Dynamiques Multi-Souche Sur Réseaux

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Dynamiques Multi-Souche Sur Réseaux THESE DE DOCTORAT DE SORBONNE UNIVERSITE Spécialité Biomathématiques ECOLE DOCTORALE PIERRE LOUIS DE SANTE PUBLIQUE A PARIS : EPIDEMIOLOGIE ET SCIENCES DE L'INFORMATION BIOMEDICALE Présentée par M. Francesco Pinotti Pour obtenir le grade de DOCTEUR de SORBONNE UNIVERSITE Sujet de la thèse : Dynamique multi-souche sur réseaux soutenue le 27/11/2019 devant le jury composé de : (préciser la qualité de chacun des membres). M. Christian L. ALTHAUS (University of Bern) Examinateur M. Pierre-Yves BOËLLE (Inserm, Sorbonne Université) Directeur de thèse Mme Clémence MAGNIEN (Sorbonne Université) Examinateur Mme Lulla OPATOWSKI (Université de Versailles Saint Quentin) Rapporteur Mme Chiara POLETTO (Inserm, Sorbonne Université) Co-encadrante M. Michele TIZZONI (Institute for Scientific Interchange Foundation) Rapporteur Sorbonne Université Tél. Secrétariat : 01 42 34 68 35 Bureau d’accueil, inscription des doctorants et base de Fax : 01 42 34 68 40 données Tél. pour les étudiants de A à EL : 01 42 34 69 54 Esc G, 2ème étage Tél. pour les étudiants de EM à MON : 01 42 34 68 41 15 rue de l’école de médecine Tél. pour les étudiants de MOO à Z : 01 42 34 68 51 75270-PARIS CEDEX 06 E-mail : [email protected] Résumé de la thèse Introduction La propagation des pathogènes résulte de l’interaction complexe entre plu- sieurs facteurs, y compris les interactions entre un pathogène et ses hôtes, l’en- vironnement ou d’autres pathogènes. Les interactions entre pathogènes sont de plus en plus étudiées. En effet, la propagation de certaines maladies ne peut être analysée sans la prise en compte de ces interactions. La modélisation mathématique représente un outil d’intérêt dans la lutte contre les maladies infectieuses. En particulier, les modèles mathématiques per- mettent de comprendre les données épidémiologiques en formulant des hypo- thèses mécaniques sur la propagation des maladies. Dans le cas particulier de plusieurs pathogènes et de leurs interactions mutuelles, les modèles mathéma- tiques peuvent être utilisés pour répondre à une série de questions écologiques et épidémiologiques. Par exemple, ils peuvent clarifier les effets des interactions spécifiques sur la co-existence ou la dominance de plusieurs souches. Cependant, bien qu’il soit important de tenir compte des interactions entre pathogènes, plu- sieurs études mettent en évidence le rôle des facteurs environnementaux et ceux liés à l’hôte. Les contacts entre les hôtes ont une importance reconnue dans la propaga- tion d’épidémie. De récentes avancées technologiques ont permis d’aquérir des quantités massives de données, à une résolution spatiale et temporelle sans pré- cédent, sur différents types de contacts humains [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]. Ces informations détaillées sur les individus et leurs relations mutuelles peuvent être pris en compte dans des modèles épidémiques en utilisant des réseaux [26, 27]. Ici, les hôtes sont représentés sous forme de noeuds dans un réseau, tandis que leurs connexions mutuelles sont représentées par des arêtes. La transmission s’effectue sur les arêtes émanant de noeuds infectés. Au cours des dernières années, notre com- préhension théorique des processus de diffusion sur les réseaux de contacts s’est considérablement améliorée [28]. Néanmoins, l’étude des propriétés des contacts humains en cas de co-existence de plusieurs souches est encore préliminaire. En effet, la majorité des études ne concerne que l’interaction de deux agents patho- gènes [29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42]. Les connaissances de l’effet des interactions simultanées et hétérogènes liées aux pathogènes sont donc limitées. 1 Interactions entre pathogènes Plusieurs mécanismes d’interaction ont été observés. Tout d’abord, les inter- actions peuvent être concurrentielles ou coopératives. La concurrence peut sur- venir en raison de ressources limitées. Il a été démontré, par exemple, que la co- lonisation par Staphylococcus aureus prévient l’invasion par d’autres souches de S. aureus [43]. Certains pathogènes comme Streptococcus pneumoniae peuvent également nuire aux concurrents en produisant des composés chimiques [44]. Enfin, certaines infections confèrent un certain degré d’immunité croisée contre d’autres pathogènes, protégeant efficacement l’hôte des infections secondaires [45]. Les pathogènes peuvent également interagir de manière synergique, facilitant ainsi leur propagation mutuelle. Par exemple, les infections grippales d’origine virale peuvent augmenter temporairement la susceptibilité aux infections bac- tériennes par S. pneumoniae et Neisseria meningitidis [46, 47, 48]. Le VIH est connu pour partager une synergie avec de nombreux pathogènes, comme Myco- bacterium tuberculosis, Plasmodium falciparum ou le HPV [49, 50, 51, 52, 53, 54, 55, 56]. En effet, l’immunosuppression induite par le VIH favorise l’acquisition de plusieurs infections. En retour, le HPV endommage la barrière épithéliale du tractus génital, ce qui augmente le risque de contracter le VIH. P. falciparum, au contraire, semble augmenter la virulence de l’infection au VIH, en augmentant sa transmissibilité. Les interactions entre les pathogènes et/ou les différentes souches d’un même agent pathogène ont des implications épidémiologiques et de santé publique im- portantes. Par exemple, pour comprendre les mécanismes à l’origine de l’émer- gence et du maintien de la résistance aux antibiotiques des bactéries S. aureus, S. pneumoniae et Neisseria gonorrhoeae, il faut prendre en compte des facteurs écologiques qui façonnent leurs écosystèmes, notamment la concurrence entre les différentes souches [57, 58, 59, 60]. Une interprétation correcte des modèles éco-épidémiologiques est également fondamentale pour évaluer l’efficacité des vaccins. Étant donné que les vaccins peuvent ne cibler que quelques souches, la compréhension de l’impact des interactions concurrentielles peut aider à quan- tifier le risque de remplacement des souches cibles par les souches non-cibles. Dans le passé, le remplacement post-vaccinal a été observé dans le cas du pneu- mocoque [61, 62]. Des augmentations sporadiques de la prévalence des types de HPV non ciblés ont également été signalées [63, 64, 65, 66], bien que le remplacement fasse encore l’objet de débats [67, 68]. Modèles mathématiques en épidémiologie Les modèles épidémiologiques sont souvent formulés en termes de comparti- ments, c’est-à-dire de groupes d’hôtes partageant des propriétés similaires telles que l’état de santé. Les individus peuvent passer d’un compartiment à l’autre lors de la survenue de certains événements tels que l’infection et le rétablisse- ment [69]. Dans le modèle Susceptible-Infected-Susceptible (SIS), par exemple, les individus peuvent être sensibles (S) ou infectés (I). Les infectés peuvent 2 transmettre l’infection aux individus sensibles à un taux de transmission β et se rétablir à un taux µ. Une fois rétablies, les personnes redeviennent sensibles aux nouvelles infections. Par conséquent, le modèle SIS décrit la propagation d’infections qui n’accordent pas l’immunité en cas de rétablissement. C’est le cas par exemple des bactéries commensales de l’homme comme S. aureus, qui entraînent généralement une colonisation asymptomatique. Dans le contexte des systèmes multi-souches, les modèles compartimentaux sont essentiels pour répondre à un grand nombre de questions écologiques et épidémiologiques, e.g. les conditions menant à la co-existence des souches [70, 71, 72, 73, 74, 75, 76]. Les modèles mathématiques peuvent également être uti- lisés pour comprendre l’émergence de pathogènes envahissants qui peuvent ap- paraître à la suite d’importations externes ou de mutations. Par exemple, des modèles multi-souches ont été utilisés pour comprendre l’émergence des bacté- ries résistantes aux antibiotiques [77] et des souches pandémiques de grippe [78, 79, 80, 81]. L’analyse de modèles multi-souches peut également aider à évaluer l’efficacité des interventions de santé publique, par exemple en évaluant l’im- pact à long terme d’un vaccin sur une population de pathogènes et le risque de remplacement [82, 83, 84]. Les modèles compartimentaux supposent souvent que les hôtes sont bien mélangés, c’est-à-dire que chaque individu a la même probabilité de rencon- trer tous les autres. Toutefois, cette approximation peut représenter une limite dans certains cas. La discipline de network epidemiology fournit le cadre appro- prié pour tenir compte de la complexité inhérente à la structure des contacts et à la dynamique épidémique. Les effets de la structure des contacts sur la propagation de l’épidémie ont été largement étudiés au cours des deux der- nières décennies [28]. Les résultats les plus importants concernent le seuil épidé- mique [85, 86, 87, 88], la prévalence [89, 90, 91, 92, 93, 94, 95] et les stratégies de vaccination [96, 97, 98, 99, 100, 101]. Les développements théoriques ont permis de traiter également des hétérogénéités découlant de la nature temporelle des contacts entre hôtes [102, 103, 104, 105, 106, 107, 108, 109]. Plusieurs travaux ont porté sur la dynamique des pathogènes en interac- tion sur des réseaux de contacts. La plupart des études se sont concentrées sur deux souches qui interagissent par exclusion mutuelle ou par immunité croi- sée [110, 111, 32, 34, 33, 112, 113, 40, 29, 31, 39, 30, 41, 42]. Il a été démontré que les hétérogénéités de la structure des contacts influent sur la probabilité de l’émergence de nouvelles souches ainsi que sur la taille des nouvelles épidé- mies. En ce qui concerne la coopération sur des réseaux de contacts, de nom- breuses études ont considéré une susceptibilité accrue comme mécanisme d’in- teraction [35, 38, 36, 37, 114]. Dans ce contexte, il a été démontré qu’à mesure que la transmissibilité augmente, les pathogènes coopératifs peuvent donner lieu à des flambées épidémiques discontinues en termes de prévalence. Néanmoins, la nature (continue ou discontinue) de cet événement dépend de la topologie du réseau. 3 Dynamique des contacts et écologie des souches multiples Les travaux présentés dans la section précédente ne considèrent que deux souches en interaction.
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