Modeling pathogen transmission: how different factors shape disease transfer between species

Bridget Menasche, 3rd year PhD candidate in Molecular, Cellular, and Developmental Biology

Now that it’s flu season, most of us are worried about catching the virus from a sneezing coworker. Though we mostly think about disease transmission between people, pathogens like influenza are also transmitted between species (remember swine flu?). This process of pathogen transmission from non-human species to humans is critical for researchers and health care providers to better understand. There are a huge number of factors in the environment that can affect how a pathogen moves between species. Despite this complexity, some interesting patterns have been uncovered by recent research from Joseph Mihaljevic and his coworkers in Dr. Piet Johnson's lab in CU Boulder’s Ecology and Evolutionary Biology department.

Over the past few decades, understanding of disease ecology has grown as many pathogens that can spread from non-human animals to humans have been identified. These include HIV, influenza, and the Lyme disease bacteria Borrelia burgdorferi. By unraveling the connections between pathogens, hosts, and environment, it may ultimately be possible to blunt the spread of some infectious diseases within and between species.

Many pathogens can be spread from wildlife or 
livestock to humans.

Source: GAO report GAO-12-55: Biosurveillance: 
Nonfederal Capabilities Should Be Considered in 
Creating a National Biosurveillance Strategy.

One goal of disease ecology is to determine how community structure affects disease transmission – not an easy task. The number of host species, abundance of each host species, efficiency of pathogen transmission, and spatial dynamics of species contact are all potential variables that may influence how a pathogen moves from one host to another.

In order to explain the dynamics of this complex system, a number of hypotheses have been proposed. One of these, the dilution hypothesis, is currently controversial and heavily debated among disease ecologists. The dilution hypothesis proposes that as biodiversity increases, the chance of disease transmission from non-human animals to humans decreases.

A number of factors influence biodiversity, and likely influence pathogen transmission if the dilution hypothesis holds true. One factor is host richness: how many different species are in a community. In addition, the abundance of organisms in the ecosystem is particularly important for determining pathogen transmission from other species into humans. The overall abundance of animals that can transmit the pathogen will affect how often humans come into contact with that pathogen.

In addition to being important metrics for determining diversity, richness and abundance are often related. How they are related can affect the link between biodiversity and pathogen transmission. Joseph investigated different types of relationships between richness and abundance. First, he looked at an additive relationship, where the total community abundance (total number of individuals) increases as species richness increases. Second, he looked at a compensatory relationship, where the total community abundance doesn’t change as species richness increases. Last, he looked at a saturating relationship, where community abundance first increases with increasing richness, and then saturates at some constant number even as richness continues to increase.

So, how does varying the relationship between total host community abundance and host richness affect community-level disease patterns? Joseph hypothesized that a saturating relationship between abundance and richness better represents what happens in nature, and could yield a range of disease patterns including amplification effects, dilution effects, or other trends.

 The Susceptible, Infected, Recovered (SIR) model. 

The blue susceptible bubble on the diagram above 
and the blue line on the graph below represent 
individuals who have yet to be infected. The 
green bubble and green line represent those that 

have been infected, and the red bubble and line 
represent the growing population of recovered 

individuals who have survived infection and are 
now resistant to the pathogen. The simple model 
shown here was used as the framework for the 

more complex population model developed
 by the authors. 
Source: Wikimedia commons.

Joseph tackled this question using computational modeling, which makes it possible to think through a large range of scenarios mathematically. The classic susceptible, infected, and recovered (SIR) model was used as a basis for the researchers’ approach. In this model, a portion of the population is thought to be susceptible to a pathogen. These individuals are infected with the pathogen and recover – and in this case remain immune to the pathogen for life. In order to think about pathogen transmission between as well as within species, Joseph also had to add additional parameters to the model. In multi-host pathogen systems, host species have different traits that affect how they interact with and transmit the pathogen. For example, different host species have different population sizes and dynamics. Different host species can also be infected at different rates, transmit the pathogen at different rates, or die from infection at different rates.

That many variables can be a lot to consider when designing experiments, but that’s why mathematical modeling is so powerful.

The SIR model takes into account varying features of different species in a community. Based on patterns that ecologists have already worked out in vertebrate communities, this model includes information about the distribution of hosts and about host susceptibility to infection. A few species are very abundant, while most species are more rare as described by Preston’s law. The most abundant species tend to be small in size, have short lifespans, and be competent pathogen hosts. As species abundance decreases in the community, size and lifespan increase, while susceptibility to infection and likelihood to transmit a pathogen decrease.

The researchers created a pool of 49 species and allowed their model to pick a random number of those (from 2 to 49) to simulate an ecological community. The researchers ran a thousand iterations of their updated SIR model for each of the additive, compensatory, or saturating relationships between richness and abundance. For each scenario, the model calculated the rate of transmission between species for the entire community. This value is calculated using complex matrices, but it is essentially determined by each species abundance, host competence, and frequency of transmission.

Joseph then simulated sets of multiple communities and looked at how the community pathogen transmission changed with increasing species richness for the three types of richness-abundance relationships.

He found that when abundance increases proportionately to richness, so does community pathogen transmission: so if population size increases similarly to species number, pathogens are transmitted more frequently. In essence, richer communities are better at transmitting disease.

When abundance remains constant as richness increases, pathogen transmission drops off drastically– because even though the total number of individuals stays the same, those that are highly competent at transmitting the pathogen become fewer and fewer.

These simple models agree with others that have been considered before. The most novel results of the paper come from looking at the saturating model, where abundance first increases with richness, but then levels off. Under these conditions when species richness is still low, Joseph found that community pathogen transmission first experiences an amplification effect. Then, as richness continues to increase, community transmission levels off and later begins to drop. In highly diverse communities, the dilution effect takes over. The nature of the saturating relationship between richness and abundance affected the balance between the amplification effect and the dilution effect. The model also suggests that this relationship doesn’t require that species present in low richness communities be competent hosts. The relationship holds even when host competence varies randomly with species abundance.

The non-monotonic relationship between richness and community pathogen transmission could inform study interpretation and design in disease ecology. For example, when looking at communities with few species, researchers might be more likely to find an additive relationship between richness and disease transmission. But when looking at very rich, diverse communities, researchers might find the dilution effect prevails instead. While this model doesn’t settle the debate over the dilution hypothesis, it does suggest a reason why the literature has been inconclusive so far.

Based on the model, Joseph and his coauthors make a few suggestions for researchers taking this work into the field or the lab. They stress the importance of incorporating disease transmission rates between species when trying to determine the relationship between abundance and disease patterns. They also suggest using abundance and transmission data gathered in the field for designing more streamlined experiments in the lab.


-----------------

You can read the original paper here, published in PLoS ONE, an open access journal: http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0097812

And you can learn more about Joseph Mihaljevic’s work in the Johnson lab here:

https://sites.google.com/site/jrmihaljevic/research

-----------------

If you’re interested in the dilution effect or want to bust out some popcorn for an academic debate, take a look at the following two blog posts. They cover the debate over the dilution hypothesis and Lyme disease, and distill complex disease ecology down to something easily understandable – and entertaining:

The Dilution Effect: numbers, densities, and prevalences -- Parasite Ecology

The Dilution Effect Debates -- Parasite Ecology