1) The relationship of climate and the transmission We will cover - - PowerPoint PPT Presentation

MMID 2018/2019 :: IHTM :: 6th February 2019

Mathematical modelling: from theory to practice

mathematical dynamic models empirical data advances in theory and ways of thinking changes in policy of intervention and control

José Lourenço

RESEARCH LECTURER IN INFECTIOUS DISEASES DEPARTMENT OF ZOOLOGY

jose.lourenco@zoo.ox.ac.uk

MMID 2018/2019 :: IHTM :: 6th February 2019

We will cover the 3 topics we discussed before. We can have a break at any time. Please ask questions during the lecture.

1) The relationship of climate and the transmission potential of viruses such as dengue and Zika. 2) The dengue modelling initiative and its role on WHO’s policy towards DengvaxiaⓇ. 3) Strain theory and its overarching impact on the fields

• f theoretical epidemiology and public health.

MMID 2018/2019 :: IHTM :: 6th February 2019

The relationship of climate and the transmission potential of viruses such as dengue and Zika

mathematical dynamic models empirical data advances in theory and ways of thinking changes in policy of intervention and control

José Lourenço

RESEARCH LECTURER IN INFECTIOUS DISEASES DEPARTMENT OF ZOOLOGY

jose.lourenco@zoo.ox.ac.uk

MMID 2018/2019 :: IHTM :: 6th February 2019

Real world complexity and host-pathogen models.

control (e.g. vaccination) diversity (pathogen / host) evolution vectors climate social interactions host mobility population structure animal reservoirs

Most models we develop and use are big simplifications

• f the real world.

These factors are generally interlinked, and many others exist.

MMID 2018/2019 :: IHTM :: 6th February 2019

Most models we develop and use are big simplifications

• f the real world.

These factors are generally interlinked, and many others exist.

control (e.g. vaccination) diversity (pathogen / host) evolution vectors climate social interactions host mobility population structure animal reservoirs

SIR-like models real world

• ther types of

models

Real world complexity and host-pathogen models.

MMID 2018/2019 :: IHTM :: 6th February 2019

Dengue

Four antigenically distinct lineages (serotypes DENV1, DENV2, DENV3, DENV4). Classically endemic to with Southeast Asia, now generally found across all tropical and semi-tropical regions of the world. Generally transmitted by mosquitoes of the genus Aedes (e.g. A. aegypti and

• A. albopictus).

Climate is an essential factor in the transmission potential of dengue viruses - but how?

Jie Alvin Tan et al. 2017 Emerging Diseases Shepard et al. 2014 PLoS Neg Trop Dis 10.1371/journal.pntd.0003306

Island of Madeira

Kyle et al. 2008 Ann Rev Microbio 10.1146/annurev.micro.62.081307.163005

MMID 2018/2019 :: IHTM :: 6th February 2019

Introduction of dengue on Madeira Island

First case of DENV1 was reported on the 3rd of October 2012. In just 3 months, more than 2000 cases were reported locally (N ~270.000). 81 cases were exported and detected in mainland Europe.

MMID 2018/2019 :: IHTM :: 6th February 2019

Introduction of dengue on Madeira Island

Extinction before next season (spring) December Peak in autumn (end of October) January Sudden start

First case of DENV1 was reported on the 3rd of October 2012. 81 cases were exported and detected in mainland Europe. In just 3 months, more than 2000 cases were reported locally (N ~270.000).

MMID 2018/2019 :: IHTM :: 6th February 2019

Dengue model

SEIR framework. Single serotype. Mosquito compartments. Climate directly affecting mosquito biology. Ideas how or why?

? ? ?

MMID 2018/2019 :: IHTM :: 6th February 2019

Model fit to epidemic

Model closely approximated the epidemic curve.

MMID 2018/2019 :: IHTM :: 6th February 2019

Model fit to epidemic

Extinction before next season (spring) December Peak in autumn (end of October) January Reconstructed introduction, weeks before the first reported case (no longer sudden start).

Model closely approximated the epidemic curve. Peak, decline and extinction were reproduced at right timings. Introduction was estimated to have taken place weeks before first reported case. So, could the model help answer on what caused the decline?

MMID 2018/2019 :: IHTM :: 6th February 2019

Model fit to epidemic

Extinction before next season (spring) December Peak in autumn (end of October) January

Model closely approximated the epidemic curve. Peak, decline and extinction were reproduced at right timings. Introduction was estimated to have taken place weeks before first reported case. So, could the model help answer on what caused the decline? Temperature in late autumn and winter!

MMID 2018/2019 :: IHTM :: 6th February 2019

Temperature & mosquito traits

Temperature can in fact modulate many mosquito traits. These are some examples of data collected in controlled laboratory conditions. Other factors also known to play a role:

• Rainfall
• Altitude
• Humidity

Mordecai et al. PLoS Neg Trop Dis 2017 doi.org/10.1371/journal.pntd.0005568

MMID 2018/2019 :: IHTM :: 6th February 2019

Climate-trait mathematical relationships

Mathematical expressions can be derived that mimic or approximate the known data points. This means that, if we know the temperature at a given time point, we can have an estimation

• f parameters which

represent important mosquito trait.

Yang et al. Epidemiol Infect 2009 doi:10.1017/S0950268809002040

MMID 2018/2019 :: IHTM :: 6th February 2019

Climate-trait model parameters

For mosquito traits which we think are relevant for a transmission model, we can therefore simply plug-in the derived mathematical expressions. These are some examples.

• viposition rate

adult death rate aquatic death rate

MMID 2018/2019 :: IHTM :: 6th February 2019

Temperature as a major determinant of R0 in Madeira Island

R0>1 was estimated for the period between June and October, when temperature was essentially above 16C. Outside this time period, the mosquitoes’ lifespan was shorter than the viral incubation period, thus R0<1.

MMID 2018/2019 :: IHTM :: 6th February 2019

Lessons from this case study

Climate factors affect mosquito life-traits, which in turn affect the transmission of mosquito-borne viruses. We understand the relationships of climate factors with mosquito life-traits ⇒ we can plug-in these relationships into models. Fitting a climate-driven model to an epidemic curve can help us understand the success or demise

• f mosquito-borne viruses.

“Food for thought”

Climate explains much of the geographical variation in transmission success of mosquito-borne viruses across the world. What if we do not have the epidemic curve? Can we evaluate transmission potential before epidemics occur? (instead of

retrospectively looking back at an epidemic that already occurred and try to understand it?)

MMID 2018/2019 :: IHTM :: 6th February 2019

The index P

(measure of transmission potential)

Pablo (IHTM 2017)

Background: Clinical consultant in infectious diseases and general (internal) medicine. Imperial College London: “Using individual-based mathematical models to gauge the differences in the burden of co-morbid conditions among HIV-positive and HIV-negative populations”.

MMID 2018/2019 :: IHTM :: 6th February 2019

Deriving the index P

R0 is the number of secondary infections expected from a single infection in a totally susceptible population.

climate dependent

M

MMID 2018/2019 :: IHTM :: 6th February 2019

Deriving the index P

R0 is the number of secondary infections expected from a single infection in a totally susceptible population. M is the number of female mosquitoes per human.

climate dependent Total number of female mosquitoes V, divided by total number of humans (M = V/ N).

M

MMID 2018/2019 :: IHTM :: 6th February 2019

Deriving the index P

R0 is the number of secondary infections expected from a single infection in a totally susceptible population. M is the number of female mosquitoes per human.

climate dependent Total number of female mosquitoes V, divided by total number of humans (M = V/ N). temperature dependent

R0 is humidity (u) and temperature (t) dependent

M M

MMID 2018/2019 :: IHTM :: 6th February 2019

Deriving the index P

R0 is the number of secondary infections expected from a single infection in a totally susceptible population. M is the number of female mosquitoes per human.

climate dependent Total number of female mosquitoes V, divided by total number of humans (M = V/ N). temperature dependent

R0 is humidity (u) and temperature (t) dependent

M M

MMID 2018/2019 :: IHTM :: 6th February 2019

Deriving the index P

R0 is the number of secondary infections expected from a single infection in a totally susceptible population. M is the number of female mosquitoes per human. P is the transmission potential of each existing female mosquito per human.

climate dependent Total number of female mosquitoes V, divided by total number of humans (M = V/ N).

M

P is humidity (u) and temperature (t) dependent.

temperature dependent

R0 is humidity (u) and temperature (t) dependent

M

MMID 2018/2019 :: IHTM :: 6th February 2019

Potential use for the index P

P is the transmission potential of each existing female mosquito per human.

MMID 2018/2019 :: IHTM :: 6th February 2019

Potential use for the index P

P is the transmission potential of each existing female mosquito per human.

We can plug-in the relationships of certain mosquito factors.

adult death rate

MMID 2018/2019 :: IHTM :: 6th February 2019

Potential use for the index P

P is the transmission potential of each existing female mosquito per human.

We can plug-in the relationships of certain mosquito factors. Parameters independent of climate can be fixed to known values.

adult death rate

MMID 2018/2019 :: IHTM :: 6th February 2019

Potential use for the index P

P is the transmission potential of each existing female mosquito per human.

We can plug-in the relationships of certain mosquito factors. Parameters independent of climate can be fixed to known values. That is, if we know temperature and humidity for a certain location on a particular day, we know the value of all parameters and can calculate P!

adult death rate

MMID 2018/2019 :: IHTM :: 6th February 2019

Examples of historical P

Köppen climate classification

Recife has tropical savanna climate. São Paulo has humid subtropical climate. Climate shows clear seasons in Recife and is noisy in São Paulo. It is cooler in São Paulo. Index P shows suitability for transmission is more stable and higher in Recife. (south coast) (north coast)

MMID 2018/2019 :: IHTM :: 6th February 2019

Mapping the index P

Satellite climate datasets are freely available online. These are snapshot examples of such data for January and June. Data is representative of climate from 1970-2000. Each pixel of these maps represents ~18Km2, for which we have humidity and temperature per month. We can estimate the index P per pixel!

MMID 2018/2019 :: IHTM :: 6th February 2019

Mapping the index P

(a) Mean yearly index P across Brazil, with transmission potential:

⚫ highest in the centre, northern and eastern coasts ⚫ weakest in the south and along elevated regions running in parallel to the eastern coast

MMID 2018/2019 :: IHTM :: 6th February 2019

Mapping the index P

(a) Mean yearly index P across Brazil, with transmission potential:

⚫ highest in the centre, northern and eastern coasts ⚫ weakest in the south and along elevated regions running in parallel to the eastern coast

(b) Transmission season peaks in different months

⚫ summer in the south and autumn in the north

MMID 2018/2019 :: IHTM :: 6th February 2019

Mapping the index P

(a) Mean yearly index P across Brazil, with transmission potential:

⚫ highest in the centre, northern and eastern coasts ⚫ weakest in the south and along elevated regions running in parallel to the eastern coast

(b) Transmission season peaks in different months

⚫ summer in the south and autumn in the north

(c) Time snapshots make these differences clearer.

MMID 2018/2019 :: IHTM :: 6th February 2019

Mapping the index P

Each month’s data can be put together to animate the index P over a year. This example now includes almost all

• f South America.

(this slide is an animation and it won’t be seen in PDF)

MMID 2018/2019 :: IHTM :: 6th February 2019

Take home messages

Climate affects key mosquito biological traits that determine the transmission potential of viruses. Climate therefore explain much of the geographical and temporal historic and future dynamics of mosquito-borne viruses such as Zika and dengue. Models can be calibrated with and driven by climate factors. Exploring such models allows us to both understand past epidemics and also, critically, to project the likelihood of future events.

MMID 2018/2019 :: IHTM :: 6th February 2019

The dengue modelling initiative and its role on WHO’s policy towards DengvaxiaⓇ

mathematical dynamic models empirical data advances in theory and ways of thinking changes in policy of intervention and control

José Lourenço

RESEARCH LECTURER IN INFECTIOUS DISEASES DEPARTMENT OF ZOOLOGY

jose.lourenco@zoo.ox.ac.uk

MMID 2018/2019 :: IHTM :: 6th February 2019

Dengue model variations

Typical SEIR framework. Four possible infections. The states of highest public health importance are related to second infection. Optional temporary state A of temporary immunity (researchers do not agree in duration or existence). Optional 2 versus 4 infections (researchers assume 2 or 4 infections offer protection to all serotypes). Optional vector dynamics.

MMID 2018/2019 :: IHTM :: 6th February 2019

Our dengue model

Individual-based. Four serotypes. Mosquito dynamics. Population structure. With vaccination.

Lourenco et al. PLoS Comp Bio 2013 doi.org/10.1371/journal.pcbi.1003308

MMID 2018/2019 :: IHTM :: 6th February 2019

DengvaxiaⓇ

Sanofi Pasteur CYD-TDV Is a live attenuated tetravalent vaccine including the E-protein (envelope) of each of the 4 serotypes. Trials presented

• Intermediate to high

efficacies

• varying efficacies across

serotypes

• consistent results across

the globe Note: efficacy to symptomatic infection.

Asia (trial phase 3) Indonesia, Malaysia, Philippines, Thailand, Vietnam Estimated efficacies DENV1 50% ∊ (25, 67) DENV2 35% ∊ (-9, 61) DENV3 78% ∊ (53,91) DENV4 75% ∊ (54,87) Latin America (trial phase 3) Brazil, Colombia, Honduras, Mexico, Puerto Rico Estimated efficacies DENV1 50% ∊ (29,65) DENV2 42% ∊ (14,61) DENV3 74% ∊ (61,82) DENV4 77% ∊ (60,88) Aggregated efficacy (across serotypes) 74% ∊ (53, 86) in seropositive individuals 35% ∊ (-27, 68) in seronegative individuals

MMID 2018/2019 :: IHTM :: 6th February 2019

Example of trial data to work with

MMID 2018/2019 :: IHTM :: 6th February 2019

Example of trial data to work with

Placebo and vaccine results were significantly overlapping. Young individuals, vaccine enhanced symptomatic infections (hospitalization)

MMID 2018/2019 :: IHTM :: 6th February 2019

WHO initiative

August 2015: the WHO

• pened a call for dengue

modellers Context: the first dengue vaccine was licensed (CYD-TDV) Objective: understand and project the possible public health impact of the vaccine Outcome: to inform WHO's

• fficial recommendation

report on dengue vaccination. Group: 8 groups across the world were selected given their previous experience with dengue modelling.

MMID 2018/2019 :: IHTM :: 6th February 2019

All models were different...

MMID 2018/2019 :: IHTM :: 6th February 2019

All models were different...

MMID 2018/2019 :: IHTM :: 6th February 2019

One key factor was agreed!

Vaccine mode of action Dengvaxia works as a silent (artificial) infection. The main implication is that the vaccine works as a primary infection for seronegative individuals and therefore primes seronegatives to secondary infection with the viruses.

artificial infection

* * *

MMID 2018/2019 :: IHTM :: 6th February 2019

Fit of the 8 models to trial data

Models did generally well in capturing the trends of the trial data. The differences in how models performed in approximating the trial data were due to the different assumptions included in the models. With the models fit to the general trends of the trials, they could then be used to simulate vaccination campaigns.

MMID 2018/2019 :: IHTM :: 6th February 2019

Projected vaccine impact

Models mostly agreed on the positive impact of the vaccine in regions with intermediate and high transmission. In regions with high transmission (SP9 90%), reduction of symptomatic and hospitalized cases would reach ~30% (at most!). In regions with low transmission (SP9 10% and 30%), models disagreed on impact, either with positive

• r negative impacts.

models disagree! low transmission intermediate and high transmission models agreed (in general)

MMID 2018/2019 :: IHTM :: 6th February 2019

WHO’s position paper

Official position (Jul 2016): Not to implement CYD-TDV for scenarios with <50% seroprevalence at the age

• f 9 years

Projected impact: Vaccination will only reduce dengue incidence up to 30% only, and only in high transmission settings.

http://www.who.int/wer/2016/wer9130.pdf?ua=1

MMID 2018/2019 :: IHTM :: 6th February 2019

Strain theory and its overarching impact on the fields of theoretical epidemiology and public health.

mathematical dynamic models empirical data advances in theory and ways of thinking changes in policy of intervention and control

José Lourenço

RESEARCH LECTURER IN INFECTIOUS DISEASES DEPARTMENT OF ZOOLOGY

jose.lourenco@zoo.ox.ac.uk

MMID 2018/2019 :: IHTM :: 6th February 2019

Multi-strain?

MMID 2018/2019 :: IHTM :: 6th February 2019

Multi-strain?

Multi-strain pathogens are agents that present genetic diversity which is ‘seen’ differently by the immune system. This sort of diversity is called antigenic diversity.

+ =

diverse pathogen susceptible and immune hosts susceptible hosts

MMID 2018/2019 :: IHTM :: 6th February 2019

Multi-strain?

+ =

diverse pathogen susceptible and immune hosts susceptible hosts

+ =

diverse pathogen susceptible and immune hosts susceptible hosts

Multi-strain pathogens are agents that present genetic diversity which is ‘seen’ differently by the immune system. This sort of diversity is called antigenic diversity. For some pathogens, the immune system can cross-recognize antigenic variants (referred to as cross-immunity). Antigenic variants are generally referred to as strains.

cross-immunity

MMID 2018/2019 :: IHTM :: 6th February 2019

Strain theory: universal multi-strain population structures

Influenza A virus HIV-1 (within-host) Streptococcus pneumoniae Neisseria meningitidis Measles

MMID 2018/2019 :: IHTM :: 6th February 2019

Conceptualizing strains and cross-immunity

image DOI: 10.1016/j.rmu.2017.09.001

DENV CHIKV ZIKV

antigens genetic loci

Instead of defining a strain by its entire genome… A strain may be defined simply by the genetic loci that encode the antigens. The antigens are the targets of immunity.

MMID 2018/2019 :: IHTM :: 6th February 2019

Conceptualizing strains and cross-immunity

image DOI: 10.1016/j.rmu.2017.09.001

DENV CHIKV ZIKV

antigens genetic loci

Instead of defining a strain by its entire genome… A strain may be defined simply by the genetic loci that encode the antigens. The antigens are the targets of immunity. Shapes, letters, colours, are all great metaphors to understand antigens, their diversity and recognition by the immune system.

2 genetic loci are targets: locus TRIANGLE locus CIRCLE

antigens

existing diversity all possible strains (4 in total)

MMID 2018/2019 :: IHTM :: 6th February 2019

Conceptualizing strains and cross-immunity

Instead of defining a strain by its entire genome… A strain may be defined simply by the genetic loci that encode the antigens. The antigens are the targets of immunity. Shapes, letters, colours, are all great metaphors to understand antigens, their diversity and recognition by the immune system.

image DOI: 10.1016/j.rmu.2017.09.001 2 genetic loci are targets: locus TRIANGLE locus CIRCLE

DENV CHIKV ZIKV

antigens genetic loci antigens

existing diversity all possible strains (4 in total) Example: if the TRIANGLE locus is more diverse, then more strains are possible (6 in total)

MMID 2018/2019 :: IHTM :: 6th February 2019

X

Host susceptible Host infected infection with Host immune infection with

Infection with one strain is assumed to hold the basic SIR norms.

Conceptualizing strains and cross-immunity

MMID 2018/2019 :: IHTM :: 6th February 2019

X

Host susceptible Host infected infection with Host immune

infection with

X

Host infected Host infected Host immune Host immune Host immune full CI no or weak CI intermediate

• r high CI

+

transmission potential of strain

+

CI against strain

infection with

Infection with one strain is assumed to hold the basic SIR norms. But what happens when a host immune to one strain is challenged by another which shares an antigen? Depending on recognition, or cross-immunity (CI), the host will either be fully protected, partially protected or not protected at all. Such scenarios have consequences for the transmissibility of the host.

Conceptualizing strains and cross-immunity

? =

MMID 2018/2019 :: IHTM :: 6th February 2019

NSS: no strain structure

No cross-immunity. Strains go through a transient epidemic period and then settle (equilibrium), following an SIR-like behaviour. Because strains are not cross-recognized by hosts, they do not compete (for hosts), and are therefore expected to be equally successful at equilibrium.

line colours corresponding strains and antigens SIR-like epidemics equilibrium

MMID 2018/2019 :: IHTM :: 6th February 2019 SIR-like epidemics equilibrium

line colours corresponding strains and antigens line colours corresponding strains and antigens line colours corresponding strains and antigens

DSS: discrete strain structure

‘Complete’ cross-immunity. Strains that persist, follow an SIR-like behaviour. Some strains get extinct or become extremely rare.

MMID 2018/2019 :: IHTM :: 6th February 2019 SIR-like epidemics equilibrium

line colours corresponding strains and antigens line colours corresponding strains and antigens line colours corresponding strains and antigens

DSS: discrete strain structure

‘Complete’ cross-immunity. Strains that persist, follow an SIR-like behaviour. Some strains get extinct or become extremely rare. Because strains are well cross-recognized by hosts, natural infection works as natural vaccination to other strains. Strains that end up co-circulating at equilibrium, will have been selected to be antigenically as different as possible.

MMID 2018/2019 :: IHTM :: 6th February 2019

CSS: cyclic strain structure

‘Partial’ cross-immunity. All strains behave as if in the transient SIR-like epidemic behaviour. Because strains are partially cross-recognized by hosts, they compete (for hosts), but natural infection works as an ‘imperfect vaccination’ to other strains. When spreading, strains can become temporarily dominant, but can not suppress the spread of similar strains as in DSS.

NO equilibrium

MMID 2018/2019 :: IHTM :: 6th February 2019

Multi-strain dynamics and modelling

Multi-strain pathogens generally appear under 3 universal dynamic behaviours. A vast literature exists on strain-theory, framework behind it, and real world pathogen examples. We have developed an R-package (MANTIS) with which you can simulate multi-strain dynamic behaviours.