Θανάσης Φωκάς: Ο διακεκριμένος Έλληνας μαθηματικός παρουσιάζει στη LiFO τα αποτελέσματα της έρευνας του για τον κορωνοϊό Πηγή: www.lifo.gr

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Όταν  Προφητικά ο Πάνος Καλτσής ανακήρυττε τον  μεγάλο
Έλληνα επιστήμονα  Καθηγητή Αθανάσιο Φωκά  σε Πολίτη των Δελφών
Ο κορυφαίος ακαδημαϊκός εξηγεί τον ρόλο των μαθηματικών μοντέλων στην πανδημία. Και δηλώνει: «Φοβάμαι μήπως το δεύτερο κύμα συμβεί πολύ νωρίτερα από το φθινόπωρο»

ΟΙ ΠΑΝΔΗΜΙΕΣ ΕΧΟΥΝ απασχολήσει κατά καιρούς τη σύγχρονη ιστορία του ανθρώπου. Τους τελευταίους μήνες, με την εξάπλωση του κορωνοϊού, επανεκτιμήθηκε η σημασία της επιστήμης. Καταλυτικός παράγοντας για τη μελέτη των επιδημιολογικών στοιχείων και την αντιμετώπιση μιας πανδημίας αποτελούν τα μαθηματικά μοντέλα. Καθημερινά ακούμε συνεχώς για ποσοστά ανοσίας, καμπύλη κρουσμάτων καθώς και για ρυθμούς αύξησης ή μείωσης σχετικά με την πορεία του κορωνοϊού. Αυτές τις μέρες ο διακεκριμένος Έλληνας μαθηματικός, Θανάσης Φωκάς, ολοκλήρωσε την έρευνά του η οποία εστιάζει στα δεδομένα της μετά lockdown περιόδου και αναλύει στη LiFO τα αποτελέσματά της. Ο διεθνούς φήμης καθηγητής στην έδρα της Μη Γραμμικής Μαθηματικής Επιστήμης του Πανεπιστημίου του Κέμπριτζ, αεροναυπηγός, γιατρός και τακτικό μέλος της Ακαδημίας Αθηνών, είναι ένας επιστήμονας που στο παρελθόν έχει ξεχωρίσει για τις μεθοδολογικές του προσεγγίσεις, προτείνοντας, για παράδειγμα, λύση σε ένα από τα μεγαλύτερα προβλήματα στην ιστορία της επιστήμης των Μαθηματικών, την υπόθεση Lindelöf. Κάποτε, ο Israel Gelfand, ένας από τους μεγαλύτερους μαθηματικούς και βιολόγους του 20ού αιώνα, είχε πει γι’ αυτόν: «Ο Φωκάς είναι μια σπάνια περίπτωση αναγεννησιακού επιστήμονα». Στη συνέντευξη που ακολουθεί ο κορυφαίος ακαδημαϊκός μιλά για την πανδημία, τον ρόλο των μαθηματικών μοντέλων, τη λύση του lockdown, την επικοινωνία του με τον κ. Τσιόδρα, τα θετικά του κορωνοϊού αλλά και για όσα αποκόμισε ο ίδιος κατά την περίοδο του εγκλεισμού.

H ΣΥΝΕΝΤΕΥΞΗ   

— Μια πανδημία, το 2020, άδειασε τις πόλεις όλου του κόσμου. Ποιο είναι το δικό σας σχόλιο για όλο αυτό που συνέβη; Ίσως να μπορούσε να είχε αποφευχθεί. Ο Παγκόσμιος Οργανισμός Υγείας, μετά τη γνωστοποίηση του κινδύνου από την Κίνα, θα έπρεπε να είχε συμβουλεύσει όλες τις χώρες να επιβάλουν καραντίνα σε Κινέζους επισκέπτες. Όχι μόνο δεν κινήθηκε εγκαίρως προς αυτή την κατεύθυνση, αλλά αργότερα διέπραξε ένα δεύτερο σοβαρό λάθος με την Ιταλία. Κατά τη γνώμη μου, αυτό αποτελεί ανεπίτρεπτη αμέλεια. — Ήταν τελικά αναπόφευκτη η λύση των lockdowns, η οποία αναμένεται να δημιουργήσει τεράστια οικονομικά προβλήματα σε χώρες και οικογένειες; Απόλυτες λύσεις, σαν αυτή του lockdown, δεν είναι ιδανικές αφού εξ ορισμού δεν λαμβάνουν υπόψη τις ιδιαιτερότητες ομάδων ή συγκεκριμένων καταστάσεων. Διαθέτουν, όμως, το πλεονέκτημα της άμεσης αντιμετώπισης του εν λόγω προβλήματος. Υπ’ αυτή την έννοια, λόγω της κρισιμότητα της κατάστασης, κάποια μορφή lockdown ήταν απαραίτητη. Προφανώς, όμως, το lockdown δεν μπορεί να συνεχιστεί. Κι όχι μόνο για οικονομικούς λόγους, αλλά και για λόγους ψυχικής υγείας.

— Τι σας έκανε να ασχοληθείτε με μαθηματικά μοντέλα για τον κορωνοϊό; Θεωρώ ότι ο ρόλος των μαθηματικών στην Ιατρική και στη Βιολογία δεν μπορεί να είναι καθοριστικός, όπως στη Φυσική. Αυτήν τη θέση αναλύω στο βιβλίο μου «Cognition, Computability, Culture, Creativity: A Unified Approach to Sciences and Humanities». Για παράδειγμα, οι νόμοι της κβαντομηχανικής παράγονται από τους νόμους της κλασικής μηχανικής με έναν απόλυτα μαθηματικό τρόπο. Δεν νομίζω ότι υπάρχει ανάλογη γενεσιουργή σχέση μεταξύ μαθηματικών και ιατρικής ή βιολογίας.   Από την άλλη μεριά, είναι γνωστό ότι τα μαθηματικά είναι η γλώσσα της πολυπλοκότητας, κατά συνέπεια η χρήση των μαθηματικών μπορεί να ωφελήσει την ανάλυση κάθε περίπλοκου φαινομένου. Για παράδειγμα, η κύρια ενασχόληση του Κέντρου Μαθηματικών της Ακαδημίας Αθηνών είναι η μελέτη ιατρικών απεικονίσεων και ιδιαίτερα PET, SPECT, και fMRI. Όσον αφορά τον Covid-19, η τελική λύση προφανώς θα δοθεί από την Ιατρική και τη Bιολογία με την κατασκευή εμβολίου και την κατάλληλη φαρμακευτική αντιμετώπιση. Δίδεται όμως τώρα στα μαθηματικά μια μοναδική ευκαιρία να διαδραματίσουν βραχυπρόθεσμα τον κύριο ρόλο στην αντιμετώπιση την πανδημίας: μέσω προβλέψεων για το ποια θα είναι η εξέλιξη των χαρακτηριστικών της επιδημίας και, κυρίως, με την ανάλυση της ιδανικής εξόδου από τον lockdown.   Κατά τη γνώμη μου, αυτό αποτελεί ένα γεγονός χωρίς προηγούμενο στην ιστορία των μαθηματικών. Ήταν ένας από τους λόγους που, με την παρότρυνση πολλών φίλων, τόσο ιατρών όσο και μαθηματικών, αποφάσισα να ασχοληθώ με το πρόβλημα της ανάπτυξης και λύσης μαθηματικών μοντέλων για τον κορωνοϊό.

— Σε έρευνα που κάνατε μιλάτε για δύο εναλλακτικά σενάρια χαλάρωσης των μέτρων, ένα καταστροφικό και ένα λογικό. Θα θέλατε να μας τα περιγράψετε; Η έρευνά μας έχει δυο διαφορετικές κατευθύνσεις. Ο στόχος της πρώτης ήταν η πρόβλεψη των τελικών χαρακτηριστικών της επιδημίας. Για παράδειγμα, χρησιμοποιώντας τα υπάρχοντα δεδομένα για τον αριθμό θανάτων, αναπτύξαμε μαθηματικά μοντέλα ικανά να προβλέψουν τον τελικό αριθμό θανάτων. Φαίνεται ότι αυτά τα μοντέλα, τα οποία αναπτύχθηκαν σε συνεργασία με τον Γεώργιο Καστή και τον Νίκο Δικαίο, ερευνητές του Κέντρου Ερευνών Μαθηματικών της Ακαδημίας Αθηνών, παρόλο που είναι πολύ απλά, είναι αρκετά ακριβή. Για παράδειγμα: Πηγή: www.lifo.gr

Ο πραγματικός έναντι του προβλεπόμενου σωρευτικού αριθμού των αναφερόμενων θανάτων, λόγω του Covid-19, παρουσιάζεται ως συνάρτηση των ημερών μετά την αναφορά 25 θανάτων για την Ισπανία. Τα τρία μοντέλα έχουν εκπαιδευτεί με δεδομένα έως την 1η Μαΐου. Με κόκκινο παρουσιάζονται τα πραγματικά δεδομένα μέχρι τις 13 Μαΐου. Πηγή: www.lifo.gr

Ο στόχος της δεύτερης ερευνητικής δραστηριότητας ήταν πιο φιλόδοξος: ο σχεδιασμός μιας ιδανικής στρατηγικής εξόδου από την τρέχουσα κατάσταση εγκλεισμού. Απρόσμενα, προς αυτήν την κατεύθυνση έχουμε ένα πολύ σημαντικό αποτέλεσμα. Συγκεκριμένα, έχουμε έναν ευσταθή μαθηματικό αλγόριθμο σύμφωνα με τον οποίο μπορούμε να υπολογίζουμε τον συνολικό αριθμό θανάτων μετά την αύξηση του αριθμού επαφών μεταξύ ατόμων. Πιο αναλυτικά, το αποτέλεσμά μας βασίζεται στο κλασικό μοντέλο που χρησιμοποιείται στην επιδημιολογία (SIR), το οποίο παρουσιάστηκε για πρώτη φορά το 1927. Έτσι, οι περισσότεροι πεπειραμένοι μελετητές θα αποδεχθούν την καταλληλόλητα του σημείου εκκίνησης.   Φυσικά, το δύσκολο ερώτημα είναι πώς μπορεί να αναλυθεί αυτό το μοντέλο, δεδομένου ότι είναι αρκετά περίπλοκο και περιλαμβάνει 6 μαθηματικές εξισώσεις που καθορίζονται από 9 φυσικές παραμέτρους. Μια από τις 9 παραμέτρους του μοντέλου, η οποία υποδηλώνεται από το σύμβολο c, καθορίζει τον αριθμό των επαφών μεταξύ ατόμων. Αυτές οι παράμετροι είναι εκ των προτέρων άγνωστες, υπάρχει όμως η υποκείμενη υπόθεση στη μαθηματική επιδημιολογία ότι θα μπορούσαν να προσδιοριστούν από τα δεδομένα του αριθμού των θανάτων, των νοσηλευόμενων κ.λ.π.   Η ιδέα μας ήταν απλή: εάν μπορούσαμε να προσδιορίσουμε τις παραπάνω 9 παραμέτρους από τα δεδομένα κατά την κατάσταση εγκλεισμού, τότε θα μπορούσαμε να αυξήσουμε το c (αντικαθιστώντας το c με ζ επί c, όπου ζ θετικός ακέραιος αριθμός) και μετά να λύσουμε το προκύπτον σύστημα 6 εξισώσεων. Με αυτό τον τρόπο θα μπορούσαμε να υπολογίσουμε το αποτέλεσμα της αύξησης των επαφών. Μαθηματικά, ο προσδιορισμός των 9 παραμέτρων από τα δεδομένα μπορεί να διατυπωθεί ως ένα συγκεκριμένο πρόβλημα που ονομάζεται «αντίστροφο πρόβλημα» (η λύση τέτοιου είδους μαθηματικών προβλημάτων αποτελεί διαχρονικά βασικό τομέα της ερευνητικής μου δραστηριότητας). Καταφέραμε να δείξουμε ότι, χρησιμοποιώντας τα δεδομένα του αριθμού των θανάτων, είναι δυνατόν να προσδιοριστεί ο συγκεκριμένος συνδυασμός αυτών των 9 παραμέτρων που χαρακτηρίζουν τον αριθμό των θανάτων.

Συνοπτικά: ξεκινώντας από τα δεδομένα του αριθμού των θανάτων κατά τη διάρκεια του εγκλεισμού (τα οποία είναι μακράν τα πιο αξιόπιστα υπάρχοντα δεδομένα), υπολογίζουμε τους 6 συνδυασμούς των 9 παραμέτρων που καθορίζουν την εξίσωση του αριθμού των θανάτων. Στη συνέχεια, πολλαπλασιάζουμε έναν από αυτούς τους συνδυασμούς με τον ακέραιο αριθμό ζ, ο οποίος καθορίζει την αύξηση των επαφών. Κατόπιν, επιλύουμε την προκύπτουσα εξίσωση, η οποία καθορίζει τον αριθμό των θανάτων που θα προκύψουν σαν αποτέλεσμα της ανωτέρω αυξήσεως του αριθμού των επαφών. Τα αποτελέσματα μας δείχνουν ότι για ζ=2, οι αλλαγές στον αριθμό των θανάτων σε σχέση αυτών της περιόδου του lockdown είναι μικρές. Για ζ=3, όμως, η κατάσταση είναι πολύ άσχημη. Κατά συνέπεια, εάν η χαλάρωση των μέτρων είναι εκτεταμένη (και αντιστοιχεί σε ζ μεγαλύτερο του 2), τότε θα προκύψει μεγάλος αριθμός θανάτων. Είναι σημαντικό ότι μια παρόμοια ανάλυση ισχύει για υπο-πληθυσμούς. Έτσι, διαχωρίζοντας τον πληθυσμό σε «νέους» (κάτω των 40) και «μεγαλύτερους» (άνω των 40) μπορούμε να μελετήσουμε ξεχωριστά το αποτέλεσμα της αυξήσεως των αλληλεπιδράσεων (α) μεταξύ των «νέων», (β) μεταξύ των «μεγαλύτερων» και (γ) μεταξύ των «μεγαλύτερων» με τους «νέους».   Διαπιστώσαμε ότι ενώ η αύξηση της αλληλεπίδρασης (α) οδηγεί σε μια σχετικά σταθερή κατάσταση, η αύξηση είτε της (β), είτε της (γ) μπορεί να έχει καταστροφικές συνέπειες. Εκτός βέβαια, αν παράγοντες που δεν υπεισέρχονται στο μοντέλο, όπως η αύξηση της θερμοκρασίας, έχουν πολύ θετική επίδραση. Πρέπει να τονιστεί ότι για την παραγωγή των παραπάνω αποτελεσμάτων, συνεργάστηκα με τον Ισπανό συνάδελφο Jesus Cuevas-Maraver και τον διακεκριμένο Έλληνα μαθηματικό Παναγιώτη Κεβρεκίδη, ο οποίος επί του παρόντος είναι επισκέπτης καθηγητής στο Πανεπιστήμιο της Οξφόρδης. Αυτή η εργασία δεν θα είχε ολοκληρωθεί χωρίς την καθοριστική συμβολή των ανωτέρω συνεργατών. Επίσης, είναι αξιοσημείωτο ότι τα μαθηματικά εργαλεία που αναπτύχθηκαν στις αρχικές μας εργασίες με τους Καστή και Δικαίο, ήταν πολύ χρήσιμα στην παραπάνω έρευνα.

— Αφού στο επίκεντρο της έρευνάς σας βρέθηκε η Ελλάδα, τι θα προτείνατε στην ελληνική κυβέρνηση να πράξει από δω και πέρα; Ο κύριος λόγος για τον οποίο επικεντρωθήκαμε στην Ελλάδα, παρά την έλλειψη παροχής δεδομένων από τον σχετικό οργανισμό, ήταν η φιλοπατρία. Θα θέλαμε να χρησιμοποιήσουμε την ηλικία των 45 ή 50 σαν όριο, αλλά δεν υπήρχαν δεδομένα. Η πρότασή μας είναι ότι οι τρέχουσες κυβερνητικές συστάσεις που ισχύουν για άτομα άνω των 65 θα πρέπει να επεκταθούν τουλάχιστον σε άτομα άνω των 50 Πηγή: www.lifo.gr

Το πολυτιμότατο αγαθό της υγείας πρέπει να είναι κοινωνικά κατοχυρωμένο για όλους. Όσο περισσότερο επενδύει η κοινωνία στην επιστήμη, τόσο μεγαλύτερα τα οφέλη για όλους. Φωτο: Πάρις Ταβιτιάν/LIFO Πηγή: www.lifo.gr

— Έχετε μεταφέρει τα δεδομένα της έρευνας στην επιστημονική επιτροπή υγείας και στον κ. Τσιόδρα, κι αν ναι, ποια ήταν η απάντηση τους; Έστειλα την εργασία μας στον κ. Τσιόδρα το ίδιο βράδυ που ολοκληρώθηκε· ακολούθησε εκτεταμένη τηλεφωνική συζήτηση. Είμαστε πολύ τυχεροί ως έθνος που ο κ. Τσιόδρας κατέχει αυτή τη νευραλγική θέση αυτή τη κρίσιμη περίοδο. — Ανησυχείτε για δεύτερο κύμα πανδημίας το φθινόπωρο; Τι συνέπειες μπορεί να έχει αυτό; Βάσει των ανωτέρω, ανησυχώ για το τι θα συμβεί τώρα ως αποτέλεσμα της χαλάρωσης των μέτρων. Φοβάμαι μήπως το δεύτερο κύμα συμβεί πολύ νωρίτερα από το φθινόπωρο. — Υπάρχει κάτι θετικό που μας αφήνει ο κορωνοϊός; Ουδέν κακόν αμιγές καλού. Έγινε προφανές ότι σε αυτόν το κόσμο τον μικρό, τον Μέγα όλα αλληλοσυνδέονται. Αφού κάθε άτομο υπάρχει μόνο ως αποτέλεσμα του ότι αποτελεί μέρος του κοινωνικό συνόλου, έχουμε υποχρέωση να θυσιάζουμε τις ατομικές μας ελευθερίες για την προστασία του κοινωνικού συνόλου. Κατά συνέπεια είναι αδύνατο να κατανοήσω επιχειρήματα του είδους «είναι δικαίωμά μου να μη φοράω μάσκα».   Η λύση βασικών προβλημάτων δεν αντιμετωπίζεται με ρατσιστικές κραυγές (όπως αυτές του Προέδρου Τραμπ) και με τη διεύρυνση του χάσματος μεταξύ φτωχών και πλουσίων (είτε σε ατομικό είτε σε κρατικό επίπεδο), άλλο μόνο με βάση ουμανιστικές αρχές. Το πολυτιμότατο αγαθό της υγείας πρέπει να είναι κοινωνικά κατοχυρωμένο για όλους. Όσο περισσότερο επενδύει η κοινωνία στην επιστήμη, τόσο μεγαλύτερα τα οφέλη για όλους. Η επιστήμη όχι μόνο θα λύσει το πρόβλημα του κορωνοϊού στο μέλλον, αλλά ήδη η προσφορά της δια μέσου του Διαδικτύου (ενός εκ των προσφάτων και μεγαλύτερων επιτευγμάτων της) είναι σωτήρια. Τέλος, έγινε προφανής η ορθότητα της γνωστής παρατήρησης του μέγιστου Αριστοτέλη ότι ο άνθρωπος είναι κοινωνικό ον· έχει ανάγκη από διαπροσωπικές επαφές που δεν δύναται να αντικατασταθούν από κανένα μέσο τεχνολογίας. — Τι είναι αυτό που μας έμαθε ο εγκλεισμός αλλά και τι αποκομίσατε εσείς προσωπικά στη διάρκεια του lockdown; Η Ρεγγίνα, η σύζυγος μου, υποστηρίζει ότι δεν νομίζει πως άλλαξε ο τρόπος ζωής κάποιου λιγότερο από ό,τι εμένα. Όντως, τα τελευταία 5 χρόνια έχω την τύχη να έχω μια μεγάλη ερευνητική υποτροφία από το Εθνικό Ίδρυμα Ερευνών της Μεγάλης Βρετανίας. Κατά συνέπεια, δεν έχω καμία διδακτική ή διοικητική υποχρέωση στο Πανεπιστήμιο του Cambridge· ασχολούμαι μόνο με την έρευνα μου. Έτσι, πριν από την πανδημία, πήγαινα στο πανεπιστήμιο μία ή το πολύ δύο φορές την εβδομάδα για να μιλήσω με φοιτητές μου και μεταδιδακτορικούς μου συνεργάτες. Τώρα αυτό γίνεται ηλεκτρονικά. Βεβαίως ανησυχώ για την κατάσταση σε παγκόσμια κλίμακα. Ο εγκέφαλος συνεχώς κατασκευάζει συνειρμούς· έτσι, αυτή την περίοδο συχνά θυμάμαι περιστατικά όταν εργαζόμουν ως γιατρός στο Πανεπιστήμιο του Stanford. Τον απίστευτο αγώνα για να σωθεί μια ανθρώπινη ζωή. Τότε κατανοείς ότι δεν υπάρχει μεγαλύτερο δώρο από το δώρο της ζωής.   Με τη γρίπη του 1918 έχασαν τη ζωή τους 50 εκατομμύρια άνθρωποι, που αναλογεί στις μέρες μας σε 200 εκατομμύρια. Πώς θα αποφύγουμε μια τέτοια καταστροφή; Πώς μπορούμε να βοηθήσουμε για να σωθεί έστω και μια ζωή; Προς αυτή την κατεύθυνση ας κάνουμε υπέρβαση ώστε να ξεπεράσουμε δογματικές αγκυλώσεις που βάζουν σε κίνδυνο τη ζωή μας. Ας μην ξεχνάμε ότι, βάσει της Ορθοδοξίας, ο Θεός μας χάρισε ελεύθερη βούληση ώστε να μπορούμε να παίρνουμε σωστές αποφάσεις, συνεπείς με την υπάρχουσα συσσωρευμένη γνώση. Επίσης, την ευαισθησία μας εναντίον της εκλαμβανομένης καταπάτησης των δικαιωμάτων μας από κρατικούς μηχανισμούς. Και, τέλος, την απολυτοποίηση της σπουδαιότητας του οικονομικού κέρδους. Ας οπλιστούμε με δύναμη και υπομονή. Η κρίση θα περάσει, παρόλο που φοβάμαι ότι θα διαρκέσει περισσότερο από ό,τι αναμένεται. Πηγή: www.lifo.gr

284 thoughts on “Θανάσης Φωκάς: Ο διακεκριμένος Έλληνας μαθηματικός παρουσιάζει στη LiFO τα αποτελέσματα της έρευνας του για τον κορωνοϊό Πηγή: www.lifo.gr”

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