Time to Extinction in Branching Processes and its Application in Epidemiology

2010 Mathematics Subject Classification: Primary 60J80; Secondary 92D30.The contemporary state of the theory of branching processes implies their application to any abstract population where individuals produce a set of new individuals. In this survey paper some recent developments in the study of time to extinction of continuous-time branching processes (BP) motivated by their applications in epidemiological modeling will be presented. The developed methodology and results are concerning Bellman−Harris (age-dependent) BP and more general Sevast'yanov's BP, as well

Comparison between Numerical and Simulation Methods for Age-dependent Branching Models with Immigration

2000 Mathematics Subject Classification: primary: 60J80, 60J85, secondary: 62M09, 92D40This work aims to provide and to compare numerical computation and simulation method to estimate the distribution of some relevant variables related to an age-dependent model allowing immigration at state zero. Specifically, we analyze the behaviour of the following variables: the extinction time and the waiting time for the beginning of the survival of population forever. They are strongly related to the population and re-population experiments in biology and to the wastewater treatment, as well. Throughout the paper, we illustrate the methods provided by some proper examples.This paper is partly supported by NFSI-Bulgaria, Grant No. MM-1101/2001

Analysing and Monitoring Surveillance Data of Mumps in Bulgaria

2000 Mathematics Subject Classification: 62P10.This paper aims to present the applicability of the Bayesian methodology for monitoring surveillance data collected for vaccine-preventable diseases, like mumps, measles and possibly others. We investigate the ability of implemetation of the R-Package "surveillance" especially written for monitoring surveillance data to the mumps data kindly provided by the National Center of Infectious and Parasitic Diseases in Bulgaria.The research was partially supported by appropriated state funds for research allocated to Sofia University (contract No 112/2010), Bulgaria

Total Progeny in a Subcritical Branching Process with two Types of Immigration

2000 Mathematics Subject Classification: 60J80, 60F05We consider subcritical Bellman-Harris branching processes with two types of immigration - one appears whenever the process hits zero state and an other one is in accordance of an independent renewal process. The law of large numbers (LLN) for the total progeny of these processes and Anscombe's type central limit theorem (CLT) for the total number of particles in the cycles completely finished by the moment t are obtained.The paper is supported by NFSI-Bulgaria, Grant No. MM-1101/2001

Poisson Random Measures and Noncritical Multitype Markov Branching Processes

We investigate noncritical multi-type Markov branching processes with immigration generated by Poisson measures. Limiting distributions are obtained when the rates of the Poisson measures are asymptotically equivalent to exponential or regularly varying functions. In particular, results analogous to a strong LLN are presented, and limiting normal distributions are obtained when the rates increase. When the rates decrease, then conditional limiting distributions are established. A stationary limiting distribution is obtained when the mean Poisson measure grows linearly. The asymptotic behaviour of the first and second moments of the processes is also investigated.NFSR of the Ministry of Education and Science of Bulgaria, grant No. KP–06-H22/3

Cyber Threats Optimization for e-government Services

A discrete model of e-government (e-gov) services, encompassing: n different components – state bodies (e.g. ministries, agencies etc., engaged after the legal basis regulations), working during m time intervals are used. One of the key measures that assure the model reliable work is the prevention from cyber attacks that will block the available e-gov services. In order to achieve business continuity of these services, a certain amount of funding has to be invested. The correct spending of these funds will assure external interventions block or repairing after passed cyber attacks

Cyber Intelligence in the Era of Big Data

Three key moments have to be solved for this complex problem proper ap- proaching: (i) selection of suitable formalism for fast and easy modelling, im- plementing both experts’ data and cyber incidents statistics on past and future cyberattacks trends; (ii) model quantification is necessary to be added, achieving a suitable machine interpretation for discrete optimization; (iii) some probabilistic elements have also to be considered, in order to achieve realistic models, practi- cal implementation decision support, benefitting from the “big data” knowledge context of the task. Practical implementation of these moments will be given further

Biochemical characterization of protease activity of Nsp3 from SARS-CoV-2 and its inhibition by nanobodies

Of the 16 non-structural proteins (Nsps) encoded by SARS CoV-2, Nsp3 is the largest and plays important roles in the viral life cycle. Being a large, multidomain, transmembrane protein, Nsp3 has been the most challenging Nsp to characterize. Encoded within Nsp3 is the papain-like protease domain (PLpro) that cleaves not only the viral polypeptide but also K48-linked polyubiquitin and the ubiquitin-like modifier, ISG15, from host cell proteins. We here compare the interactors of PLpro and Nsp3 and find a largely overlapping interactome. Intriguingly, we find that near full length Nsp3 is a more active protease compared to the minimal catalytic domain of PLpro. Using a MALDI-TOF based assay, we screen 1971 approved clinical compounds and identify five compounds that inhibit PLpro with IC50s in the low micromolar range but showed cross reactivity with other human deubiquitinases and had no significant antiviral activity in cellular SARS-CoV-2 infection assays. We therefore looked for alternative methods to block PLpro activity and engineered competitive nanobodies that bind to PLpro at the substrate binding site with nanomolar affinity thus inhibiting the enzyme. Our work highlights the importance of studying Nsp3 and provides tools and valuable insights to investigate Nsp3 biology during the viral infection cycle

Repurposing of the antibiotic nitroxoline for the treatment of mpox

The antiviral drugs tecovirimat, brincidofovir, and cidofovir are considered for mpox (monkeypox) treatment despite a lack of clinical evidence. Moreover, their use is affected by toxic side‐effects (brincidofovir, cidofovir), limited availability (tecovirimat), and potentially by resistance formation. Hence, additional, readily available drugs are needed. Here, therapeutic concentrations of nitroxoline, a hydroxyquinoline antibiotic with a favourable safety profile in humans, inhibited the replication of 12 mpox virus isolates from the current outbreak in primary cultures of human keratinocytes and fibroblasts and a skin explant model by interference with host cell signalling. Tecovirimat, but not nitroxoline, treatment resulted in rapid resistance development. Nitroxoline remained effective against the tecovirimat‐resistant strain and increased the anti‐mpox virus activity of tecovirimat and brincidofovir. Moreover, nitroxoline inhibited bacterial and viral pathogens that are often co‐transmitted with mpox. In conclusion, nitroxoline is a repurposing candidate for the treatment of mpox due to both antiviral and antimicrobial activity