Dr. Joseph Challenger�
MRC Centre for Global Infectious Disease Analysis
��School of Public Health�Imperial College London
Mathematical models of vector-borne diseases:
from theory to research
My Background
My Background
During this time, I have worked on a wide range of projects, using both dynamical and statistical modelling. Topics have included:
Simple models – wrong, but useful
Let’s start with a simple model for a vector-borne disease, such as malaria. Our model tracks the infection-status of a human population and a mosquito population. We include a latent period within the mosquito (Em)
Sh
Ih
Sm
Im
Human population
Mosquito population
Em
µ
µ
µ
Simple models
We can calculate R0 for this type of model. To do this, we combine the force of infection from mosquitoes to humans with the force of infection from humans to mosquitoes.
Simple models
We can calculate R0 for this type of model
Simple models
This is quite messy but it shows that there are lots of different ways to reduce the transmissibility of malaria. For example:
Simple models
This is quite messy but shows that there are lots of different ways to reduce the transmissibility of malaria. For example:
Impact on transmission
In my own research, I often focus on interventions that reduce transmission. Let’s briefly discuss how the efficacy of these interventions can be evaluated via mosquito feeding assays.
Typically, mosquitoes in a laboratory are fed on blood (which contains gametocytes) through a membrane. These are called membrane feeding assays
In certain circumstances, it is also possible to feed mosquitoes directly on human skin. This is known as a direct skin feeding assay
Mosquito feeding assays
In my own research, I often focus on interventions that reduce transmission. Let’s briefly discuss how the efficacy of these interventions can be evaluated via mosquito feeding assays.
Typically, mosquitoes in a laboratory are fed on blood (which contains gametocytes) through a membrane. These are called membrane feeding assays
In certain circumstances, it is also possible to feed mosquitoes directly on human skin. This is known as a direct skin feeding assay
Figure from: Bousema et al. PLoS ONE 7(8): e42821 (2012)
Mosquito feeding assays - metrics
In these assays, after mosquitoes have blood fed, they are kept in the insectary for a period of time (normally 7 days), to allow parasites to develop within the mosquito. Then, mosquitoes are dissected, to check for the presence of oocysts. In a sample of mosquitoes, we can either quantify:
The relationship between the two metrics is not completely straightforward to predict. It will depend on the oocyst intensity in the absence of intervention, which could be measured in the control arm of an experiment.
Case study- a transmission-blocking mAb
Currently, there is much interest in transmission-blocking vaccines, which are being assessed via mosquito feeding studies (via either membrane or direct feeding methods).
It is also possible to produce monoclonal antibodies (mAbs) that block infection. In a study in Dutch adults, one mAb, known as TB31F, was shown to be highly efficacious.
Case study- a transmission-blocking mAb
In a study in Dutch adults, one mAb, known as TB31F, was shown to be highly efficacious. (See van der Boor et al. Lancet Infect Dis 2022; 22: 1596–605).
Case study- a transmission-blocking mAb
In a study in Dutch adults, one mAb, known as TB31F, was shown to be highly efficacious. (See van der Boor et al. Lancet Infect Dis 2022; 22: 1596–605).
Figure from: Challenger et al. JID 228:212
(2023)
Case study- a transmission-blocking mAb
The authors behind this study contacted us to ask our thoughts on the results. Can we predict how their entomological endpoints could translate into epidemiological endpoints?
We used the Imperial malaria model to do this (Griffin et al. Plos Med 2010 7(8): e1000324). It is an individual-based model, which tracks both a human and a mosquito population. An individual’s susceptibility to malaria varies with age and the degree of prior exposure.
Case study- a transmission-blocking mAb
Our challenge: use the information on TRA, from the trial of Dutch volunteers, to model the impact of delivering TB31F to a malaria-endemic population in a mass campaign.
How does the impact of TB31F enter the transmission model? Via the c parameter, which quantifies how infectious a human is to a feeding mosquito.
Case study- a transmission-blocking mAb
However, the trial provides information on efficacy in terms of TRA- the reduction in parasite abundance in the mosquito.
For our purpose, TBA is the more relevant metric: in the model, we will quantify TB31F’s ability to block mosquito infection.
So, we need to think about the expected relationship between TRA & TBA in the field, not the laboratory.
Ask me for more details if you’re curious!
Case study- a transmission-blocking mAb
We now had all the ingredients to include TB31F in our transmission model. What scenarios did we look at? There are some factors to be aware of:
Case study- a transmission-blocking mAb
We looked at the impact of TB31F in a low-transmission setting, and a high transmission setting.
We also varied the age group targeted.
As not all locations use SMC, we examined the impact of the intervention with and without the presence of SMC.
Case study- a transmission-blocking mAb
Here we show some projections for the high transmission setting.
The modelling projections indicate that an intervention like TB31F could have significant public health impact.
However, we note that SMC provides direct protection to a vulnerable part of the population. Whereas the impact of TB31F is more diffuse (across the whole community)
Figure from: Challenger et al. JID 228:212
(2023)
Case study- a transmission-blocking mAb
From the model we can output how the infectivity of the population changes over time, as interventions are introduced.
Here we modelled the delivery of TB31F to school-aged children (SAC)
Figure from: Challenger et al. JID 228:212
(2023)
How useful are these results?
For a novel intervention such as this one, it is not easy to translate entomological endpoints into epidemiological endpoints.
Of course, the product will still have to be assessed via clinical trials, especially in endemic populations.
How useful are these results?
For a transmission-blocking vaccine (or mAb), trials with epidemiological endpoints are challenging, as randomization has to be done at a cluster level, rather than at an individual level. This makes trials very large, and expensive to perform
Modelling can guide the design of these trials. It also may be useful in convincing regulators of the utility of the entomological endpoints- we know how malaria is transmitted!
With regard to TB31F, we should note that mAb are currently expensive, and rollout would be complicated in a low-income setting. But the technology is improving over time.
Case study- a bacterium to block infection
A few years ago, scientists at GSK serendipitously discovered that bacteria which had infected their mosquito colony was reducing the transmissibility of malaria parasites through the mosquitoes. This was identified as Delftia tsuruhatensis TC1, which is a naturally occurring symbiotic bacterium.
We (Thomas Churcher & I) were asked to provide input on a delivery mechanism for this intervention and some modelling projections.
Figure from: Huang et al., Science 381, 533–540 (2023)
Case study- a bacterium to block infection
We modelled delivery via mosquito bait stations (containing sugar sources), which could be placed outside people’s houses. In panel B, the colours show the duration of the intervention (2,4,6 months)
Figure from: Huang et al., Science 381, 533–540 (2023)
Thank you for listening!
Any Questions?
Extra material
Extra slides that might be useful for questions
Impact of drugs on transmission
Recall: in the blood stage of a malaria infection in human, we have asexual-stage parasites and sexual-stage parasites (gametocytes). Asexual–stage parasites invade red blood cells, multiplying every 48 hours. Each generation, a small fraction of these parasites commit to becoming gametocytes.
Antimalarial drugs primarily target asexual stage parasites, as these cause disease and represent the ‘engine’ of the infection.
Remaining gametocytes can still be transmitted.
Figure from: Challenger et al. BMJ Global Health
2019;4:e001856
Simple models
Even when we want a very simple model, there is one addition commonly made to this system of equations.
In reality, it is observed that there is a relatively long delay between mosquitoes becoming infected and becoming infectious. This time period, known as the extrinsic incubation period (EIP), is around 10 days. This is quite similar to the lifespan of wild Anopheles mosquitoes!
This is important: of the mosquitoes that become infected, only a minority of them will survive for long enough to transmit malaria to a human!
Simple models
Why is the EIP so important?
Look at survival rates of wild mosquitoes (note: mosquitoes can survive for much longer in laboratories!)
Figure taken from Hughes et al. Parasites & Vectors 13 17 (2020)
Impact of drugs on transmission
In this study, two different antimalarial therapies were compared, to examine their impact on gametocyte carriage.
In this study, the treatment arms were:
Gametocyte presence was detected by quantitative nucleic acid sequence based amplification (QT-NASBA)
Figure from: Bousema et al. Malaria Journal 2010, 9:136
Case study- a transmission-blocking mAb
However, the trial provides information on efficacy in terms of TRA- the reduction in parasite abundance in the mosquito.
For our purpose, TBA is the more relevant metric: in the model, we will quantify TB31F’s ability to block mosquito infection.
So, we need to think about the expected relationship between TRA & TBA in the field, not the laboratory.
Case study- a transmission-blocking mAb
We used this data to fit a (zero-truncated) negative binomial distribution to describe the oocyst counts. This allowed us to fit a mathematical relationship between TRA & TBA.
This may vary according to setting. But this data is rarely collected.
Figure from: Challenger et al. JID 228:212
(2023)
Case study- a transmission-blocking mAb
To do this, we utilized data from an unusual study carried out in Burkina Faso in 2014. Here, wild mosquitoes were collected from the inside of people’s homes, first thing in the morning. Those mosquitoes who had blood-fed, were retained for later dissection.
The distribution of oocyst counts that were collected were highly overdispersed. Look at the scale on the x-axis!
Figure from: Bompard et al. Int J Para 50 985-996 (2020)