Descripción



In the present Thesis we present the results of the study of a set of problems related to the propagation of viruses in multilayered networks, ecology of populations and dynamics of ecosystems, as well as the techniques and mathematical models used in these studies. The first problem of interest is the propagation of computer viruses in multilayer networks. Current viruses use a propagation method known as multivector. This implies that they use, simultaneously, different communication standards in the infection process. In addition to the usual infection process using the communications network, they use propagation techniques that involve external devices connected to computers, software applications, email, etc. These forms of communication between the nodes have network topologies that are different from each other, although the nodes that constitute the networks are the same in all of them. That is, they constitute a single multilayer network. In this Thesis document we present mathematical models that allow us to study the propagation of multivector virus infection in a more realistic way than the models existing up to now, which assume that the nodes are different in each layer, or analyze the propagation in the layers separately. The model is based on previous models of SIS infection in networks. As main results it has been determined that the density of infected nodes in multilayer networks is higher than expected if the propagations if each layer are analyzed separately. In addition, the proposed model allows the design of immunization strategies for the nodes in order to slow down or prevent the epidemic in computer networks. This has immediate applications in the protection of computer networks against infections that may affect the continuity of the business. The model has been used with the experimental data of a multilayer network formed by the members of a scientific community, their collaborations and the existing computer networks in their research centers or universities. In order to study different types of interspecific interaction, two biological situations related to the ecosystems of bacteria existing in the human body have been modeled and analyzed. One of them is the treatment of symptoms of Cystic Fibrosis (CF) disease, which is a genetic disease whose symptomatology is related to the microbiota of the lung. For this problem has been proposed the introduction into that microbiota of a predatory bacteriophage of certain types of bacteria as a virulence factor modulator as an ecological strategy in order to control pathogenic bacteria in the lungs of the CF patient. We propose a predatorprey model on which stability is analyzed, as well as an agentoriented model. It has been determined through these models that the proposed treatment has, in fact, a theoretical basis and that there is a minimum threshold of predatory bacteria that must be introduced to achieve the desired therapeutic effect. This makes it possible to design strategies for treating the symptoms of CF patients. The third problem that is used as a framework in the models is that of infection by C. difficile in the human intestine, which, in certain cases, can cause death. A very effective treatment consists of performing a transplant of feces from a healthy donor, introducing a quantity of feces with bacteria in the intestine of the patient. In our study, several models of the microbiota have been made, including an agentoriented model. These models have allowed to determine that there is a relative threshold of minimum proportion of bacteria corresponding to the donor that must be introduced so that the ecosystem of the intestine can be altered and therefore the population of the pathogen is displaced. The behavior observed in the distribution of populations in the microbiota after a transplant has been reproduced qualitatively. The effect of the different interspecific interactions on the stability of the microbiota system has also b  
Internacional

No 
ISBN


Tipo de Tesis

Doctoral 
Calificación

Sobresaliente cum laude 
Fecha

18/03/2019 