Environmentally-transmitted disease

• In 1990, 76% of pop had access to ‘improved drinking water’. Up to 91% by 2015

• This still leaves 663 million people relying on unimproved sources, including 159 million dependent on surface water

• 1.8 billion people use drinking water source contaminated with feces

• Water-borne disease, especially for fecal-oral pathogens, is a huge risk to these populations

• Contaminated water causes at around 500k diarrhoeal deaths per year

Water-borne disease

• Bacteria (salmonellosis, shigellosis, leptospirosis, typhoid fever, cholera)

• Viruses (rotavirus, norovirus, hepatitis A)

• Protozoa (ascaris, ringworm, crytposporidiosis)

Reservoirs in the water include the sediment and biota (e.g., snails)

Transmission

• fecal-oral (enteric)

  • direct ingestion
  • indirect ingestion

• dermal

• wound

• eyes

• ears

Risk and illness often proportional to duration of exposure and pollution level

Risk and illness is related to susceptibility (age, immune status, etc.)

Barriers to transmission

pre-emptive:

• Improved sanitation

• Improved water distribution infrastructure

reactionary:

• Treatment of disease

• Isolation of cases

Improved sanitation

Improved sanitation

Improved sanitation

Improved hygeine/access/infrastructure

Improved hygeine/access/infrastructure

Improved hygeine/access/infrastructure

Case study: Cholera

Sanitation, hygeine, environment, etc.

• Cholera is a tough one (known since Hippocrates ~450 BC)

• First epidemic described in 1563 in India

• 7 known cholera pandemics (7th was in 1961)

History of Cholera

• Cholera linked to water-borne transmission in 1854

• 500+ fatal cases over 10 days during London cholera outbreak

• Linked to a single water pump (Broad St. pump)

• John Snow identified and disabled the pump handle

• Robert Koch isolated bacteria (Vibrio cholerae) in 1883

Vibrio cholerae

• Infection via

  • water
  • shellfish
  • person-to-person

• Only freshwater Vibrio species

• Water temperature constrains pathogen growth and survival

Vibrio cholerae

Vibrio cholerae

• But can also grow on biofilms and in other aquatic species

Cholera

Cholera

Cholera

Cholera prevention

• improved infrastructure

• filtering water

• treating water

an ongoing problem, as the disease spreads incredibly quickly

How we model environmentally-transmitted pathogens?

The standard SIR

\[ \begin{aligned} \frac{dS}{dt} &= -\beta SI \\ \frac{dI}{dt} &= \beta SI - dI \\ \frac{dR}{dt} &= dI \end{aligned} \]

How we model environmentally-transmitted pathogens?

Environmental SIR

\[ \begin{aligned} \frac{dS}{dt} &= -\beta SP \\ \frac{dI}{dt} &= \beta SP - dI \\ \frac{dR}{dt} &= dI \\ \frac{dP}{dt} &= bP + \omega I - cP \end{aligned} \]

\(b\) : pathogen growth in the environment

\(\omega\) : infected host shedding

\(c\) : pathogen death rate

Model dynamics

What happens when the pathogen can survive a bit better in the environment?

Bad stuff

\(R_0\)

We could go into how we would go about calculating \(R_0\) here…but…

• it involves a Jacobian matrix, some linear algebra like …

Why does it get so rough to compute?

• \(R_0\) calculation is based on infective stages

• When we had 1 infective stage (\(I\)), it was easy to solve

• But \(P\) is also an infective stage here

_{Bani-Yaghoub et al. 2012 J of Biological Dynamics}

Questions to think about

• How would each of those parameters in the model influence resulting disease dynamics?

• What are some other control measures we did not discuss?

• What determines how we should allocate resources to different control measures?

End of lecture 1

What have we learned?

• Environmentally-transmitted diseases are a big deal

• Modeling environmentally-transmitted disease represents some interesting challenges

• Don’t drink out of streams!

Sexually-transmitted infections

• Pathogens that are transmitted through sexual contact

Background

• Frequency-dependent transmission
• Less virulent and generally more asymptomatic than other diseases
  • good cases of virulence evolution towards reduced virulence
• Some symptoms definitely don’t help with transmission (e.g., postules)
• Can include micro (bacteria, fungi, viruses) and macroparasites (lice)
• Can have serious consequences (e.g., monkeypox, HIV, etc.)

_{Sexually Transmitted Diseases issue 48(4) 2021}

_{Sexually Transmitted Diseases issue 48(4) 2021}

_{Sexually Transmitted Diseases issue 48(4) 2021}

why should we in particular care?

• SC has some of the highest rates of common STIs

Not just a human problem

• We will talk about STIs in humans, plants, and animals

• The reason why this is an entirely different lecture is so we can talk about how we model these types of diseases

• 200 STIs in 27 orders of hosts (that we know of)

• mammals, birds, insects, earthworms, snails, etc. etc.

Chlamydia

_CDC

Chlamydia

_CDC

Chlamydia in animals (Koalas!)

• Different pathology than in humans

• Infects eyes, leaving them partially or wholly blind

• Infect urogenital tracts, resulting in co-infection with bacteria and the bad effects of that (bladder inflamation/kidney issues)

• Some populations with extremely high prevalence, as a result of numerous transmission pathways

  • mothers produce a type of “food poop” which babies eat, and that can lead to infection (https://peerj.com/articles/4452/)

• 8+ species of Chlamydia, most host-specific (3 or so infect humans)

Gonorrhea

• Neisseria gonorrhoeae bacterium

• High tissue tropism (cervix, uterus, fallopian tubes, urethra, mucuous membranes of mouth/throat/eyes)

Gonorrhea

_CDC

The global burden of STIs

_{Zheng et al. 2021 Lancet Infectious Diseases}

The global burden of STIs

_{Zheng et al. 2021 Lancet Infectious Diseases}

What is the most common STI in humans?

• HPV (Human papillomavirus)

• Why?

  • 100 varieties, often no symptoms, very transmissible (skin to skin contact)
  • Sometimes referred to as the ‘cost of being sexually active’

• Linked to multiple types of cancer

• HPV vaccine exists

Insect STIs

• STIs are far from a human (or even animal) issue
• A review found evidence for 73 parasite species of insects capable of sexual transmission
• Most of these were multi-cellular ectoparasites (which is different from humans and plants)
• Life history determines number of STIs (need overlapping adult generations to persist)

_{Knell and Webberley 2003 Biological Reviews}

Plant STIs

• Corn smut (similar transmission pathway and tissue tropism as other smut species)

• Fungal pathogen

• Infects ovaries of plants creating galls of 4-5 inches

• Infected corn can be eaten, and is delicious (huitlacoche originated from Aztec cuisine, but is fairly common in contemporary Mexican cuisine)

Vertical transmission

• Infected mothers can pass the disease

  • either through placenta or at birth

• Multiple transmission modes and asymptomatic infections makes STIs tough to treat

• e.g., HIV, gonorrhea, and chlamydia

What’s the perfect STI?

• no symptoms

• long persistent infection

• non-virulent

• resistant (or quickly evolving)

Antibiotic resistance

• Many common STIs are increasingly becoming resistant to antibiotics

• How does this happen?

_{Tien et al. 2019 J of Travel Medicine}

Antibiotic resistance

_CDC

modeling STIs

• importance of contact
• frequency-dependent transmission

Transmission is rarely from environment

Transmission depends largely on sexual contact

• So we must consider the network of sexual contacts to understand disease spread

• The role of the few

  • hubs in networks drive infection patterns, and sex contact networks tend to be a bit hubby

Network models

How infection occurs on a network

SIR model on network

library(igraph)
g <- sample_gnm(100, 100)
sm <- igraph::sir(g, beta=5, gamma=1)
plot(sm)

How important is network structure?

• Here is an epidemic on a random graph (Sexual contact networks are very non-random though)

• The idea of preferential attachment (remember aggregation lecture?)

Degree distribution and link aggregation

• We talked about aggregation of parasites within hosts, leading to heavy-tailed distributions of parasite diversity and infection intensity

Degree distribution and link aggregation

• The distribution of number of sexual partners is also heavy-tailed

How we simulate infection

• pick a random node to infect

• probabilistic infection process of sexual contacts of infected individuals

• recovery of infected individuals occurs at rate \(\gamma\)

Epidemic size on these different graphs

g0SIR <- SIRnetwork(g0, gamma=0.8)
r0SIR <- SIRnetwork(r0, gamma=0.8)
g1SIR <- SIRnetwork(g1, gamma=0.8)
g2SIR <- SIRnetwork(g2, gamma=0.8)

epidemicSize <- c(r0SIR$R[100], g0SIR$R[100], 
  g1SIR$R[100], g2SIR$R[100])

epidemicSize 

## [1]  81 100 100 100

But recall that infection is probabilistic

• I run that code again and I get a different result (maybe)

g0SIR <- SIRnetwork(g0, gamma=0.8)
r0SIR <- SIRnetwork(r0, gamma=0.8)
g1SIR <- SIRnetwork(g1, gamma=0.8)
g2SIR <- SIRnetwork(g2, gamma=0.8)

epidemicSize <- c(r0SIR$R[100], g0SIR$R[100], 
  g1SIR$R[100], g2SIR$R[100])

epidemicSize 

## [1]  81 100 100 100

Let’s run it 20 times

The role of connectance

• All the networks above had the same number of nodes (people) and the same number of edges (sexual contact links)

• Connectance is the fraction of realized links in the network

  • Value of 1 means every single node is connected to every single other node
  • Value of 0 means nobody is connected to anyone

• This is super important to disease spread, as it determines transmission

Connectance

cSIR <- lapply(cG, SIRnetwork, gamma=0.8)
epidemicSize <- sapply(cSIR, function(x){x$R[100]})
epidemicSize 

## [1]   5  81  94 100 100 100

Connectance

plot(x=con, y=epidemicSize, col='dodgerblue', 
  pch=16, las=1, type='b', cex=1.5, 
  ylab='Epidemic size', xlab='Connectance')

The role of initial infection

• The randomness in these simulations is not only due to the probabilistic infection process

• The initial person infected is chosen randomly

• What makes a node “good” at spreading disease?

What are some assumptions the model makes?

• Transmission is equally likely for all individuals

• No sex structure (everyone is just as likely to have sex with any other node)

• others?

How would we start to calculate \(R_0\) here?

\[ R_0 = \dfrac{\beta}{\gamma} \]

• This ignores all the fun bits about network structure and connectance

• This is from a model that assumes that all individuals contact all other individuals

• So a better \(R_0\) would be something like …

• \(R_0\) = infection parameters x network structure

Most common approach

\[ R_0 = \dfrac{\beta}{\gamma} \times \dfrac{\sigma_{\langle k \rangle}}{\langle k \rangle} \]

_{McKee & Dallas 2024 Infectious Disease Modeling}

Things that complicate this approach

• The only important part of network structure is the variance in degree divided by the mean?

  • Many different graph structures can have the same var/mean relationship, but have wildly different disease dynamics

• Does not incorporate individual variation in infection probability (above we treated \(\beta = 1\))

• Host behavior is important

The role of host behavior

• Avoidance behaviors

_{Stockmaier et al. 2021 Science}

_{Stockmaier et al. 2021 Science}

Questions to think about

• How would mitigation efforts differ between environmentally-transmitted diseases and sexually-transmitted pathogens?

• How would you design a mitigation strategy for an STI?

• Why don’t we model other infectious disease using networks?