Programa de Pós-Graduação em Matemáticahttp://repositorio.ufsm.br/handle/1/23462024-05-24T12:38:07Z2024-05-24T12:38:07ZUm modelo SIS com taxas de recuperação e infecção variáveisMolina, Tatiane Mirandahttp://repositorio.ufsm.br/handle/1/312702024-01-24T15:02:37Z2023-10-31T00:00:00ZUm modelo SIS com taxas de recuperação e infecção variáveis
Molina, Tatiane Miranda
Rodrigues, Luiz Alberto Díaz
In this dissertation we present a qualitative theoretical study of modifications to the SIS
epidemiological model for infectious diseases that do not confer immunity. We first study the
classic SIS model, which considers constant infection and recovery rates. We then analyze a
model in wich the recovery rate decreases rate with infectious individuals. This model assumes
that recovery depends on a treatment that may become scarce as the infection spreads. Our
results show that if the decline in the recovery rate is very steep, a threshold of infectious people
appears. Above this threshold, the disease reaches the endemic level even with R0 < 1. In what
follows, we analyze two models with infection rate that varies with the number of infectious
people. We suppose that susceptible people adopt measures to prevent contagion when the
density of infectious people increases, so that hte infection rate is a decreasinf function of
infectious. We studied the effects of two types of behavior. In the first one, prevention measures
begin as soon as the first infectious appear. In the second model, we assume that preventive
measures are taken after the number of infectious people reaches an intermediate value. The
results depend on R0. For a small R0, it is better to start contact reduction measures as soon as
the first infectious are detected. On the other hand, when R0 is large, the best strategy, according
to our results, is to start contact reduction more slowly and increase the reduction as the number
of infectious people increases.
Universidade Federal de Santa Maria
Dissertação
2023-10-31T00:00:00ZUm modelo SIR com duas cepas circulantesOliveira, Maiquel Juliano Rodrigues dehttp://repositorio.ufsm.br/handle/1/312692024-01-24T14:05:35Z2023-10-27T00:00:00ZUm modelo SIR com duas cepas circulantes
Oliveira, Maiquel Juliano Rodrigues de
Rodrigues, Luiz Alberto Díaz
To understand the evolution of many diseases such as influenza and COVID-19, for
example, it is necessary to consider the presence of multiple strains of the pathogen.
Models with multiple strains of the disease-causing agent can be used to identify the
dominant strains and thus design more efficient control strategies. In this work, using
the SIR model with vital dynamics, we study the dynamics of a disease in which there
are two strains of the pathogen. As in ecological models, the strains compete for a
common resource, in this case, susceptibles. We show that when there is complete
cross-immunity, the strain with the highest basic reproductive number will be the dominant strain. The coexistence of the two strains is impossible in this case. We then
present a model that indirectly considers the mutation of the pathogen. A fraction of
the infected by strain 1 is transferred to the class of those infected by strain 2. We
conclude that this mechanism makes it possible for the two strains to coexist.
Universidade Federal de Santa Maria
Dissertação
2023-10-27T00:00:00ZA solução fundamental no cálculo da resposta forçada de uma viga Euler-Bernoulli sobre fundação elástica e com condições de contorno não-clássicasPetermann, Rubiarahttp://repositorio.ufsm.br/handle/1/310292024-01-09T12:26:16Z2023-10-26T00:00:00ZA solução fundamental no cálculo da resposta forçada de uma viga Euler-Bernoulli sobre fundação elástica e com condições de contorno não-clássicas
Petermann, Rubiara
Copetti, Rosemaira Dalcin
In this work we consider an Euler-Bernoulli beam on elastic foundation. The solution to
problems with and without external force was obtained through modal analysis and the fundamental
solution was used to write the characteristic equations for some combinations
of classical and non-classical boundary conditions, the free response and the forced response.
We obtained orthogonality relations that allowed us to decouple the equations from
motion and write the solutions. In the case of non-classical boundary conditions, the orthogonality
relation obtained was written in terms of the devices attached to the end of the
beam. We perform simulations for some cases of boundary conditions and vary the values
of the mass and spring devices attached to the ends of the beam. We compare the natural
frequencies and graph the vibration modes, the free response and the forced response.
Universidade Federal de Santa Maria
Dissertação
2023-10-26T00:00:00ZExistência e unicidade de solução global para um modelo termoelástico com domínio ilimitadoAnjos, Luis Jorge Souza doshttp://repositorio.ufsm.br/handle/1/308482023-12-13T11:56:34Z2023-08-30T00:00:00ZExistência e unicidade de solução global para um modelo termoelástico com domínio ilimitado
Anjos, Luis Jorge Souza dos
Buriol, Celene
The main objective of this dissertation is to demonstrate the existence of a global solution
for a system of partial differential equations of the hyperbolic type. The equation studied
is a formulation of the heat equation following the model proposed by Cataneo. For the
solution of the system we use the theory of semigroups and to show the existence of such
solution we rely on results of nonlinear Functional Analysis to show the existence.
Universidade Federal de Santa Maria
Dissertação
2023-08-30T00:00:00Z