José Lourenço RESEARCH LECTURER IN INFECTIOUS DISEASES DEPARTMENT OF ZOOLOGY jose.lourenco@zoo.ox.ac.uk Mathematical modelling: from theory to practice changes in policy of intervention and control empirical mathematical data dynamic models advances in theory and ways of thinking MMID 2018/2019 :: IHTM :: 6th February 2019
1) The relationship of climate and the transmission We will cover the 3 potential of viruses such as dengue and Zika. topics we discussed before. 2) The dengue modelling initiative and its role on WHO’s We can have a break policy towards Dengvaxia Ⓡ . at any time. Please ask questions 3) Strain theory and its overarching impact on the fi elds during the lecture. of theoretical epidemiology and public health. MMID 2018/2019 :: IHTM :: 6th February 2019
José Lourenço RESEARCH LECTURER IN INFECTIOUS DISEASES DEPARTMENT OF ZOOLOGY jose.lourenco@zoo.ox.ac.uk The relationship of climate and the transmission potential of viruses such as dengue and Zika changes in policy of intervention and control empirical mathematical data dynamic models advances in theory and ways of thinking MMID 2018/2019 :: IHTM :: 6th February 2019
Real world complexity and control climate host-pathogen evolution vectors (e.g. vaccination) host mobility models. Most models we animal diversity social population reservoirs (pathogen / host) interactions develop and use are structure big simpli fi cations of the real world. These factors are generally interlinked, and many others exist. MMID 2018/2019 :: IHTM :: 6th February 2019
Real world complexity and control climate host-pathogen evolution vectors (e.g. vaccination) host mobility models. Most models we animal diversity social population reservoirs (pathogen / host) interactions develop and use are structure big simpli fi cations of the real world. These factors are generally interlinked, and many others exist. SIR-like models other types of real world models MMID 2018/2019 :: IHTM :: 6th February 2019
Island of Madeira Dengue Four antigenically distinct lineages (serotypes DENV1, DENV2, DENV3, DENV4). Classically endemic to with Southeast Asia, now Shepard et al. 2014 PLoS Neg Trop Dis generally found across all 10.1371/journal.pntd.0003306 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 Jie Alvin Tan et al. 2017 Kyle et al. 2008 Ann Rev Microbio Emerging Diseases viruses - but how? 10.1146/annurev.micro.62.081307.163005 MMID 2018/2019 :: IHTM :: 6th February 2019
Introduction of dengue on Madeira Island First case of DENV1 In just 3 months, more than 81 cases were was reported on the 2000 cases were reported exported and detected 3rd of October 2012. locally (N ~270.000). in mainland Europe. MMID 2018/2019 :: IHTM :: 6th February 2019
Introduction of dengue on Madeira Island First case of DENV1 In just 3 months, more than 81 cases were was reported on the 2000 cases were reported exported and detected 3rd of October 2012. locally (N ~270.000). in mainland Europe. Peak in autumn Sudden (end of October) start Extinction before next season (spring) December January 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 fi t to epidemic Model closely approximated the epidemic curve. MMID 2018/2019 :: IHTM :: 6th February 2019
Model fi t to Peak in autumn (end of October) epidemic Model closely approximated the epidemic curve. Peak, decline and extinction were reproduced at right Extinction before next timings. season (spring) Introduction was estimated to have taken place weeks before fi rst reported case. So, could the model help answer on what caused the decline? Reconstructed introduction, January December weeks before the fi rst reported case (no longer sudden start). MMID 2018/2019 :: IHTM :: 6th February 2019
Model fi t to Peak in autumn (end of October) epidemic Model closely approximated the epidemic curve. Peak, decline and extinction were reproduced at right timings. Introduction was estimated to have taken place weeks before fi rst reported case. So, could the model help answer on what caused the decline? Extinction Temperature in late autumn before next and winter! season (spring) December January 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 Mordecai et al. PLoS Neg Trop Dis 2017 doi.org/10.1371/journal.pntd.0005568 ● Altitude ● Humidity 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 of parameters which represent important Yang et al. Epidemiol Infect 2009 mosquito trait. doi:10.1017/S0950268809002040 MMID 2018/2019 :: IHTM :: 6th February 2019
Climate-trait oviposition rate adult death rate model parameters For mosquito traits which we think are relevant for a transmission model, we can therefore simply plug-in the derived mathematical expressions. aquatic death rate These are some examples. MMID 2018/2019 :: IHTM :: 6th February 2019
Temperature as a major determinant of R0 in Madeira Island R0 >1 was estimated for the period Outside this time period, the between June and October, when mosquitoes’ lifespan was shorter than temperature was essentially above 16C. the viral incubation period , thus R0 <1. MMID 2018/2019 :: IHTM :: 6th February 2019
Lessons from this case study “Food for thought” Climate factors affect mosquito Climate explains much of the life-traits, which in turn affect the geographical variation in transmission transmission of mosquito-borne success of mosquito-borne viruses viruses. across the world. We understand the relationships of climate factors with mosquito What if we do not have the epidemic life-traits ⇒ we can plug-in these curve? relationships into models. Can we evaluate transmission potential Fitting a climate-driven model to an before epidemics occur? (instead of epidemic curve can help us retrospectively looking back at an epidemic that already occurred and try to understand it?) understand the success or demise of mosquito-borne viruses. 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
climate dependent Deriving the index P M R0 is the number of secondary infections expected from a single infection in a totally susceptible population. MMID 2018/2019 :: IHTM :: 6th February 2019
climate dependent Deriving the index P M R0 is the number of secondary infections expected from a single infection in a totally Total number of female mosquitoes V, divided by total number of humans (M = V/ N). susceptible population. M is the number of female mosquitoes per human. MMID 2018/2019 :: IHTM :: 6th February 2019
climate dependent Deriving the index P M R0 is the number of secondary infections expected from a single infection in a totally Total number of female mosquitoes V, divided by total number of humans (M = V/ N). susceptible population. temperature dependent M is the number of female M mosquitoes per human. R0 is humidity (u) and temperature (t) dependent MMID 2018/2019 :: IHTM :: 6th February 2019
climate dependent Deriving the index P M R0 is the number of secondary infections expected from a single infection in a totally Total number of female mosquitoes V, divided by total number of humans (M = V/ N). susceptible population. temperature dependent M is the number of female M mosquitoes per human. R0 is humidity (u) and temperature (t) dependent MMID 2018/2019 :: IHTM :: 6th February 2019
climate dependent Deriving the index P M R0 is the number of secondary infections expected from a single infection in a totally Total number of female mosquitoes V, divided by total number of humans (M = V/ N). susceptible population. temperature dependent M is the number of female M mosquitoes per human. P is the transmission R0 is humidity (u) and temperature (t) dependent potential of each existing female mosquito per human. P is humidity (u) and temperature (t) dependent. 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
Recommend
More recommend
