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In the game of rock-paper-scissors with three players, this paper identifies conditions for a correlated equilibrium that differs from the mixed strategy Nash equilibrium and is evolutionarily stable. For this to occur, the correlation device attaches more probability to three-way ties and solo-winner outcomes than would result from the Nash equilibrium. The correlated equilibrium is evolutionarily stable because any mutant fares worse than a signal-following player when facing two players who follow their own correlated signals. The critical quality of the correlation device is to make this true both for potential mutants who would disobey their signal and instead choose the action which would beat the action signaled to the player, as well as for potential mutants who would deviate to the action that would be beaten by what the device signals to the player. These findings reveal how a strict correlated equilibrium can produce evolutionarily stable strategies for rock-paper-scissors with three players.

The degradation of paper is due to complex physical and chemical processes that occur as the paper ages, and is enhanced by environmental factors, such as the temperature and relative humidity, and by intrinsic parameters, such as the acidity of the paper. The literature reports that a large percentage of historic documents, manuscripts, and paper objects in museums, libraries and collections is susceptible to degradation phenomena, which may ultimately affect their integrity and longevity. This contribution presents a novel computational model to predict the degradation and lifetime of historic paper. The approach is based on: i) a multi-physics modelling framework, which considers the relevant chemical and mechanical degradation processes and the influence by the ambient environmental conditions, and ii) a multi-scale description, which includes the effect of the intrinsic hierarchical structure of paper, from the fibre- and fibrous network levels to the effective macro-scale, paper sheet level. The paper fibres constructing the fibrous network are characterized by an age-dependent, chemo-mechanical constitutive behaviour. In particular, an evolution equation describes the reduction of the degree of polymerization of cellulose as a function of time and the specific environmental conditions, which in turn is used for determining the fibre tensile strength. The fibre stresses induced by hygro-expansion and hygro-contraction under a change in relative humidity are computed using a coupled hygro-mechanical model, and lead to brittle damage once the fibre tensile strength is reached. Accordingly, the chemical degradation of individual fibres affects the local damage development and stress distribution in the fibrous network, and thereby governs the material response at the paper sheet scale. Asymptotic homogenization is used to calculate the effective hygro-mechanical properties of the fibrous network. A set of numerical simulations is performed to predict the time-dependent degradation of historic paper under a range of temperature, relative humidity and acidity conditions. From these results, isochrone degradation maps are constructed that illustrate the expected lifetime of historic paper as a function of the ambient climate conditions and the acidity of the paper. Further, a practical, analytical degradation function is derived that can be used for a fast estimation of the time-dependent stiffness degradation of paper. The outcome of this work may help conservators to determine the optimal indoor climate conditions in museums, archives and libraries for limiting or delaying time-dependent degradation of historic paper artefacts.

In simple dyadic games such as rock, paper, scissors (RPS), people exhibit peculiar sequential dependencies across repeated interactions with a stable opponent. These regularities seem to arise from a mutually adversarial process of trying to outwit their opponent. What underlies this process, and what are its limits? Here, we offer a novel framework for formally describing and quantifying human adversarial reasoning in the rock, paper, scissors game. We first show that this framework enables a precise characterization of the complexity of patterned behaviors that people exhibit themselves, and appear to exploit in others. This combination allows for a quantitative understanding of human opponent modeling abilities. We apply these tools to an experiment in which people played 300 rounds of RPS in stable dyads. We find that although people exhibit very complex move dependencies, they cannot exploit these dependencies in their opponents, indicating a fundamental limitation in people’s capacity for adversarial reasoning. Taken together, the results presented here show how the rock, paper, scissors game allows for precise formalization of human adaptive reasoning abilities.

We run stochastic simulations of the spatial version of the rock-paper-scissors game, considering that individuals use sensory abilities to scan the environment to detect the presence of enemies. If the local dangerousness level is above a tolerable threshold, individuals aggregate instead of moving randomly on the lattice. We study the impact of the locally adaptive aggregation on the organisms' spatial organisation by measuring the characteristic length scale of the spatial domains occupied by organisms of a single species. Our results reveal that aggregation is beneficial if triggered when the local density of opponents does not exceed $30\%$; otherwise, the behavioural strategy may harm individuals by increasing the average death risk. We show that if organisms can perceive further distances, they can accurately scan and interpret the signals from the neighbourhood, maximising the effects of the locally adaptive aggregation on the death risk. Finally, we show that the locally adaptive aggregation behaviour promotes biodiversity independently of the organism's mobility. The coexistence probability rises if organisms join conspecifics, even in the presence of a small number of enemies. We verify that our conclusions hold for more complex systems by simulating the generalised rock-paper-scissors models with five and seven species. Our discoveries may be helpful to ecologists in understanding systems where organisms' self-defence behaviour adapts to local environmental cues., 8 pages, 9 figures

This paper serves as a conceptualisation of how the principles of Whole Brain® thinking can be used to inform lecturer identity. The objective of this position paper is to engage discourse on the educational professional development of early-career academics in health sciences. It is about laying a scholarly foundation for self-study. As a scholarly community of practice in family medicine we wanted to determine to what extent the literature – theoretical framework – is silent on innovative means to ensure that academics take responsibility for their development, using self-regulated learning and self-empowerment. In our search for literature on theories of professional learning we came across the theory about Whole Brain® thinking. Our action research initiatives revolve around the notion of individuals’ preferences for different modes of thinking. Our preferred modes of thinking inform our teaching practice and lecturer identity. Este documento sirve como una conceptualización de como los principios del pensamiento Whole Brain® pueden usarse para informar la identidad del profesor. El objetivo de este documento de posición es participar en el discurso sobre el desarrollo profesional educativo de los académicos en las primeras carreras de ciencias de la salud. Se trata de sentar una base académica para el autoestudio. Como comunidad académica de práctica en medicina familiar, queríamos determinar en que medida la literatura – el marco teórico – guarda silencio sobre los medios innovadores para garantizar que los académicos asuman la responsabilidad de su desarrollo, utilizando el aprendizaje autorregulado y el autoempoderamiento. En nuestra búsqueda de literatura sobre teorías del aprendizaje profesional nos encontramos con la teoría del pensamiento Whole Brain®. Nuestras iniciativas de investigación-acción giran en torno a la noción de las preferencias de los individuos por diferentes modos de pensamiento. Nuestros modos preferidos de pensamiento informan nuestra práctica docente y nuestra identidad como profesor. O presente artigo busca uma conceitualização sobre como os princípios do pensamento holístico (ou baseado no modelo Whole Brain®) podem ser usados para informar a identidade do professor. O objetivo deste artigo de posição é envolver o discurso sobre o desenvolvimento profissional educacional de acadêmicos em início de carreira nas ciências da saúde; trata-se de estabelecer uma base acadêmica para o autoestudo. Como comunidade de prática em medicina familiar, queríamos determinar até que ponto a literatura – quadro teórico – está silenciosa sobre meios inovadores para garantir que os acadêmicos assumam a responsabilidade por seu desenvolvimento, usando a aprendizagem autorregulada e o autoempoderamento. Na nossa busca por literatura sobre teorias de aprendizagem profissional, encontramos a teoria sobre o pensamento Whole Brain®. Todas as iniciativas estão em torno da noção das preferências individuais por diferentes modos de pensamento; os modos de pensar que preferimos informam a nossa prática de ensino e a identidade docente.

Antipredator behaviour is a self-preservation strategy present in many biological systems, where individuals join the effort in a collective reaction to avoid being caught by an approaching predator. We study a nonhierarchical tritrophic system, whose predator-prey interactions are described by the rock-paper-scissors game rules. We performed a set of spatial stochastic simulations where organisms of one out of the species can resist predation in a collective strategy. The drop in predation capacity is local, which means that each predator faces a particular opposition depending on the prey group size surrounding it. Considering that the interference in a predator action depends on the prey's physical and cognitive ability, we explore the role of a conditioning factor that indicates the fraction of the species apt to perform the antipredator strategy. Because of the local unbalancing of the cyclic predator-prey interactions, departed spatial domains mainly occupied by a single species emerge. Unlike the rock-paper-scissors model with a weak species because a nonlocal reason, our findings show that if the predation probability of one species is reduced because individuals face local antipredator response, the species does not predominate. Instead, the local unbalancing of the rock-paper-scissors model results in the prevalence of the weak species' prey. Finally, the outcomes show that local unevenness may jeopardise biodiversity, with the coexistence being more threatened for high mobility., 9 pages, 11 figures

The possibility to dispose of paper mill sludge as part of a composition of container cardboard from secondary raw materials has been investigated. The fractional composition of the sludge was studied and it was shown that the main part of the fibers is represented by small particles with a size of up to 1.2mm. Studying the processes of formation of container cardboard when using paper mill sludge showed that an increase in the consumption of fibrous-inorganic waste leads to a deterioration in the physical and mechanical properties of cardboard. However, the increase in sludge consumption does not affect the surface absorption of water during one-sided wetting. The value of these indicators is within the normal range and is 25 and 70g/m2, respectively. In addition, an increase in sludge consumption from 10 to 50% in the manufacture of cardboard leads to a decrease in the degree of fiber retention on the grid from 86.3 to 82.1%. Regularities of using strengthening additives, namely industrial cationic and anionic flocculants, as well as native corn and modified starches for the strength of cardboard and the quality of sub-grid waters, have been established. Research results show that the effect of flocculants is quite ambiguous. On the one hand, there is a clearly observed positive impact on the quality of the sub-grid waters. This is due to the reduction of their turbidity due to smaller fiber washes. Nevertheless, the positive effect on physical and mechanical parameters is minimal, and in some cases, there is a decrease in strength indicators. The greater the efficiency of keeping fine fiber on the grid when using flocculants, the lower the values of physical and mechanical indicators. In general, when using sludge in the composition of cardboard in combination with flocculants and starch, the indicators were achieved that are considered standard for waste paper container cardboard of grade KT-1 according to TU U 17.1-41085075-002:2017

Document forgeries that involve modification of the materials used, such as ink and paper, provide evidence of any malpractices being performed. Forensic specialists use different techniques to identify and classify these samples; however, the most preferred method is to use nondestructive techniques to avoid any potential damage to the original specimen under investigation. Hyperspectral imaging has already been explored in several application domains and used as a powerful method in forensic investigations to extract information about the materials under examination. To precisely classify the material information and utilize the hyperspectral imaging technique's potential, we probed the potential of some hybrid spectral similarity measures to classify different commonly used paper samples. A comparison of these methods is quantitatively presented in this article.

Paper is a complex material consisting of a network of cellulose fibres at the micro-level. During manufacturing, the network is dried under restraint conditions due to tension in the paper web in machine direction. This gives rise to internal strains that are stored in the produced sheet. Upon exposure to a moisture cycle, these strains may be released. This results in permanent shrinkage that may cause instabilities such as curl or waviness of the sheet. The prime objective of this paper is to model this irreversible shrinkage and to link its magnitude to the properties of the fibres and of the network. For this purpose, randomly generated fibrous networks of different coverages (i.e. ratio of the area occupied by fibres and that of the sheet) are modeled by means of a periodic representative volume element (RVE). Within such RVEs, a finite element method combined with a kinematic hardening plasticity model at the scale of the fibres is used to capture the irreversible response. The computational results obtained demonstrate that the magnitude of the irreversible strains increases with coverage until a certain coverage and beyond that coverage decreases in magnitude. This phenomenon is explained by considering the area fraction of free-standing fibre segments relative to bonded fibre segments in the network. A structure–property dependency of irreversible strains at the sheet-level on the micro-structural parameters of the network is thereby established., SCOPUS: ar.j, info:eu-repo/semantics/published

International audience; We clarify some analytical expressions existing in the literature, • Within the correct formulae we conclude that there is no need for an ad hoc improvement on the opposite to the title paper, • We highlight the symmetry properties of the function to be integrated in order to agree with the usual assumptions made to derive the Kramers-Kronig relations, • The analytical formula we provide may be used to increase the accuracy of the "Poor Man's Kramers-Kronig analysis" method and the "Kramers-Kronig constrained variational analysis" method.

In this paper, we present a class of integer codes capable of correcting burst asymmetric errors. The presented codes are constructed with the help of a computer and have the potential to be used in various practical systems, such as optical networks and VLSI memories. In order to evaluate the performance of the proposed codes, the paper analyzes the probability of erroneous decoding for different bit error rates. The presented codes are also analyzed from a rate-efficiency point of view. The obtained results show that for many data lengths they require less check-bits than optimal burst error correcting codes. This is the peer-reviewed version of the paper: Pokhrel, Nabin Kumar, Das, Pankaj Kumar, Radonjic, Aleksandar, "Integer codes capable of correcting burst asymmetric errors" in Journal of Applied Mathematics and Computing (2022), [https://doi.org/10.1007/s12190-022-01770-7]

The coronavirus disease 2019 (COVID-19) pandemic has fatalized 216 countries across the world and has claimed the lives of millions of people globally. Researches are being carried out worldwide by scientists to understand the nature of this catastrophic virus and find a potential vaccine for it. The most possible efforts have been taken to present this paper as a form of contribution to the understanding of this lethal virus in the first and second wave. This paper presents a unique technique for the methodical comparison of disastrous virus dissemination in two waves amid five most infested countries and the death rate of the virus in order to attain a clear view on the behaviour of the spread of the disease. For this study, the data set of the number of deaths per day and the number of infected cases per day of the most affected countries, the USA, Brazil, Russia, India, and the UK, have been considered in the first and second waves. The correlation fractal dimension has been estimated for the prescribed data sets of COVID-19, and the rate of death has been compared based on the correlation fractal dimension estimate curve. The statistical tool, analysis of variance, has also been used to support the performance of the proposed method. Further, the prediction of the daily death rate has been demonstrated through the autoregressive moving average model. In addition, this study also emphasis a feasible reconstruction of the death rate based on the fractal interpolation function. Subsequently, the normal probability plot is portrayed for the original data and the predicted data, derived through the fractal interpolation function to estimate the accuracy of the prediction. Finally, this paper neatly summarized with the comparison and prediction of epidemic curve of the first and second waves of COVID-19 pandemic to visualize the transmission rate in the both times.

The methods for identification of near-duplicates in electronic scientific papers, which include the content of the same type, for example, text data, mathematical formulas, numerical data, etc. were described. For text data, the method of locally sensitive hashing with the finding of Hamming distance between the elements of indices of electronic scientific papers was formalized. If Hamming distance exceeds a fixed numerical threshold, a scientific paper contains a near-duplicate. For numerical data, sub-sequences for each scientific work are formed and the proximity between the papers is determined as the Euclidian distance between the vectors consisting of the numbers of these sub-sequences. To compare mathematical formulas, the method for comparing the sample of formulas is used and the names of variables are compared. To identify near-duplicates in graphic information, two directions are separated: finding key points in the image and applying locally sensitive hashing for individual pixels of the image. Since scientific papers often include such objects as schemes and diagrams, subscriptions to them are examined separately using the methods for comparing text information. The combined method for identification of near-duplicates in electronic scientific papers, which combines the methods for identification of near-duplicates of various types of data, was proposed. To implement the combined method for the identification of near-duplicates in electronic scientific papers, an information-analytical system that processes scientific materials depending on the content type was devised. This makes it possible to qualitatively identify near-duplicates and as widely as possible identify possible abuses and plagiarism in electronic scientific papers: scientific articles, dissertations, monographs, conference materials, etc.

Social media has been playing a vital importance in information sharing at massive scale due to its easy access, low cost, and faster dissemination of information. Its competence to disseminate the information across a wide audience has raised a critical challenge to determine the social data provenance of digital content. Social Data Provenance describes the origin, derivation process, and transformations of social content throughout its lifecycle. In this paper, we present a Big Social Data Provenance (BSDP) Framework for key-value pair (KVP) database using the novel concept of Zero-Information Loss Database (ZILD). In our proposed framework, a huge volume of social data is first fetched from the social media (Twitter's Network) through live streaming and simultaneously modelled in a KVP database by using a query-driven approach. The proposed framework is capable in capturing, storing, and querying provenance information for different query sets including select, aggregate, standing/historical, and data update (i.e., insert, delete, update) queries on Big Social Data. We evaluate the performance of proposed framework in terms of provenance capturing overhead for different query sets including select, aggregate, and data update queries, and average execution time for various provenance queries.

Natural language undergoes significant transformation from the domain of specialized research to general news intended for wider consumption. This transition makes the information vulnerable to misinterpretation, misrepresentation, and incorrect attribution, all of which may be difficult to identify without adequate domain knowledge and may exist even in the presence of explicit citations. Moreover, newswire articles seldom provide a precise correspondence between a specific claim and its origin, making it harder to identify which claims, if any, reflect the original findings. For instance, an article stating “Flagellin shows therapeutic potential with H3N2, known as Aussie Flu.” contains two claims (“Flagellin ... H3N2,” and “H3N2, known as Aussie Flu”) that may be true or false independent of each other, and it is prima facie unclear which claims, if any, are supported by the cited research. We build a dataset of sentences from medical news along with the sources from peer-reviewed medical research journals they cite. We use these data to study what a general reader perceives to be true, and how to verify the scientific source of claims. Unlike existing datasets, this captures the metamorphosis of information across two genres with disparate readership and vastly different vocabularies and presents the first empirical study of health-related fact-checking across them.

During the outbreak of emerging infectious diseases, media coverage and medical resource play important roles in affecting the disease transmission. To investigate the effects of the saturation of media coverage and limited medical resources, we proposed a mathematical model with extra compartment of media coverage and two nonlinear functions. We theoretically and numerically investigate the dynamics of the proposed model. Given great difficulties caused by high nonlinearity in theoretical analysis, we separately considered subsystems with only nonlinear recovery or with only saturated media impact. For the model with only nonlinear recovery, we theoretically showed that backward bifurcation can occur and multiple equilibria may coexist under certain conditions in this case. Numerical simulations reveal the rich dynamic behaviors, including forward-backward bifurcation, Hopf bifurcation, saddle-node bifurcation, homoclinic bifurcation and unstable limit cycle. So the limitation of medical resources induces rich dynamics and causes much difficulties in eliminating the infectious diseases. We then investigated the dynamics of the system with only saturated media impact and concluded that saturated media impact hardly induces the complicated dynamics. Further, we parameterized the proposed model on the basis of the COVID-19 case data in mainland China and data related to news items, and estimated the basic reproduction number to be 2.86. Sensitivity analyses were carried out to quantify the relative importance of parameters in determining the cumulative number of infected individuals at the end of the first month of the outbreak. Combining with numerical analyses, we suggested that providing adequate medical resources and improving media response to infection or individuals' response to mass media may reduce the cumulative number of the infected individuals, which mitigates the transmission dynamics during the early stage of the COVID-19 pandemic.

We developed an endemic model of COVID-19 to assess the impact of vaccination and immunity waning on the dynamics of the disease. Our model exhibits the phenomenon of backward bifurcation and bi-stability, where a stable disease-free equilibrium coexists with a stable endemic equilibrium. The epidemiological implication of this is that the control reproduction number being less than unity is no longer sufficient to guarantee disease eradication. We showed that this phenomenon could be eliminated by either increasing the vaccine efficacy or by reducing the disease transmission rate (adhering to non-pharmaceutical interventions). Furthermore, we numerically investigated the impacts of vaccination and waning of both vaccine-induced immunity and post-recovery immunity on the disease dynamics. Our simulation results show that the waning of vaccine-induced immunity has more effect on the disease dynamics relative to post-recovery immunity waning and suggests that more emphasis should be on reducing the waning of vaccine-induced immunity to eradicate COVID-19.

The composition of legumes and sugar beet contains a large number of useful mineral and vitamin substances. The use of composite flour from leguminous crops for the preparation of bakery products helps increase food and biochemical properties. The main objects of this research are chickpea flour, bean flour, dry sugar beet powder, and wheat flour of the first grade. The main problem is an insufficient amount of minerals and vitamins, so the purpose of this work is to enrich bakery products and replace sugar in the recipe with sugar beet powder. The results showed that composite flour and sugar beet increased calcium content by 13.54mg/100g, iron ‒ by 0.57mg/100g, potassium ‒ by 141.03mg/100g, phosphorus ‒ by 38.89mg/100g, vitamin A ‒ by 0.002mg/100g, vitamin B2 ‒ by 0.016mg/100g, vitamin E ‒ by 0.32mg/100g, and vitamin PP ‒ by 0.405mg/100g. Microbiological indicators meet the established norms and requirements; the amount of mesophilic aerobic and facultative-anaerobic microorganisms, yeast, and mold in the test bun was the least compared to the control sample. As a result, it was proved that the use of composite flour of leguminous crops contributes to an increase in the nutritional and biological values of bakery products, and the application of dried sugar beet powder makes it possible to completely exclude sugar from the formulation of the resulting product. Employing this technology and formulations for obtaining bakery products makes it possible to expand the range of bakery products, reduce the duration of the manufacturing process, improve the quality of finished products, increase labor productivity. That also contributes to the improvement of the socio-economic indicators of bakery and confectionery enterprises

Current explosive outbreak of COVID-19 around the world is a complex spatiotemporal process with hidden interactions between viruses and humans. This study aims at clarifying the transmission patterns and the driving mechanism that contributed to the COVID-19 prevalence across the provinces of China. Thus, a new dynamical transmission model is established by an ordinary differential system. The model takes into account the hidden circulation of COVID-19 virus among/within humans, which incorporates the spatial diffusion of infection by parameterizing human mobility. Theoretical analysis indicates that the basic reproduction number is a unique epidemic threshold, which can unite infectivity in each region by human mobility and can totally determine whether COVID-19 proceeds among multiple regions. By validating the model with real epidemic data in China, it is found that (1) if without any intervention, COVID-19 would overrun China within three months, resulting in more than 1.1 billion clinical infections and 0.2 billion subclinical infections; (2) high frequency of human mobility can trigger COVID-19 diffusion across each province in China, no matter where the initial infection locates; (3) travel restrictions and other non-pharmaceutical interventions must be implemented simultaneously for disease control; and (4) infection sites in central and east (rather than west and northeast) of China would easily stimulate quick diffusion of COVID-19 in the whole country. Supplementary Information The online version supplementary material available at 10.1007/s11071-021-07001-1.

We show the direct applicability of the Brouwer fixed point theorem for the existence of equilibrium points and periodic solutions for differential systems on general domains satisfying geometric conditions at the boundary. We develop a general approach for arbitrary bound sets and present applications to the case of convex and star-shaped domains. We also provide an answer to a question raised in a recent paper of Cid and Mawhin., Comment: 22 pages, 3 figures

Cloudiness or formation is a concept routinely used in industry to address deviations from homogeneity in nonwovens and papers. Measuring a cloudiness index based on image data is a common task in industrial quality assurance. The two most popular ways of quantifying cloudiness are based on power spectrum or correlation function on the one hand or the Laplacian pyramid on the other hand. Here, we recall the mathematical basis of the first approach comprehensively, derive a cloudiness index, and demonstrate its practical estimation. We prove that the Laplacian pyramid as well as other quantities characterizing cloudiness like the range of interaction and the intensity of small-angle scattering are very closely related to the power spectrum. Finally, we show that the power spectrum can be measured easily by image analysis methods and carries more information than the alternatives.

Meat-containing bread with the use of hemp flour has been devised, with the subsequent assessment of its physical and chemical, sensory properties involving the study into the technological indicators of new products. Three experimental formulations for meat-containing bread were developed, which included semi-fat pork, poultry, mechanically deboned turkey, pumpkin pulp, and 8, 10, 12% of hemp flour. A meat-containing bread from combined raw materials was adopted as control. All samples were evaluated taking into consideration their physical and chemical, technological, and sensory characteristics. It has been proven that the addition of hemp flour to the formulation improved the consumer value of products by increasing the content of protein, fat, andminerals. It was found that the protein content in the developed products was 18.03‒19.53g/100g, which is 3.21‒11.80% higher than that of the analog. The fat content increased by 17.84–56.83%, which also led to an increase in the calorie content of products. It has been experimentally confirmed that the introduction of hemp flour into bread'sminced meat improves the functional and technological indicators of model meat systems. An increase in water-binding capacity was observed, by 13.46‒22.15%; in water-holding capacity, by 10.34‒21.43%; in fat-holding capacity, by 17.2‒26.9%. The combination of semi-fat pork, poultry, mechanically deboned turkey, and hemp flour increases the ductility of theminced meat while reducing the shear stress, contributes to the good forming properties of theminced meat. The sensory analysis of the prototypes showed their high consumer value. The organoleptic assessment and sensory analysis of the prototypes demonstrated high consumer properties of the manufactured products, which makes it possible to recommend them for inclusion in the diets of various segments of the population

One of the main concerns during the COVID-19 pandemic was the protection of healthcare workers against the novel coronavirus. The critical role and vulnerability of healthcare workers during the COVID-19 pandemic leads us to derive a mathematical model to express the spread of coronavirus between the healthcare workers. In the first step, the SECIRH model is introduced, and then the mathematical equations are written. The proposed model includes eight state variables, i.e., Susceptible, Exposed, Carrier, Infected, Hospitalized, ICU admitted, Dead, and finally Recovered. In this model, the vaccination, protective equipment, and recruitment policy are considered as preventive actions. The formal confirmed data provided by the Iranian ministry of health is used to simulate the proposed model. The simulation results revealed that the proposed model has a high degree of consistency with the actual COVID-19 daily statistics. In addition, the roles of vaccination, protective equipment, and recruitment policy for the elimination of coronavirus among the healthcare workers are investigated. The results of this research help the policymakers to adopt the best decisions against the spread of coronavirus among healthcare workers.

Taking two susceptible groups into account, we formulate a modified subhealthy-healthy-infected-recovered (SHIR) model with time delay and nonlinear incidence rate in networks with different topologies. Concretely, two dynamical systems are designed in homogeneous and heterogeneous networks by utilizing mean field equations. Based on the next-generation matrix and the existence of a positive equilibrium point, we derive the basic reproduction numbers \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{0}^{1}$$\end{document}R01 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{0}^{2}$$\end{document}R02 which depend on the model parameters and network structure. In virtue of linearized systems and Lyapunov functions, the local and global stabilities of the disease-free equilibrium points are, respectively, analyzed when \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{0}^{1}1$$\end{document}R01>1. Finally, numerical simulations are performed to conduct sensitivity analysis and confirm theoretical results. Moreover, some conjectures are proposed to complement dynamical behavior of two systems.