Spatially Extended SHAR Epidemiological Framework of Infectious Disease Transmission

Mathematical models play an important role in epidemiology. The inclusion of a spatial component in epidemiological models is especially important to understand and address many relevant ecological and public health questions, e.g., when wanting to differentiate transmission patterns across geographical regions or when considering spatially heterogeneous intervention measures. However, the introduction of spatial effects can have significant consequences on the observed model dynamics and hence must be carefully analyzed and interpreted. Cellular automata epidemiological models typically rely on simplified computational grids but can provide valuable insight into the spatial dynamics of transmission within a population by suitably accounting for the connections between individuals in the considered community. In this paper, we describe a stochastic cellular automata disease model based on an extension of the traditional Susceptible-Infected-Recovered (SIR) compartmentalization of the population, namely, the Susceptible-Hospitalized-Asymptomatic-Recovered (SHAR) formulation, in which infected individuals either present a severe form of the disease, thus requiring hospitalization, or belong to the so-called mild/asymptomatic class. The critical transmission threshold is derived analytically in the nonspatial SHAR formulation, and this generalizes previously obtained theoretical results for the SIR model. We present simulation results discussing the effect of key model parameters and of spatial correlations on model outputs and propose an algorithm for tracking the evolution of infection clusters within the considered population. Focusing on the role of import and criticality on the overall dynamics, we conclude that the current spatial setting increases the critical transmission threshold in comparison to the nonspatial model

A multiscale network-based model of contagion dynamics: heterogeneity, spatial distancing and vaccination

Lockdown and vaccination policies have been the major concern in the last year in order to contain the SARS-CoV-2 infection during the COVID-19 pandemic. In this paper we present a model able to evaluate alternative lockdown policies and vaccination strategies. Our approach integrates and refines the multiscale model proposed by Bellomo et al. , 2020, analyzing alternative network structures and bridging two perspectives to study complexity of living systems. Inside dierent matrices of contacts we explore the impact of closures of distinct nodes upon the overall contagion dynamics. Social distancing is shown to be more effective when targeting the reduction of contacts among and inside the most vulnerable nodes, namely hospitals/nursing homes. Moreover, our results suggest that school closures alone would not signicantly affect the infection dynamics and the number of deaths in the population. Finally, we investigate a scenario with immunization in order to understand the effectiveness of targeted vaccination policies towards the most vulnerable individuals. Our model agrees with the current proposed vaccination strategy prioritising the most vulnerable segment of the population to reduce deaths.Marie Sklodowska-Curie grant agreement No 79249

Understanding COVID-19 Epidemics: A Multi-Scale Modeling Approach

COVID-19 was declared a pandemic by the World Health Organization in March 2020 and, since then, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease spreading and control under different scenarios. In this chapter, two different approaches to model the spread of COVID-19 are presented. The model frameworks are described and results are presented in connection with the current epidemiological situation of vaccination roll-out. This chapter is structured as follows. Section 2 presents the stochastic SHARUCD modeling framework developed within a modeling task force created to support public health managers during the COVID-19 crisis. As an extension of the basic SHAR (Susceptible-Hospitalized-Asymptomatic-Recovered) model, the SHARUCD models were parameterized and validated with empirical data for the Basque Country, Spain, and have been used (up until now) to monitor COVID-19 spreading and control over the course of the pandemic. Section 3 introduces the kinetic theory of active particles (KTAP) model for the spread of a disease. With an exploratory analysis, we present a possible way to deal with heterogeneity and multiscale features. Section 4 concludes this work, with a discussion on both models and further research perspectives description

Modeling dengue immune responses mediated by antibodies: A qualitative study

Dengue fever is a viral mosquito-borne infection and a major international public health concern. With 2.5 billion people at risk of acquiring the infection around the world, disease severity is influenced by the immunological status of the individual, seronegative or seropositive, prior to natural infection. Caused by four antigenically related but distinct serotypes, DENV-1 to DENV-4, infection by one serotype confers life-long immunity to that serotype and a period of temporary cross-immunity (TCI) to other serotypes. The clinical response on exposure to a second serotype is complex with the so-called antibody-dependent enhancement (ADE) process, a disease augmentation phenomenon when pre-existing antibodies to previous dengue infection do not neutralize but rather enhance the new infection, used to explain the etiology of severe disease. In this paper, we present a minimalistic mathematical model framework developed to describe qualitatively the dengue immunological response mediated by antibodies. Three models are analyzed and compared: (i) primary dengue infection, (ii) secondary dengue infection with the same (homologous) dengue virus and (iii) secondary dengue infection with a different (heterologous) dengue virus. We explore the features of viral replication, antibody production and infection clearance over time. The model is developed based on body cells and free virus interactions resulting in infected cells activating antibody production. Our mathematical results are qualitatively similar to the ones described in the empiric immunology literature, providing insights into the immunopathogenesis of severe disease. Results presented here are of use for future research directions to evaluate the impact of dengue vaccines.A.S, H.F., and E.S. E.S. has received funded from the Indonesian RistekBrin Grant No. 122M/IT1.C02/TA.00/2021, 2021 (previously RistekDikti 2018-2021). M.A. received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No 792494

Modeling Dengue Immune Responses Mediated by Antibodies: Insights on the Biological Parameters to Describe Dengue Infections

Dengue fever is a viral mosquito-borne disease, a significant global health concern, with more than one third of the world population at risk of acquiring the disease. Caused by 4 antigenically distinct but related virus serotypes, named DENV-1, DENV-2, DENV-3, and DENV-4, infection by one serotype confers lifelong immunity to that serotype and a short period of temporary cross immunity to other related serotypes. Severe dengue is epidemiologically associated with a secondary infection caused by a heterologous serotype via the so-called antibody-dependent enhancement (ADE), an immunological process enhancing a new infection. Within-host dengue modeling is restricted to a small number of studies so far. With many open questions, the understanding of immunopathogenesis of severe disease during recurrent infections is important to evaluate the impact of newly licensed vaccines. In this paper, we revisit the modeling framework proposed by Sebayang et al. and perform a detailed sensitivity analysis of the well-known biological parameters and its possible combinations to understand the existing data sets. Using numerical simulations, we investigate features of viral replication, antibody production, and infection clearance over time for three possible scenarios: primary infection, secondary infection caused by homologous serotype, and secondary infection caused by heterologous serotype. Besides, describing well the infection dynamics as reported in the immunology literature, our results provide information on parameter combinations to best describe the differences on the immunological dynamics of secondary infections with homologous and heterologous viruses. The results presented here will be used as baseline to investigate a more complex within-host dengue model.Marie Skłodowska-Curie grant agreement No 79249

Critical fluctuations in epidemic models explain COVID‑19 post‑lockdown dynamics

As the COVID-19 pandemic progressed, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease spreading. The momentary reproduction ratio r(t) of an epidemic is used as a public health guiding tool to evaluate the course of the epidemic, with the evolution of r(t) being the reasoning behind tightening and relaxing control measures over time. Here we investigate critical fluctuations around the epidemiological threshold, resembling new waves, even when the community disease transmission rate β is not signifcantly changing. Without loss of generality, we use simple models that can be treated analytically and results are applied to more complex models describing COVID-19 epidemics. Our analysis shows that, rather than the supercritical regime (infectivity larger than a critical value, β>βc) leading to new exponential growth of infection, the subcritical regime (infectivity smaller than a critical value, β<βc) with small import is able to explain the dynamic behaviour of COVID-19 spreading after a lockdown lifting, with r(t) ≈ 1 hovering around its threshold value.BMTF “Mathematical Modeling Applied to Health” Project European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 79249

Seasonally Forced SIR Systems Applied to Respiratory Infectious Diseases, Bifurcations, and Chaos

We investigate models to describe respiratory diseases with fast mutating virus pathogens such that after some years the aquired resistance is lost and hosts can be infected with new variants of the pathogen. Such models were initially suggested for respiartory diseases like influenza, showing complex dynamics in reasonable parameter regions when comparing to historic empirical influenza like illness data, e.g., from Ille de France. The seasonal forcing typical for respiratory diseases gives rise to the different rich dynamical scenarios with even small parameter changes. Especially the seasonality of the infection leads for small values already to period doubling bifurcations into chaos, besides additional coexisting attractors. Such models could in the future also play a role in understanding the presently experienced COVID-19 pandemic, under emerging new variants and with only limited vaccine efficacies against newly upcoming variants. From first period doubling bifurcations, we can eventually infer at which close by parameter regions complex dynamics including deterministic chaos can arise.Marie Skłodowska-Curie grant agreement No. 79249

Metformin improves skin capillary reactivity in normoglycaemic subjects with the metabolic syndrome

WSTĘP. Insulinooporność i rodzinne występowanie cukrzycy niezależnie wiążą się z dysfunkcją śródbłonka. Stres oksydacyjny odgrywa kluczową rolę w patofizjologii uszkodzenia naczyń krwionośnych. Metformina, oprócz obniżania stężenia glukozy, działa ochronnie na naczynia. Celem niniejszej pracy by&#179;o zbadanie, czy metformina korzystnie wpływa na krążenie w odżywczych naczyniach włosowatych skóry oraz czy zmniejsza stres oksydacyjny u osób wysokiego ryzyka wystąpienia cukrzycy typu 2 i chorób sercowo-naczyniowych. METODY. Badaniem objęto 30 pacjentów z prawidłowym stężeniem glukozy i zespołem metabolicznym (MS), którzy mieli krewnych chorych na cukrzycę typu 2. średni wiek wynosił 39,1 &#177; 8,4 roku, a wskaźnik masy ciała (BMI) 35,8 &#177; 4,8 kg/m2 (średnia &#177; odchylenie standardowe). Pacjentów losowo podzielono na 2 grupy za pomocą metody podwójnie &#156;lepej próby w stosunku 1:1 - 14 osób otrzymywało placebo, a 16 metforminę (1700 mg/d.). Wyjściowo i po zakończeniu badania pobrano krew do analizy biochemicznej oraz mocz w celu określenia stężenia 8-epi-prostaglandyny F2&#945; (8-epi-PGF2&#945;). Krążenie w naczyniach włosowatych oceniano za pomocą wideokapilaroskopii obrąbka naskórkowego, podczas której analizowano średnicę pętli naczyń włosowatych doprowadzających (AF), odprowadzających (EF) i wierzchołkowych (AP), funkcjonalną gęstość naczyń włosowatych (FCD), prędkość przepływu czerwonych ciałek krwi w spoczynku (RBCV) oraz po 1 minucie od okluzji naczyń tętniczych (RBCVmax), a także czas potrzebny do jej osiągnięcia (TRBCVmax). WNIOSKI. Metformina poprawiła reaktywność naczyń włosowatych skóry u osób z prawidłową glikemią i zespołem metabolicznym, niezależnie od zmian stężenia 8-epi-PGF2&#945;.AIMS. Insulin resistance and a parental history of diabetes mellitus are independently associated with endothelial dysfunction. Oxidative stress has a pivotal role in the pathophysiology of vascular injury. Metformin, in addition to its glucose-lowering properties, has vasculoprotective effects. We investigated whether metformin has beneficial effects on the nutritive skin capillary circulation and deceases oxidative stress in a group at high risk for type 2 diabetes mellitus (T2DM) and cardiovascular disease. METHODS. Thirty normoglycaemic subjects with the metabolic syndrome (MS), who had first-degree relatives with T2DM, participated. The mean age was 39.1 &#177; 8.4 years and body mass index (BMI) 35.7 &#177; &#177; 4.8 kg/m2 (mean &#177; SD). Subjects were randomized 1:1 to receive placebo (n = 14) or metformin (n = 16; 1700 mg/day) in a double-blind study. At baseline and post treatment, blood and urine samples were collected for biochemical and 8-epi-prostaglandin F2&#945; (8-epi-PGF2&#945;) analysis, respectively. Microcirculation was assessed by nailfold videocapillaroscopy, analysing afferent (AF), efferent (EF) and apical (AP) diameters of capillary loops, functional capillary density (FCD), red blood cell velocity at rest (RBCV), after 1 min arterial occlusion (RBCVmax) and time (TRBCVmax) taken to reach it. RESULTS. Groups did not differ significantly in anthropometric, clinical, laboratory or microvascular measurements at baseline. In the metformin group, weight, BMI, systolic blood pressure and fasting plasma glucose fell, and lipid profile and microcirculatory parameters FCD, AF, EF, AP, RBCVmax and TRBCVmax improved (all p < 0.01). No relationship between clinico-laboratory parameters and microvascular reactivity was observed, except for changes in total and lowdensity lipoprotein-cholesterol and RBCVmax. 8-epi-PGF2&#945; did not change significantly in either group. CONCLUSIONS. Metformin improved skin capillary reactivity in normoglycaemic MS subjects independently of significant changes in 8-epi-PGF2&#945; levels

Hopf algebras and Markov chains: Two examples and a theory

The operation of squaring (coproduct followed by product) in a combinatorial Hopf algebra is shown to induce a Markov chain in natural bases. Chains constructed in this way include widely studied methods of card shuffling, a natural "rock-breaking" process, and Markov chains on simplicial complexes. Many of these chains can be explictly diagonalized using the primitive elements of the algebra and the combinatorics of the free Lie algebra. For card shuffling, this gives an explicit description of the eigenvectors. For rock-breaking, an explicit description of the quasi-stationary distribution and sharp rates to absorption follow.Comment: 51 pages, 17 figures. (Typographical errors corrected. Further fixes will only appear on the version on Amy Pang's website, the arXiv version will not be updated.