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DSABNS 2020
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DSABNS
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The 11th International Conference DSABNS was held at the Dipartimento di Economia e Management of University of Trento, in Italy, from 4-7 February, 2020. The conference has both theoretical methods and practical applications, covering research topics in population dynamics, epidemiology of infectious dis-eases, eco-epidemiology, molecular and antigenic evolution and methodological topics in the natural sciences and mathematics.
Local Organizers: Ma´ıra Aguiar, UniTN & BCAM; Giorgio Guzzetta, FBK; Mattia Manica, FEM; Giovanni Marini,FEM; Valentina Marziano, FBK; Stefania Ottaviano, UniTN; Piero Poletti, FBK; Andrea Pugliese, UniTN; Federico Reali, UniTN; Roberto Ros, UniTN; Mattia Sensi, UniTN; Filippo Trentini, FBK. International Organizers: Carlos Braumann, UE; Mimmo Iannelli, UniTN; Bob Kooi, VU; Paula Patr´ıcio; UNL; Nico Stollenwerk, UL; Ezio Venturino, UT. Administration Staff: Luca Valenzin, UniTN; Lara Fiamozzini, UniTN.
NB. UniTN: Universit`a degli Studi di Trento, Italy; BCAM: Basque Center for Applied Mathematics, Basque Country, Spain; FBK: Fondazione Bruno Kessler;
FEM: Fondazione Edmund Mach; UE: Universidade de ´Evora, Portugal; VU:
Vrije Universiteit Amsterdam, The Netherlands; UNL: Universidade Nova de Lis-boa, Portugal; UL: Universidade de LisLis-boa, Portugal; UT: Universit`a degli Studi di Torino, Italy.
Sponsors: The organizers are grateful for the sponsorship and support of the Universit`a degli Studi di Trento and its Dipartimento di Economia e Manage-ment, who have hosted the Conference. We thank the European Union’s Hori-zon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement with No 792494, the European Society for Mathematical and
Theoretical Biology (ESMTB), the Basque Center for Applied Mathematics (BCAM)
and the Universit`a degli Studi di Torino for funding, along with the Gruppo Nazionale
per l’Analisi Matematica, la Probabilit`a e le loro Applicazioni (GNAMPA), as well
as the SurvEthi project which is co-funded by the Autonomous Province of Trento and the Italian Agency for Development Cooperation.
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H IN T S F R O M B E H A V IO U R A L E P ID E M IO L O G Y R O S S A N A V E R M IG L IO N U M E R IC A L A P P R O X IM A T IO N O F T H E B A S IC R E P R O D U C T IO N N U M B E R F O R S T R U C T U R E D P O P U L A T IO N S E Z IO V E N T U R IN O D Y N A M IC S O F H S V -2 I N F E C T IO N W IT H A T H E R A P E U T IC V A C C IN E R o s s e ll a D e ll a M a rc a R A P ID V A C C IN E O P IN IO N S W IT C H IN G : O P T IM A L A W A R E N E S S C A M P A IG N S V IA D E T E R M IN IS T IC A N D H E U R IS T IC A L G O R IT H M S P E R IO D IC IT Y , D E L A Y S A N D N U M E R IC A L M E T H O D S IN B IO M A T H E M A T IC S : A R E C E N T A C C O U N T T W O -L E V E L E V O L U T IO N O F C H R O N IC V IR A L IN F E C T IO N S A N D T H E E F F E C T O F T H E P O P U L A T IO N -L E V E L C O N T R O L M A T H E M A T IC A L M O D E L IN G O F P U B L IC H E A L T H P O L IC IE S B ru n o M . P . M . O li v e ir a F IT O F I M M U N E R E S P O N S E S B Y C D 4 + T C E L L S T R IG G E R E D B Y L C M V I N F E C T IO N P E R IO D IC V A C C IN A T IO N S T R A T E G IE S I N T H E R E IN F E C T IO N S IR I M O D E L O th m a n C h e rk a o u i D e k k a k i V IA B IL IT Y A N A L Y S IS F O R A S T O C K -C A P IT A L F IS H E R Y M O D E L J o ã o M a u rí c io d e C a rv a lh o C A N C E R D Y N A M IC S I N H IV I N F E C T E D P A T IE N T S U N D E R D IF F E R E N T I M M U N E F U N C T IO N S IN C O R P O R A T IO N O F A W A R E N E S S P R O G R A M S I N T O A M O D E L O F T H E S P R E A D O F H IV /A ID S A M O N G S T P E O P L E W H O I N J E C T D R U G S ( P W ID s ) A L L E E E F F E C T B IF U R C A T IO N I N T H E γ -R IC K E R P O P U L A T IO N M O D E L U S IN G T H E L A M B E R T W F U N C T IO N S o n ja R a d o s a v lj e v ic O P T IM A L C O N T R O L P R O B L E M O F IN F L U E N Z A M O D E L S W IT H I N E Q U A L IT Y C O N S T R A IN T S N O N -L O C A L B O U N D A R Y C O N D IT IO N I N A C O M P U T A T IO N A L D O M A IN O F E X T E R IO R P R O B L E M S A D E L A Y D IF F E R E N T IA L E Q U A T IO N S M O D E L F O R T H E A C T IO N O F T H E I M M U N E S Y S T E M IN M A L A R IA R E B E C C A T Y S O N P H A S E -S E N S IT IV E C R IT IC A L T R A N S IT IO N S IN P R E D A T O R -P R E Y S Y S T E M S “ M a th e m a ti c a l E p id e m io lo g y / V e c to r s a n d V e c to r -b o r n e D is e a s e s I I” C h a ir : P ie r r e -A le x a n d r e B li m a n “ M a th e m a ti c a l E p id e m io lo g y / M o d e ls f o r S o c ia l B e h a v io r ” C h a ir : P a o lo F r e g u g li a “ M a th e m a ti c a l M o d e ls i n P o p u la ti o n B io lo g y / P r e d a to r -P r e y S y s te m s ” C h a ir : A n g e la M a r ti r a d o n n a E D Y S O E W O N O C A U S A L IT Y A N A L Y S IS O F D E N G U E T R A N S M IS S IO N I N B A N D U N G , IN D O N E S IA A L B E R T O D ’O N O F R IO B E H A V IO U R I N D U C E D P H A S E T R A N S IT IO N S I N E P ID E M IO L O G Y O F I N F E C T IO U S D IS E A S E S C H R IS T IA N K U E H N M O D E R N N U M E R IC A L C O N T IN U A T IO N M E T H O D S F O R B IO L O G IC A L S Y S T E M S M a h m o u d Ib ra h im T H R E S H O L D D Y N A M IC S I N A P E R IO D IC M O D E L F O R Z IK A V IR U S D IS E A S E R E IN F E C T IO N T H R E S H O L D S D E T E R M IN E D B Y T H E M A X IM U M C U R V A T U R E O F T H E E N D E M IC S T A T E H a m le t C a s ti ll o A lv in o IN T E R F E R E N C E C O M P E T IT IO N O N G R O U P D E F E N S E W IT H H O L L IN G T Y P E I V C O M P E T IT IV E R E S P O N S E J a i P ra k a s h T ri p a th i A S O C IA L I N T E R A C T IO N M O D E L W IT H H O L L IN G T Y P E I I F U N C T IO N A L R E S P O N S E P ra s h a n t K .S ri v a s ta v a IM P A C T O F I N F O R M A T IO N O N T R E A T M E N T A S W E L L A S O N D IS E A S E D Y N A M IC S O k s a n a R e v u ts k a y a C O M P L E X D Y N A M IC S O F D IS C R E T E -T IM E P R E D A T O R -P R E Y S Y S T E M W IT H S T A G E -S T R U C T U R E D P R E Y U rs z u la S k w a ra N U M E R IC A L A S P E C T S I N M A T H E M A T IC A L M O D E L L IN G O F V E C T O R -B O R N E D IS E A S E S O P T IM A L S T R A T E G IE S M IN IM IZ IN G T H E C O N T R O L O P E R A T IO N C O S T S I N B IO C E L L C O M P O S T IN G D Y N A M IC A L B E H A V IO R O F P R E D A T O R -P R E Y M O D E L S U B J E C T E D T O A L L E E E F F E C T I N T H E P R E D A T O R M O D E L IN G T H E I M P A C T O F E A R L Y C A S E D E T E C T IO N O N D E N G U E T R A N S M IS S IO N : D E T E R M IN IS T IC V S S T O C H A S T IC R o m in a T ra v a g li n i A N O P T IM A L C O N T R O L P R O B L E M F O R D E G R A D A T IO N O F W A S T E I N L A N D F IL L S U N D E R A N A E R O B IC C O N D IT IO N S P a rt h a S a ra th i M a n d a l IM P A C T O F A D D IT IV E A L L E E E F F E C T O N T H E D Y N A M IC S O F A I N T R A G U IL D P R E D A T IO N M O D E L W IT H S P E C IA L IS T P R E D A T O R IN D IV ID U A L D E B -B A S E D S T R U C T U R E D P O P U L A T IO N M O D E L IN G D S A B N S 2 0 2 0 D S A B N S 2 0 2 0
A u la A z z u rr a A u la 2 B A u la 2 C 0 8 :4 5 – 9 :0 0 R e gi s tra ti o n C h a ir : B o b W . K o o i 0 9 :0 0 – 0 9 :4 5 --0 9 :4 5 – 1 0 :3 0 M A ÍR A A G U IA R --1 0 :3 0 – 1 1 :0 0 C o ff e e B re a k “ M u lt i-S c a le S y s te m s ” C h a ir : D im it ri B re d a 1 1 :0 0 – 1 1 :3 0 P A U L O D O U T O R A E D E S A E G Y P T I A N D W O L B A C H IA I N T E R A C T IO N 1 1 :3 0 – 1 1 :5 0 F a b io M iln e r 1 1 :5 0 – 1 2 :1 0 G iu lia S im o n i A lb e rt o B e rs a n i 1 2 :1 0 – 1 2 :3 0 E ri c a I p o c o a n a 1 2 :3 0 – 1 2 :5 0 S te fa n S c h u s te r M a tt ia S e n s i 1 2 :5 0 – 1 4 :0 0 L u n c h --1 4 :0 0 – 1 4 :3 0 S A R A P A S Q U A L I --1 4 :3 0 – 1 4 :5 0 A n n a lis a I u o ri o --1 4 :5 0 – 1 5 :1 0 F a b io T e d o n e --1 5 :1 0 – 1 5 :3 0 In d ra jit G h o s h --1 5 :3 0 – 1 6 :1 5 R O U N D T A B L E N o v e l C o ro n a v ir u s ( 2 0 1 9 -n C o V ) --1 6 :1 5 – 1 6 :3 0 C lo s in g F E B R U A R Y 7 th 2 0 2 0 C O N S T A N T IN O S S IE T T O S C A N D Y N A M IC A L M O D E L S I N B IO L O G Y A N D N A T U R A L S C IE N C E S G O B E Y O N D I N F IN IT Y ? O N T H E O R IG IN O F C O M P L E X D Y N A M IC S I N M U LT I-S T R A IN D E N G U E M O D E L S “ M a th e m a ti c a l E p id e m io lo g y / P h y s io lo g ic a l M o d e ls ” C h a ir : P a u la P a tr íc io “ M a th e m a ti c a l E p id e m io lo g y / G e n e ti c s ” C h a ir : H e ik k i H a a ri o D E L A Y IN G A G E O F I N F E C T IO N : A P E R N IC IO U S E F F E C T O F V A C C IN A T IO N N IC O S T O L L E N W E R K T IM E S C A L E S E P A R A T IO N : C O M P A R IS O N O F S IN G U L A R P E R T U R B A T IO N A N D C E N T E R M A N IF O L D A N A LY S IS U N D E R S C A L IN G C L A U D IA F E R R E IR A A M O D E L F O R A C U T E M Y E L O ID L E U K E M IA (A M L ) P a n a g io ti s P a p a io a n n o u F O R E X F O R E C A S T IN G U S IN G P R IN C IP A L C O M P O N E N T A N A LY S IS A N D L O C A L L IN E A R E M B E D D IN G M a n u e l M o lin a M A T H E M A T IC A L M O D E L IN G O F P O P U L A T IO N D Y N A M IC S I N B IO L O G IC A L S P E C IE S P O P U L A T IO N -B A S E D A N D P A T IE N T -S T R A T IF IC A T IO N A P P R O A C H E S A P P L IE D T O A H U M A N C A R D IA C M O D E L O F E L E C T R O P H Y S IO L O G Y S IN G U L A R P E R T U R B A T IO N T E C H N IQ U E S A N D A S Y M P T O T IC E X P A N S IO N S F O R A U X IL IA R Y E N Z Y M E R E A C T IO N S To rs te n L in d s tr ö m D E S T A B IL IZ A T IO N , S T A B IL IZ A T IO N , A N D M U LT IP L E A T T R A C T O R S I N S A T U R A T E D M IX O T R O P H IC E N V IR O N M E N T S B R E A T H IN G A S A P E R IO D IC G A S E X C H A N G E IN A D E F O R M A B L E P O R O U S M E D IU M E v a n g e lo s G a la ri s U S IN G D A T A M IN IN G T O C O N S T R U C T D Y N A M IC A L E Q U A T IO N S F R O M A G E N T -B A S E D P E D E S T R IA N S IM U L A T O R S O k s a n a Z h d a n o v a M A T H E M A T IC A L M O D E L L IN G O F S E L E C T IO N B Y A S E X -L IM IT E D F E M A L E T R A IT : T O T H E Q U E S T IO N O F L IT T E R S IZ E P O LY M O R P H IS M I N N A T U R A L P O P U L A T IO N S O F A R C T IC F O X E S J E N S E N ’S I N E Q U A L IT Y A S A T O O L F O R E X P L A IN IN G T H E E F F E C T O F O S C IL L A T IO N S O N T H E A V E R A G E V A L U E S O F V A R IA B L E S A G S P T A P P R O A C H T O E P ID E M IC S O N H O M O G E N E O U S G R A P H S T a ti a n a G u s e v a H O M E O B O X G E N E S : IN V E S T IG A T IN G T H E D E V E L O P M E N T O F P IN U S S Y LV E S T R IS ( S C O T S P IN E ) “ P o p u la ti o n B io lo g y / P la n t D y n a m ic s ” C h a ir : M im m o Ia n n e ll i “ M a th e m a ti c a l E p id e m io lo g y / D is e a s e C o n tr o l” C h a ir : P ie ro P o le tt i A S T A G E S T R U C T U R E D D E M O G R A P H IC M O D E L F O R I N S E C T P E S T D Y N A M IC S G IO V A N N I P U T O T O U S IN G D IG IT A L M E T H O D S I N E P ID E M IO L O G Y T O A D D R E S S D IS E A S E C O N T R O L IN S U B S A H A R A N A F R IC A : E X P E R IE N C E S A N D P E R S P E C T IV E S O F D O C T O R S W IT H A F R IC A C U A M M M O D E L L IN G C O M P E T IT IV E I N T E R A C T IO N S A N D P L A N T -S O IL F E E D B A C K I N V E G E T A T IO N D Y N A M IC S M a rg h e ri ta G a lli E F F E C T IV E N E S S O F M E A S L E S S U R V E IL L A N C E I N S O U T H W E S T S H O A Z O N E O F T H E O R O M IA R E G IO N , E T H IO P IA M O D E L L IN G T H E R O O T G R O W T H : A N O P T IM A L C O N T R O L A P P R O A C H T O L IN K B IO L O G Y A N D R O B O T IC S V a le n ti n a V e ro n e s i M O D E L IN G T H E I N F L U E N C E O F M A L N U T R IT IO N O N M E A S L E S E P ID E M IO L O G Y I N E T H IO P IA E S T IM A T IN G T H E P R O P O R T IO N O F S E X U A L T R A N S M IS S IO N O N Z IK A V IR U S S P R E A D A b h is h e k S e n a p a ti E F F E C T O F A D U LT M O S Q U IT O C O N T R O L O N D E N G U E P R E V A L E N C E I N A M U LT I-P A T C H S E T T IN G : A C A S E S T U D Y I N K O L K A T A ( 2 0 1 4 – 2 0 1 5 ) C h a ir s :A n d re a P u g li e s e , P ie ro M a n fr e d i a n d C o n s ta n ti n o s S ie tt o s D S A B N S 2 0 2 0 D S A B N S 2 0 2 0
11th I
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INCORPORATING MATHEMATICAL MODELS
AND BIOCONTROL INTO IPM PROGRAMS FOR
INVASIVE ALIEN INSECTS
Gianfranco Anfora
∗1,2,
Andrea Pugliese
3, Livia Zapponi
1,
Marco Valerio Rossi Stacconi
1,4and Claudio Ioriatti
51Research and Innovation Centre,
Fondazione Edmund Mach (FEM),
via E. Mach 1, 38010, San Michele allAdige (TN), Italy
2Centre Agriculture Food Environment (C3A),
University of Trento,
via E. Mach 1, 38010, San Michele allAdige (TN), Italy
3Department of Mathematics, University of Trento,
via Sommarive, 14, Povo, Italy
4Department of Horticulture, Oregon State University,
Corvallis, OR 97331
5Technological Transfer Centre,
Fondazione Edmund Mach (FEM),
via E. Mach 1, 38010, San Michele allAdige (TN), Italy
[email protected] (*corresponding author)
Biological invasions are now considered a major form of human-induced global change, due to trade globalization and the increasing movements of people, goods and vehicles, combined with climatic and environmental variability. In particu-lar, climate change is expected to favour the spread of several species also toward higher altitudes and latitudes. The spotted wing drosophila Drosophila suzukii and the brown marmorated stink bug Halyomorpha halys, both native to Asia, are polyphagous insects with a broad climate range tolerance, facility to passive trans-portation and a high invasive potential. They became noxious crop pests anywhere introduced, causing heavy economic losses, and represent a serious threat for agri-culture in Trento Province. Since their first detection in Trentino, many efforts have been made to develop nontoxic effective management strategies, nonethe-less chemical control remains the principal tool used by farmers to reduce the pest population. There are a number of drawbacks associated with the massive use of pesticides, including increased risk of residues on fruit, worker safety reduction
and ecological imbalances resulting in secondary pest outbreaks. Moreover, the use of broad-spectrum chemistries jeopardizes the results obtained with IPM on cultivated fruits. In this context, the development of alternative control methods appears urgent to ensure an economic future for the concerned fruit industry. Pos-sible solutions would only arise from a multidisciplinary approach, from genetics to biological control and mathematical population models, aiming at understand-ing the fundamental aspects of the ecology of these pests and pavunderstand-ing the way for implementing effective and sustainable control strategies. In particular, for D.
suzukiiwe have characterized the life history traits of the pest and the population
structure after key bottleneck periods, such as winter diapause, in order to bet-ter predict serious outbreaks and improve the effectiveness of pest management decisions. We also evaluated the potentiality of the D. suzukii indigenous para-sitoids in open field and semi-field conditions, and the effectiveness of different biocontrol techniques. A similar approach is ongoing also for H. halys, for which adventive populations of the native parasitoids have been recently found in our territory.
40 YEARS OF DEVELOPMENT AND
APPLICATION OF DYNAMIC ENERGY
BUDGET THEORY
S. A. L. M. Kooijman
∗and
B. W. Kooi
VU University Amsterdam
[email protected] (*corresponding author), [email protected]
I started to develop Dynamic Energy Budget (DEB) theory (8) in 1979, with the aim to apply it in physiologically-structured population models for any species of organism on earth (micro-organisms, plants, animals) and evaluate effects of toxicants at the population level, modelled as dynamic changes in (particular toxicant-specific) parameter values. The research program radiated substantially over time to ensure coherence with physiology, ecology and evolution (6; 11), involving many co-workers. Metabolic transformations and behaviour are taken into account by Synthesizing Units (5), that exploit the principle of time conser-vation within the class of Markov processes, while a food-depending aging mod-ule (12; 13) specifies the bottom-line exit dynamics. Attention has been given to a wide range of topics, such as surface area-volume relationships, cytoplasm-mitochondria interactions, organ size and function dynamics, including tumour development, isotope dynamics, mixotrophy, parasitism and symbiosis. A large number of popular seemingly-unrelated empirical models turn out to be special cases of DEB theory, or very good numerical approximations, such a Kleiber’s “law” (1932), stating that respiration is proportional to body weight to the power of (about) 3/4, and Lavoisier’s indirect calorimetry (1780), stating that heat pro-duction equals a weighted sum of dioxygen consumption and carbon dioxide and nitrogen-waste production. This is remarkable, since DEB theory makes no direct assumption about respiration, but still specifies it (and water dynamics) by closing the balances for chemical elements. Being firmly based on mass and energy con-servation and other thermodynamic principles (20), I discuss arguments to expect that DEB theory will have no alternatives with a similar level of generality and simplicity (14). Simplicity is required for testing generality, due to practical limi-tations on data availability, and even the present level of simplicity motivated the development of advanced parameter estimation methods (18; 17). At the same, such a theory must be detailed enough to respect biodiversity for links to
evo-lution; a fine balance indeed. Meanwhile some 850 publications (3) have been written about the theory and its applications by a rapidly expanding community of research workers from all over the world. The Add-my-Pet collection (1) of data, parameters and implied properties has been set up to test the generality of the theory for animals. This collection now has over 2000 species from all larger animal phyla; model predictions for some 3e4 data sets have a mean relative error of 0.07, supporting the generality of the theory. Apart from a priory predictable patterns in the co-variation of parameter values on plain physical grounds (4), pat-terns have been identified that relate to ecological and evolutionary adaptations, such as metabolic acceleration (9), ‘waste-to-hurry’(8), supply-demand (15) and altricial-precocial spectra (1). We also found explanations for some remarkable findings, such as why the allocation fraction of mobilised reserve to soma follows a beta-distribution among animal species, with perplexing accuracy (16). The mean value of this parameter of all species is larger than 0.9, while a value around 0.45 maximizes reproductive output (10). My expectation is that DEB theory will eventually affect the way we think about ecology and evolution, in satisfying har-mony with an army of early workers in this field (19).
References
[1] Augustine, S. and Lika, K. and Kooijman, S. A. L. M. (2011). Altricial-precocial spectra in animal kingdom.Journal of Sea Research, 143, 27–34.
[2] Anonymous. (2019). Add-my-Pet https://www.bio.vu.nl/thb/deb/deblab/add my pet/.
[3] Anonymous. (2019). Zotero https://www.zotero.org/groups/500643/deb library/.
[4] Kooijman, S. A. L. M. (1986). Energy budgets can explain body size relations. Journal of Thereotical Biology, 121, 269–282.
[5] Kooijman, S. A. L. M. (1998). The Synthesizing Unit as model for the stoichiometric fusion and branching of metabolic fluxes..Biophysical Chemistry, 73, 179–188.
[6] Kooijman, S. A. L. M. (2004). On the coevolution of life and its environment.. In: Schneider, S.H., Miller, J. P., Crist, E. and Boston, P. J. (eds) Scientists Debate Gaia; the next century.Cambridge, Mass: MIT Press.
[7] Kooijman, S. A. L. M. (2010). Dynamic Energy Budget Theory for Metabolic Or-ganisation. 3rd edition. Cambridge: Cambridge University Press.
[8] Kooijman, S. A. L. M. (2013). Waste to hurry: Dynamic Energy Budgets explain the need of wasting to fully exploit blooming resources.Oikos, 122, 348–357.
[9] Kooijman, S. A. L. M. (2014). Metabolic acceleration in animal ontogeny: An evo-lutionary perspective.Journal of Sea Research, 94, 128–137.
[10] Kooijman, S. A. L. M. and Lika, K. (2014). Resource allocation to reproduction in animals.Biological Reviews, 89, 849–859.
[11] Kooijman, S. A. L. M. and Troost, T. A. (2007). Quantitative steps in the evolu-tion of metabolic organisaevolu-tion as specified by the Dynamic Energy Budget theory. Biological Reviews, 82, 1–30.
[12] Leeuwen, I. M. M. and Kelpin, F. D. L. and Kooijman, S. A. L. M. (2002). A mathe-matical model that accounts for the effects of caloric restriction on body weight and longevity.Biogerontology, 3, 373–381.
[13] Leeuwen, I. M. M. and Vera, J. and Wolkenhauer, O. (2010). Dynamic Energy Bud-get approaches for modelling organismal ageing.Philosophical Transactions of the Royal Society B, 365, 3443–3454.
[14] Lika, K. and Kooijman, S. A. L. M. (2011). The comparative topology of energy allocation in budget models.Journal of Sea Research, 66, 381–391.
[15] Lika, K. and Augustine, S. and Pecquerie, L. and Kooijman, S. A. L. M. (2011). The bijection from data to parameter space with the standard DEB model quantifies the supply-demand spectrum.Journal of Theoretical Biology, 354, 35–47.
[16] Lika, K. and Augustine, S. and Kooijman, S. A. L. M. (2011). Body size as emergent property of metabolism.Journal of Sea Research, 143, 8–17.
[17] Lika, K. and Augustine, S. and Kooijman, S. A. L. M. (2011). The use of augmented loss functions for estimating Dynamic Energy Budget parameters.Ecological mod-elling, in preparation.
[18] Marques, G. M. and Lika, K. and Augustine, S. and Pequerie, L. and Kooijman, S. A. L. M. (2019). Fitting Multiple Models to Mutiple Data Sets. Journal of Sea Research, 143, 48–56.
[19] Sousa, T. and Domingos, T. and Poggiale, J. C. and Kooijman, S. A. L. M. (2006). The thermodynamics of organisms in the context of DEB theory. Philosophical Transactions of the Royal Society B, 365, 3433–3428.
[20] Sousa, T. and Mota, R. and Domingos, T. and Kooijman, S. A. L. M. (2006). For-malised DEB theory restores coherence in core biology. Physical Reviews E, 74, 1–15.
11th I
NTERNATIONAL
C
ONFERENCE
D
YNAMICAL
S
YSTEMS
A
PPLIED TO
B
IOLOGY
AND
N
ATURAL
S
CIENCES
PLENARY TALKS
D
IPARTIMENTO DI
E
CONOMIA E
M
ANAGEMENT
U
NIVERSITY OF
T
RENTO
, I
TALY
c
ON THE ORIGIN OF COMPLEX DYNAMICS IN
MULTI-STRAIN DENGUE MODELS
Ma´ıra Aguiar
1,2,31Dipartimento di Matematica, Universit`a degli Studi di Trento
Via Sommarive, 14 - 38123 Povo (Trento), Italy
2Basque Center for Applied Mathematics (BCAM)
Alameda Mazarredo, 14 - 49008 Bilbao, Spain
3Ikerbasque, Basque Foundation for Science, Bilbao, Spain
Dengue fever epidemiological dynamics shows large fluctuations in disease in-cidence, and several mathematical models describing the transmission of dengue viruses have been proposed to explain the irregular behavior of dengue epidemics. Multi-strain dengue models are often modelled with SIR-type models where the SIR classes are labeled for the hosts that have seen the individual strains. The ex-tended models show complex dynamics and qualitatively a very good result when comparing empirical data and model simulations. However, modeling insights for epidemiological scenarios characterized by chaotic dynamics, such as for dengue fever epidemiology, have been largely unexplored. The problem is mathematically difficult and to make the urgently needed progress in our understanding of such dynamics, concepts from various fields of mathematics as well the availability of good data for model evaluation are needed.
In this talk, I will present a set of models motivated by dengue fever epidemiol-ogy and compare different dynamical behaviors originated when increasing com-plexity into the model framework.
Acknowledgements
This work has received funding from the European Unions Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 792494.
STOCHASTIC AND TIME-DELAYED EFFECTS
IN AUTOIMMUNE DYNAMICS
Konstantin B. Blyuss
∗1,
Farzad Fatehi
2and Yuliya N. Kyrychko
11Department of Mathematics, University of Sussex,
Falmer, BN1 9QH, United Kingdom
2Department of Mathematics, University of York,
York, YO10 5DD, United Kingdom
[email protected] (*corresponding author)
Among various causes of autoimmunity, a particularly important role is played by infections that can lead to a breakdown of immune tolerance. In this talk, I will discuss a model of immune response to a viral infection, and subsequent onset of autoimmunity, with particular account for cytokines and different types of T cells. Of particular biological relevance is the analysis of stochastic oscillations around deterministically stable states, as well as the effects of stochasticity on dynamics of the system in a bi-stable regime. I will show how variance of stochastic fluctu-ations and their coherence depend on system parameters (1). To make the model more realistic, it is important to also consider the effects of time delays associated with various processes involved in the development of immune response. I will discuss a method for deriving stochastic delayed differential equations and a cor-responding numerical simulation algorithm, and will show how it can be used to simulate stochastic dynamics in a time-delayed model of autoimmunity (2).
References
[1] Fatehi, F., Kyrychko, S. N., Ross, A., Kyrychko, Y. N., & Blyuss, K. B. (2018). Stochastic effects in autoimmune dynamics. Frontiers in Physiology, 9, 45. https://doi.org/10.3389/fphys.2018.00045
[2] Fatehi, F., Kyrychko, Y. N., & Blyuss, K. B. (2019). Stochastic dynamics in a time-delayed model for autoimmunity. Submitted.
OSCILLATING SYSTEMS WITH COINTEGRATED
PHASE PROCESSES
Jacob Østergaard
1, Anders Rahbek
2and
Susanne Ditlevsen
∗11Department of Mathematical Sciences,
University of Copenhagen
2Department of Economy,
University of Copenhagen
[email protected] (*corresponding author)
I will present cointegration analysis (2; 2) as a method to infer the network structure of a linearly phase coupled oscillating system. By defining a class of oscillating systems with interacting phases, a data generating process is derived with a specified coupling structure of the network that resembles biological pro-cesses. In particular we study a network of Winfree oscillators (3), for which we present a statistical analysis of various simulated networks, where we conclude on the coupling structure: the direction of feedback in the phase processes and proportional coupling strength between individual components of the system. We show that we can correctly classify the network structure for such a system by cointegration analysis, for various types of coupling, including uni-/bi-directional and all-to-all coupling. I will also touch upon how to deal with high-dimensional systems. Finally, we analyze a set of EEG recordings and discuss the current ap-plicability of cointegration analysis in the field of neuroscience. The talk is based on the papers (1; 4).
References
[1] Granger, C. (1981). Some properties of time series data and their use in econometric model specification. Journal of Econometrics, 16(1):121–130.
[2] Johansen, S. (1996). Likelihood-based inference in cointegrated vector autoregres-sive models. Oxford University Press, Oxford.
[3] Winfree, A.T. (1967). Biological rhythms and the behavior of populations of cou-pled oscillators. Journal of Theoretical Biology, 16(1):15–42.
[4] Østergaard, J., Rahbek, A. & Ditlevsen, S. (2017). Oscillating systems with cointe-grated phase processes. Journal of Mathematical Biology, 75(4), 845–883.
[5] Østergaard, J., Rahbek, A. & Ditlevsen, S. (2019). Cointegration analysis of high-dimensional linear Kuramoto networks. Soon to be submitted.
INDIVIDUAL DEB-BASED STRUCTURED
POPULATION MODELING
B. W. Kooi
∗and S. A. L. M. Kooijman
Faculty of Science, VU University,
de Boelelaan 1087,1081 HV Amsterdam, The Netherlands [email protected] (*corresponding author), [email protected]
In unstructured or compartmental population models the state of the popula-tion is described by one or a set of ordinary differential equapopula-tions for one or a few scalar variables as a function of time. Examples are number of individuals or total biomass. In structured models time depending individual variables such as age, size, mass or energy content are taken into account (10). The dependent variables that describe the state of the population and are not scalars but a density function of these independent of all the individuals that make up the population. They can be considered as emerging properties of the group of co-specific individuals living an a bounded spatial homogeneous well-mixed environment.
The individual model used is the DEB model described in (8; 7). The Add-my-Pet collection (1) contains estimated parameters of over 2000 species from all larger animal phyla. Besides age, structural biovolume, energy reserves and maturation are the individuals state variables.
The population model will be formulated for the whole life-cycle consisting of three life-stages: embryo, juvenile and adult including the criteria for the tran-sitions, like in the physiologically structured populations approach (11). We will assume that reproduction occurs simultaneously for all individuals and periodi-cally, for instance with fish populations as a specific short period of the year with spawning related to mating success but also by food availability for the offspring. The resulting model is called the Cohort Projection Model (CPM) since each individual lives in one cohort as a group of individuals that are born at the same time. It is related to a projection matrix formulation, especially the Integral Projec-tion Model (IPM) (2; 9) method which is intermediately between the continuous-time and the well known discrete matrix projection model. Recently in (12) this approach was applied based on a previous version of the DEB model.
The CPM-method was already used in (5; 6) with the DEB model for asexual microorganisms having one juvenile life stage that propagate by binary fission in (4; 3). In a case study the results for the marbled electric ray fish Torpedo
marmoratapopulation are shown where all model parameter values are taken from
References
[1] Anonymous. (2019). Add-my-Pet https://www.bio.vu.nl/thb/deb/deblab/add my pet/.
[2] M. R. Easterling, S. P. Ellner, and P. M. Dixon. Size-specific sensitivity: Applying a new structured population model. Ecology, 81(3):694–708, 2000.
[3] B. W. Kooi and S. A. L. M. Kooijman. Discrete event versus continuous approach to reproduction in structured population dynamics. Theoretical Population Biology, 56(1):91–105, 1999.
[4] B. W. Kooi and S. A. L. M. Kooijman. Existence and Stability of Microbial Prey-Predator Systems. Journal Theoretical Biology, 170:75–85, 1994.
[5] B. W. Kooi, T. G. Hallam, F. D. L. Kelpin, C. M. Krohn, and S. A. L. M. Kooi-jman. Iteroparous reproduction strategies and population dynamics. Bulletin of Mathematical Biology, 63(4):769–794, 2001.
[6] B. W. Kooi and J. van der Meer. Bifurcation theory, adaptive dynamics and dynamic energy budget-structured populations of iteroparous species. Philos T Roy Soc B, 365:3523–3530, 2010.
[7] S. A. L. M. Kooijman. 40 Years of development and application of dynamic energy budget theory. 11th Workshop Dynamical Systems Applied to Biology and Natural Sciences DSABNS 2020.
[8] S. A. L. M. Kooijman. Dynamic Energy Budget theory for metabolic organisation. Cambridge University Press, 2010.
[9] C. Merow, J. Dahlgren, C. Jessica, E. Metcalf, D. Z. Childs, M. E. K. Evans, E. Jongejans, S. Record, M. Rees, R. Salguero-G´omez, and S. M. McMahon. Advancing population ecology with integral projection models: a practical guide. Methods in Ecology and Evolution, 5(2):99–110, 2014.
[10] J. A. J. Metz and O. Diekmann. The dynamics of physiologically structured pop-ulations, volume 68 of Lecture Notes in Biomathematics. Springer-Verlag, Berlin, 1986.
[11] A. M. de Roos. A gentle introduction to physiologically structured population mod-els. in: S. Tuljapurkar and H. Caswell Structured-Population models in marine, terrestrial, and freshwater systemspp. 119-204 Chapman & Hall, New York, 1997.
[12] I. M. Smallegange, H. Caswell, M. E. M. Toorians, and A. M. de Roos. Mechanistic description of population dynamics using dynamic energy budget theory incorpo-rated into integral projection models. Methods in Ecology and Evolution, 8(2):146– 154, 2017.
MECHANISMS OF SYMMETRY-BREAKING AND
PATTERN FORMATION DURING DEVELOPMENT:
INSIGHTS FROM MATHEMATICAL MODELLING
Anna Marciniak-Czochra
Heidelberg University, Germany
Cells and tissues are objects of the physical world, and therefore they obey the laws of physics and chemistry, notwithstanding the molecular complexity of biological systems. A natural question arises about the mathematical principles at play in generating such complex entities from simple laws. In this talk, I show how different pattern formation concepts may stand challenges arising from the current experimental research. Specifically, Turing-style morphogen-based mod-els are compared to mechano-chemical modmod-els exhibiting de novo pattern forma-tion. The latter are using geometric singular perturbation allowing separating fast and slow-scale subsystems. Patterning potential of mechano-chemical interac-tions is investigated using two classes of mathematical models coupling dynamics of diffusing molecular signals with a model of tissue deformation. The first class of models is based on energy minimization that leads to 4-th order partial differen-tial equations of evolution of infinitely thin deforming tissue (pseudo-3D model), coupled with a surface reaction-diffusion equation. The second approach (full-3D model) consists of a continuous model of large tissue deformation coupled with a discrete description of spatial distribution of cells to account for active de-formation of single cells. We discuss analytical and numerical challenges of the proposed models and compare the resulting patterns of tissue invagination and evagination to those observed in developmental biology.
MATHEMATICAL MODELING OF
CELL-EXTRACELLULAR MATRIX
INTERACTIONS TO EXPLAIN COLLECTIVE
CELL BEHAVIOR AND CELL MIGRATION
Roeland M.H. Merks
1,21Mathematical Institute, Leiden University,
Leiden, The Netherlands
2Institute of Biology, Leiden University,
Leiden, The Netherlands
During embryonic development, the behavior of individual cells must be co-ordinated to create the large scale patterns and tissue movements that shape the whole embryo. Apart from chemical signals exchanged between cells, a promi-nent role is played by the extracellular matrix (ECM); these are the hard or jelly materials (e.g. collagens, fibronectin) that form the micro-environment of many cells in tissues. To get a better grip on the role of the extracellular matrix in deter-mining the behavior of cells, we are developing mathematical and computational approaches to analyse the interactions off the mechanics of cells and the extracel-lular matrix (ECM) (1; 2; 3). The cell models are usually based on the Celextracel-lular Potts model, whereas the ECM is model is based on a variety of approaches, in-cluding the finite-element model and molecular dynamics. I will show how these mathematical approaches help to elucidate the regulation of cell migration and collective cell behavior during angiogenesis and other mechanisms, including im-mune cell migration.
References
[1] Van Oers, R. F. M., & Rens, E. G., &LaValley, D. J., & Reinhart-King, C. A., & Merks, R. M. H. (2014). Mechanical Cell-Matrix Feedback Explains Pairwise and Collective Endothelial Cell Behavior In Vitro. PLOS Computational Biology, 10(8), e1003774. https://doi.org/10.1371/journal.pcbi.1003774
Mechanical Cell-Substrate Reciprocity and Focal Adhesion Dynamics: A Unifying Mathematical Model. arXiv:1906.08962. https://arxiv.org/abs/1906.08962
[3] Schakenraad, K., & Ernst, J., & Pomp, W., & Danen, E. H. J., & Merks, R. M. H., & Schmidt, T., & Giomi, L. (preprint) Mechanical interplay between cell shape and actin cytoskeleton organization. arXiv:1905.09805. https://arxiv.org/abs/1905.09805
THE DYNAMICS OF RING NETWORKS
OF DYNAMICAL SYSTEMS WITH
PERIODICALLY FORCED INPUTS
Lucia Russo
Consiglio Nazionale delle Ricerche, Istituto di Scienze e Technologie per l’ Energia e
la Mobilita´a Sostenibile, Naples, Italy [email protected]
Networks describe how dynamical systems interact. A cell, or node, represents a component subsystem, and a connection represents an input from one cell to an-other. Applications are widespread and they include gene regulation networks, food webs, and neural networks, naming just a few. Networks often display pat-terns of synchrony, in which clusters of cells behave in the same manner. A related phenomenon, occurring when the system oscillates periodically, is phase-locking: cells behave the same way, except for a time delay. Coupled cell systems and sym-metry group theory provide a general mathematical context for studying networks. The theory provides a classification, for any network, of all possible rigid patterns of synchrony and phase-locking: those that persist when the model equations are perturbed. It also provides methods for finding these patterns in a given model. Stability of synchronous states and periodic regimes in symmetric network can be analyzed with systematic methods based on a group theoretical approach. In this talk, I analyze transitions between symmetric and asymmetric regimes in ring net-works with periodically forced connections. In particular, the network consists of a ring where the connections are periodically switched (ON/OFF) with a circular law. I consider, as an example, a sequence of n reactors where the feed position is periodically shifted according to a permutation law. I analyze the symmetry-breaking phenomena which are consequence of interaction between the natural and external forcing action. As the main parameters are varied due to the presence of Neimark-Sacker bifurcations, the system exhibits periodic regimes where the periods are exact multiples of the period of the forcing or quasi-periodic regimes. In addition to the standard phenomenon of frequency locking, we observe sym-metry breaking bifurcations. While in a symmetric regime all the reactors in the network have the same time history, symmetry breaking is always coupled to a situation in which one or more reactors of the ring exhibit a greater temperature than the others. I found that symmetry is broken when the rotational number of
the resonant limit cycle, which arises from the Neimark-Sacker bifurcation, is an specific ratio. Symmetry locking and resonance regions are computed through the bifurcation analysis to detect the critical parameters which mark the symmetry-breaking transitions. Finally, I will present numerical results when the dynamical systems of the network are PDEs.
