequency-dependent (FD) transmission?
the per-capita contact rate is independent of population density, transmission rates do not change with density
(Begon et al., 2002)
Spread of diseases: density versus frequency
DD equation
FD equation
Meaning of:
λ
c
v
I/N
DD: λ = c * v * SI/N = β * SI/A
C = k * N/A
FD: λ’ = c’ * v * SI/N = β’ * SI/N
C’ = n
λ: Force of infection (per-capita infection probability)
c = contact rate
v = probability of disease transmission if S meets I
I/N = probability/rate that a given contact is with an infected individual
Severe acute respiratory syndrome (SARS)
1. what is it?
2. emerged from where?
3. origin? likely reservoir?
4. where does the human-to-human transmission of SARS-CoV mainly occur?
- highly pathogenic coronavirus
- emerged in southern China with pandemic in 2002-2003
- origin remains elusive but bats a likely reservoir
- in health care settings (large dose-response ratio)
Severe acute respiratory syndrome (SARS)
No matter how much data, what questions are important to ask?
- What is the period of time between infection and the onset of infectiousness?
- For how long do patients remain infectious?
- How many further infections will each patient produce?
- How many people will get infected during the epidemic?
- Will the current public health measures be enough to bring SARS under control?
- Is SARS here to stay?
Spanish Flu (1918-19) versus SARS (2002-03) (and versus Covid-19, 2020-2022)
1. type of disease?
2. number of fatalities?
3. percentage of humans infected?
4. percentage of case fatality risk?
5. R0 value?
Spanish Flu (1918-19)
1. Influenza pandemic
2. 50M fatalities
3. 20 - 30 % of humans infected
4. 10% case fatality risk
5. Basic reproductive ratio, R0: 1.2 - 3
SARS (2002-03)
1. Coronavirus
2. 774 fatalities
3. 0.001% of humans infected
4. 10% case fatality risk
5. R0: ~ 3
Covid-19 (2020-22)
1. Coronavirus
2. >6.5M fatalities
3. ~10% of humans infected
4. 1.5-3% case fatality risk
5. R0: 2-3
Natural history of disease meaning?
progression of disease in an individual over time
Incubation period meaning?
Time period between exposure to an infectious agent and the onset of symptoms of the disease
Latency period meaning?
Time period between exposure to an infectious agent and the point at which the individual becomes infectious to others (even if symptoms are absent)
Serial interval meaning?
Time period between the onset of symptoms in one person (the primary case) and the onset of symptoms in a second person (the secondary case) who is infected by the first
Natural history of disease may include?
incubation period (time to onset of symptoms) and latency period (time to infectiousness)
What is natural disease history important for?
individual treatment and spread of pathogen through populations
Natural history of Covid-19
1. When was the understanding of Covid-19 clinical course and investigational treatment?
2. How long was the period of viable shedding?
- in autumn 2020: multiple stages during the first three weeks after infection
- relatively short (< 20 days)
(Marineli et al., 2013)
Superspreaders
“Typhoid Mary” case
Mary Mallon, emigrated to the US in 1884
Outbreaks in New York soon as she started career as cook in 1906, responsible for the contamination of > (or the same as) 120 people, including 5 fatal cases
First person identified as “healthy carrier” of Salmonella typhi, denial of being ill
Forced into quarantine on two separate occasions on North Brother Island for a total of 26 years… ‘laboratory pet’, never informed about her being a risk
Transmission heterogeneity meaning?
some host individuals/species or habitat patches are amplifiers (their presence increases transmission of the pathogen), others may dampen transmission (their presence decreases transmission)
(Ferrari et al., 2004)
Transmission heterogeneity
Yellow-necked mouse (Apodemus flavicolis)
Few (mostly male) yellow-necked mouse individuals released most of the total eggs of the nematode, Heligmosomoides polygyrus
(Kilpatrick et al., 2006)
Transmission heterogeneity
American robins (Turdus migratorius)
infect a much greater percentage of mosquitoes with West Nile virus than other bird species
(Johnson, unpublished)
Transmission heterogeneity
Ponds
Few ponds have very high percentages of snails infected with the trematode, Ribeiroia ondatrae
(Lee et al., 2020)
SARS-CoV-2 - unprecedented spread across scales
1. ‘Engines’ of spread at different scales?
2. transmission most frequent in?
3. interactions?
4. complex interplay of?
- Households <-> Communities <-> Interregional
- social groups but community transmission sustain the epidemic
- Heterogeneous mix of interactions
- pathogen attributes, host characteristics, timing, and setting
(Levin, 1969) (Hanski & Gilpi, 1997)
Disease and metapopulation models
1. Equation and what each component stands for?
2. Metapopulations persist only if?
3. Assessment of metapopulation viability in response to?
- dN/dt = cN(1 - N/T) - mN
N: Number of patches colonized
c: colonization rate
m: extinction rate
T: Total number of patches - m < c
- habitat destruction
(Levin, 1969) (Hanski & Gilpi, 1997)
Disease and metapopulation models
1. What can metapopulations models combine?
2. What is it also useful to consider?
- concept of colonization and extinction dynamics with spatial network structures
- that individuals and social groups can be structured into populations with disease spread being determined by connectivity at different organisational levels
Heterogeneities in pathogen transmission
What determines the number of secondary infections produced by an infected individual?
- contact rate (at which it contacts susceptible individuals)
- Infectiousness (of how strongly infectious agent is transmitted)
- Infection duration (during which infectious agent can be transmitted)
-> Individual-level variation in transmission can emerge in each of these components through a combination of behavioural and physiological mechanisms
