- in memoriam: José Rodrigues Dias (1951-2023)
- in memoriam: Vladimir Goncharov (1962-2017)
- in memoriam: Graça Carita (1975-2016)
- Notícias
- Eventos
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Seminários
- The representation theory of the unitriangular group and other related groups
- On Computational Properties of Cauchy Problems
- Sets as Properties
- Artinian algebras and Jordan type
- Iterated Systems, Networks and Applications
- Isogeometric Analysis: mathematical and implementational aspects, with applications
- Sampling elusive populations: methods and applications
- Existence, non-existence and multiplicity results for some third-order periodic problems
- Convergence: what’s logic got to do with it?
- The Mathematics of Fires
- Old-age mortality deceleration and the modal age at death: insights from dynamic laws of adult mortality
- Stochastic differential equations models of animal growth and profit optimization in cattle raising
- Multidisciplinary approach for a real problem: modeling road traffic accidents
- The finite elements method and Freefem software
- DeepParticle: deep-learning invariant measure by minimizing Wasserstein distance on data generated from an interacting particle
- Kinematics: classification methods and combinatorial invariants for complex motion in biology
- Fractional Poisson Analysis in one Dimension
- Mathematics driven by epidemics
- ALMOST-POSITIONED NUMERICAL SEMIGROUPS
- A Delta approximation method on estimation for SDE mixed models
- Classificação de uma família de nós de Lorenz redutíveis
- Categoria de Lusternik-Schinrelmann e Grupos de Lie
- Euclides, Taylor, e a perspectiva esférica enquanto objecto matemático
- Time Series Clustering
- Condições geométricas para a existência e unicidade de projeção
- Sobre o volume de campos vetoriais
- Multiple criteria optimization: methods and applications
- Selective Base Revisions
- Nonautonomous attractors and bifurcation structures on nonautonomous families of flat topped tent maps
- Strongly nonlinear third order impulsive boundary value problems
- Solvability of second order coupled systems on the half-line
- Stochastic differential equations: brief introduction and profit optimization in fisheries
- Positioned Numerical Semigroups
- Tipo de Jordan de álgebras artinianas
- Complexidade em sistemas dinâmicos de baixa dimensão
- CFD Analysis in cerebral aneurysms
- Variational problems involving nonlocal supremal functionals
- Different Types of Stabilities in Times of Instability
- Non-linear systems of PDEs. Two examples from applications.
- Modelação de eventos extremos – uma introdução: aplicação ao decatlo e ao heptatlo atlético
- Comportamento assimptótico de soluções de problemas com valores na fronteira
- A característica de Euler de hipersuperfícies de espaços forma
- Brief introduction to stochastic differential equations and applications in Biology and Finance
- Sampling strategies in rural and urban settings in Africa - Looking from the sky
- Epidemiologia espácio-temporal no controlo da tuberculose
- Connectivity and Reliability of Mobile Ad-Hoc Networks
- Mathematical modeling, optimal control and complex network of epidemic models: case study of COVID-19 in Portugal
- Feature selection for marine species origin prediction
- Provas de Mestrado
- Provas de Doutoramento
- Apontadores
Mathematical modeling, optimal control and complex network of epidemic models: case study of COVID-19 in Portugal
In this talk, we propose a SAIRP mathematical model, for the transmission dynamics of SARS-CoV-2, given by a system of ordinary differential equations, which is fitted to the number of active infected individuals with COVID-19 in Portugal. We apply optimal control theory to the SAIRP model, to maximize the number of people returning to “normal life” and minimizing the number of active infected individuals with minimal economical costs while warranting a low level of hospitalizations.
After we generalize the SAIRP model, considering piecewise constantparameters, and construct a complex network of dynamical systems, in order to take into account the mobilities of individuals, which are known to play a decisive role in the dynamics of the epidemic. We prove the existence of pseudo-periodic solutions of the epidemic model and analyze its relation with multiple epidemic waves in COVID-19 pandemic. The model with piecewise constant parameters is calibrated in order to fit with the real data of the COVID-19 active infected individuals in six regions of Portugal mainland, namely Norte, Centro, Lisboa e Vale do Tejo, Alentejo, Algarve and Pinhal Litoral. Through numerical simulations, we explore the effectof the topology of the network on the dynamics of the epidemics (disposal of connections and coupling strength) and identify which type of topology minimizes the level of infection of the epidemic.
This seminar is based on the work developed under the project Project Nr.147 ”Controlo Ótimo e Modelação Matemática da Pandemia COVID-19:contributos para uma estratégia sistémica de intervenção em saúde na comunidade”, in the scope of the ”RESEARCH 4 COVID-19” call, financed by the Portuguese Foundation for Science and Technology (FCT).
