The spread of a financial virus through Europe and beyond

Kostylenko, Olena; Rodrigues, Helena Sofia; Torres, Delfim F. M.

doi:10.3934/math.2019.1.86

Cited by 9 publications

(5 citation statements)

References 26 publications

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“…This process resembles epidemic spreading in networks [5]. Under a simplifying assumption and to better explore the network potential for risk transmission, we model them in a similar way as epidemic spreading as was recently done in [6][7][8]. This is an oversimplification, the basic mechanisms of default propagation and epidemic spreading have similarities as branching process and chain reactions.…”

Section: Introductionmentioning

confidence: 99%

Assessing the risk of default propagation in interconnected sectoral financial networks

et al. 2019

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Systemic risk of financial institutions and sectoral companies relies on their inter-dependencies. The inter-connectivity of the financial networks has proven to be crucial to understand the propagation of default, as it plays a central role to assess the impact of single default events in the full system. Here, we take advantage of complex network theory to shed light on the mechanisms behind default propagation. Using real data from the BBVA, the second largest bank in Spain, we extract a financial network from customer-supplier transactions among more than 140,000 companies, and their economic flows. Then, we introduce a computational model, inspired by the probabilities of default contagion, that allow us to obtain the main statistics of default diffusion given the network structure at individual and system levels. Our results show the exposure of different sectors to default cascades, therefore allowing for a quantification and ranking of sectors accordingly. This information is relevant to propose countermeasures to default propagation in specific scenarios.

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Section: Introductionmentioning

confidence: 99%

Assessing the risk of default propagation in interconnected sectoral financial networks

et al. 2019

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“…For an example of an experimental study that quantifies the effects of therapy, see, e.g., [5], where data on SIV and CTL cell kinetics during primary monkey infection is provided. For similar compartmental models in different contexts see [11,13]. The main novelty here is to consider that the antibody growth depends not only on the virus and on the antibodies concentration but also on the uninfected cells concentration.…”

mentioning

confidence: 99%

Optimal control of an HIV model with a trilinear antibody growth function

Allali¹,

Harroudi²,

Torres³

2022

DCDS-S

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<p style='text-indent:20px;'>We propose and study a new mathematical model of the human immunodeficiency virus (HIV). The main novelty is to consider that the antibody growth depends not only on the virus and on the antibodies concentration but also on the uninfected cells concentration. The model consists of five nonlinear differential equations describing the evolution of the uninfected cells, the infected ones, the free viruses, and the adaptive immunity. The adaptive immune response is represented by the cytotoxic T-lymphocytes (CTL) cells and the antibodies with the growth function supposed to be trilinear. The model includes two kinds of treatments. The objective of the first one is to reduce the number of infected cells, while the aim of the second is to block free viruses. Firstly, the positivity and the boundedness of solutions are established. After that, the local stability of the disease free steady state and the infection steady states are characterized. Next, an optimal control problem is posed and investigated. Finally, numerical simulations are performed in order to show the behavior of solutions and the effectiveness of the two incorporated treatments via an efficient optimal control strategy.</p>

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mentioning

confidence: 99%

Optimal control of an HIV model with a trilinear antibody growth function

Allali,

Harroudi,

Torres

2021

Preprint

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We propose and study a new mathematical model of the human immunodeficiency virus (HIV). The main novelty is to consider that the antibody growth depends not only on the virus and on the antibodies concentration but also on the uninfected cells concentration. The model consists of five nonlinear differential equations describing the evolution of the uninfected cells, the infected ones, the free viruses, and the adaptive immunity. The adaptive immune response is represented by the cytotoxic T-lymphocytes (CTL) cells and the antibodies with the growth function supposed to be trilinear. The model includes two kinds of treatments. The objective of the first one is to reduce the number of infected cells, while the aim of the second is to block free viruses. Firstly, the positivity and the boundedness of solutions are established. After that, the local stability of the disease free steady state and the infection steady states are characterized. Next, an optimal control problem is posed and investigated. Finally, numerical simulations are performed in order to show the behavior of solutions and the effectiveness of the two incorporated treatments via an efficient optimal control strategy.

show abstract

The spread of a financial virus through Europe and beyond

Cited by 9 publications

References 26 publications

Assessing the risk of default propagation in interconnected sectoral financial networks

Assessing the risk of default propagation in interconnected sectoral financial networks

Optimal control of an HIV model with a trilinear antibody growth function

Optimal control of an HIV model with a trilinear antibody growth function

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