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Projeto de investigação
Mathematical Modelling of Multi-scale Control Systems: applications to human diseases
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Group centrality in optimal and suboptimal vaccination for epidemic models in contact networks
Publication . Cerdeira, J. Orestes; Chalub, Fabio A.C.C.; Hansen, Matheus; CMA - Centro de Matemática e Aplicações; DM - Departamento de Matemática; Royal Society Publishing
The pursuit of strategies that minimize the number of individuals needing vaccination to control an outbreak is a well-established area in mathematical epidemiology. However, for certain diseases, public policy tends to prioritize immunizing vulnerable individuals over epidemic control. As a result, optimal vaccination strategies may not always be effective in supporting real-world public policies. A similar situation happens when a new vaccine is introduced and is in short supply, as target priority groups for vaccination have to be defined. In this work, we focus on a disease that results in long-term immunity and spreads through a heterogeneous population, represented by a contact network. We study four well-known group centrality measures and show that the GED-Walk offers a reliable means of estimating the impact of vaccinating specific groups of individuals, even in suboptimal cases. Additionally, we depart from the search for target individuals to be vaccinated and provide proxies for identifying optimal groups. While the GED-Walk is the most useful centrality measure for suboptimal cases, the betweenness (a related, but different centrality measure) stands out when looking for optimal groups. This indicates that optimal vaccination is not concerned with breaking the largest number of transmission routes, but interrupting geodesic ones.
Insuperable Strategies in Two-Player and Reducible Multi-Player Games
Publication . Chalub, Fabio A.C.C.; Souza, Max O.; CMA - Centro de Matemática e Aplicações; DM - Departamento de Matemática; Springer Science + Business Media
Real populations are seldom found at the Nash equilibrium strategy. The present work focuses on how population size can be a relevant evolutionary force diverting the population from its expected Nash equilibrium. We introduce the concept of insuperable strategy, a strategy that guarantees that no other player can have a larger payoff than the player that adopts it. We show that this concept is different from the rationality assumption frequently used in game theory and that for small populations the insuperable strategy is the most probable evolutionary outcome for any dynamics that equal game payoff and reproductive fitness. We support our ideas with several examples and numerical simulations. We finally discuss how to extend the concept to multiplayer games, introducing, in a limited way, the concept of game reduction.
Social vs. individual age-dependent costs of imperfect vaccination
Publication . Chalub, Fabio A. C. C.; Doutor, Paulo; Patrício, Paula; Soares, Maria do Céu; CMA - Centro de Matemática e Aplicações; DM - Departamento de Matemática; Elsevier
In diseases with long-term immunity, vaccination is known to increase the average age at infection as a result of the decrease in the pathogen circulation. This implies that a vaccination campaign can have negative effects when a disease is more costly (financial or health-related costs) for higher ages. This work considers an age-structured population transmission model with imperfect vaccination. We aim to compare the social and individual costs of vaccination, assuming that disease costs are age-dependent, while the disease's dynamic is age-independent. A model for pathogen deterministic dynamics in a population consisting of juveniles and adults, assumed to be rational agents, is introduced. The parameter region for which vaccination has a positive social impact is fully characterized and the Nash equilibrium of the vaccination game is obtained. Finally, collective strategies designed to promote voluntary vaccination, without compromising social welfare, are discussed.
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Entidade financiadora
Fundação para a Ciência e a Tecnologia
Programa de financiamento
Concurso de Projetos de I&D em Todos os Domínios Científicos - 2022
Número da atribuição
2022.03091.PTDC