Comprehensive analysis of a stochastic wireless sensor network motivated by Black-Karasinski process

Wireless sensor networks (WSNs) encounter a significant challenge in ensuring network security due to their operational constraints. This challenge stems from the potential infiltration of malware into WSNs, where a single infected node can rapidly propagate worms to neighboring nodes. To address this issue, this research introduces a stochastic S E I R S model to characterize worm spread in WSNs. Initially, we established that our model possesses a globally positive solution. Subsequently, we determine a threshold value for our stochastic system and derive a set of sufficient conditions that dictate the persistence or extinction of worm spread in WSNs based on the mean behavior. Our study reveals that environmental randomness can impede the spread of malware in WSNs. Moreover, by utilizing various parameter sets, we obtain approximate solutions that showcase these precise findings and validate the effectiveness of the proposed S E I R S model, which surpasses existing models in mitigating worm transmission in WSNs.

Analysis and comparative study of a deterministic mathematical model of SARS-COV-2 with fractal-fractional operators: a case study

In this paper, we investigate a fractal-fractional-order mathematical model with the influence of hospitalized patients and the impact of vaccination with fractal-fractional operators. The respective derivatives are considered in the Caputo, Caputo Fabrizio, and Atangana-Baleanu senses of fractional order α and fractal dimension τ . For the proposed problem, some results regarding basic reproduction number and stability are given. Using the next-generation matrix approach, we have investigated the global and local stability of several types of equilibrium points. We provide a detailed analysis of the existence and uniqueness of the solution. Moreover, we fit the model with the real data of Pakistan from June 01, 2020, till March 24, 2021. Then, we use the fractal-fractional derivative to find a numerical solution for the model. MATLAB software is used for numerical illustration. Graphical presentations corresponding to different parameteric values are given as well.

Modeling and Analyzing Xylem Vulnerability to Embolism as an Epidemic Process

Xylem vulnerability to embolism can be quantified by "vulnerability curves" (VC) that are obtained by subjecting wood samples to increasingly negative water potential and monitoring the progressive loss of hydraulic conductivity. VC are typically sigmoidal, and various approaches are used to fit the experimentally obtained VC data for extracting benchmark data of vulnerability to embolism. In addition to such empirical methods, mechanistic approaches to calculate embolism propagation are epidemic modeling and network theory. Both describe the transmission of "objects" (in this case, the transmission of gas) between interconnected elements. In network theory, a population of interconnected elements is described by graphs in which objects are represented by vertices or nodes and connections between these objections as edges linking the vertices. A graph showing a population of interconnected xylem conduits represents an "individual" wood sample that allows spatial tracking of embolism propagation. In contrast, in epidemic modeling, the transmission dynamics for a population that is subdivided into infection-relevant groups is calculated by an equation system. For this, embolized conduits are considered to be "infected," and the "infection" is the transmission of gas from embolized conduits to their still water-filled neighbors. Both approaches allow for a mechanistic simulation of embolism propagation.

A mathematical model for the impact of disinfectants on the control of bacterial diseases

Here, we investigate a mathematical model to assess the impact of disinfectants in controlling diseases that spread in the population via direct contacts with the infected persons and also due to bacteria present in the environment. We find that the disease-free and endemic equilibria of the system are related via a transcritical bifurcation whose direction is forward. Our numerical results show that controlling the transmissions of disease through direct contacts and bacteria present in the environment can help in reducing the disease prevalence. Moreover, fostering the recovery rate and the death rate of bacteria play significant roles in disease eradication. Our numerical observations convey that reducing the bacterial density at the source discharged by the infected population through the use of chemicals has prominent effect in disease control. Overall, our findings manifest that the disinfectants of high quality can completely control the bacterial density and the disease outbreak.

Estimating effective reproduction number revisited

Accurately estimating the effective reproduction number is crucial for characterizing the transmissibility of infectious diseases to optimize interventions and responses during epidemic outbreaks. In this study, we improve the estimation of the effective reproduction number through two main approaches. First, we derive a discrete model to represent a time series of case counts and propose an estimation method based on this framework. We also conduct numerical experiments to demonstrate the effectiveness of the proposed discretization scheme. By doing so, we enhance the accuracy of approximating the underlying epidemic process compared to previous methods, even when the counting period is similar to the mean generation time of an infectious disease. Second, we employ a negative binomial distribution to model the variability of count data to accommodate overdispersion. Specifically, given that observed incidence counts follow a negative binomial distribution, the posterior distribution of secondary infections is obtained as a Dirichlet multinomial distribution. With this formulation, we establish posterior uncertainty bounds for the effective reproduction number. Finally, we demonstrate the effectiveness of the proposed method using incidence data from the COVID-19 pandemic.

Tobacco smoking model containing snuffing class

In recent years, the world has faced many destructive diseases that have taken many lives across the globe. To resist these diseases, humankind needs medicine to control, cure, and predict the behaviour of such problems. Recently, the Corona virus, which primarily affects the lungs, has threatened the globe. Similarly, tobacco-related illnesses impair the immune system, and this reduces the ability to fight against Covid-19. This tobacco-smoking version is vital for the researchers to reap the solution by using the q-homotopy analysis transform method with the useful resource of the Atangana-Baleanu-Caputo impression. Hence, the graphical illustrations have been discussed to achieve a solution for this mathematical model. This work applies the q-homotopy analysis transform method to the preeminent fractional operator Atangana-Baleanu-Caputo to better comprehend the infectious model of tobacco snuffing and smoking. Figures and tables are used to display the outcomes. The paper also aids in the analysis of the practical theory by predicting how it would behave when compared to the rules when considering the replica. It offers accurate grid point outcomes and fixes. The system's accuracy in the convergent zone is shown by the curves. The smoking model has been illustrated using graphical findings and fractional derivatives for easier comprehension. It's feasible that applications in the real world will make use of fractional derivatives.

Imperfect and Bogdanov-Takens bifurcations in biological models: from harvesting of species to isolation of infectives

A natural biological system under human interventions may exhibit complex dynamical behaviors which could lead to either the collapse or stabilization of the system. The bifurcation theory plays an important role in understanding this evolution process by modeling and analyzing the biological system. In this paper, we examine two types of biological models that Fred Brauer made pioneer contributions: predator-prey models with stocking/harvesting and epidemic models with importation/isolation. First we consider the predator-prey model with Holling type II functional response whose dynamics and bifurcations are well-understood. By considering human interventions such as constant harvesting or stocking of predators, we show that the system under human interventions undergoes imperfect bifurcation and Bogdanov-Takens bifurcation, which induces much richer dynamical behaviors such as the existence of limit cycles or homoclinic loops. Then we consider an epidemic model with constant importation/isolation of infective individuals and observe similar imperfect and Bogdanov-Takens bifurcations when the constant importation/isolation rate varies.

Social Pressure from a Core Group can Cause Self-Sustained Oscillations in an Epidemic Model

Let the individuals of a population be divided into two groups with different personal habits. The core group is associated with health risk behaviors; the non-core group avoids unhealthy activities. Assume that the infected individuals of the core group can spread a contagious disease to the whole population. Also, assume that cure does not confer immunity. Here, an epidemiological model written as a set of ordinary differential equations is proposed to investigate the infection propagation in this population. In the model, migrations between these two groups are allowed; however, the transitions from the non-core group into the core group prevail. These migrations can be either spontaneous or stimulated by social pressure. It is analytically shown that, in the scenario of spontaneous migration, the disease is either naturally eradicated or chronically persists at a constant level. In the scenario of stimulated migration, in addition to eradication and constant persistence, self-sustained oscillations in the number of sick individuals can also be found. These analytical results are illustrated by numerical simulations and discussed from a public health perspective.

Exploring epidemic voluntary vaccinating behavior based on information-driven decisions and benefit-cost analysis

A complex dynamic interplay exists between epidemic transmission and vaccination, which is significantly influenced by human behavioral responses. We construct a research framework combining both the function modeling of the cumulative global COVID-19 information and limited individuals' information processing capacity employing the Gompertz model for growing processes. Meanwhile, we built a function representing the decision to get vaccinated following benefit-cost analysis considered the choices made by people in each scenario have an influence from altruism, free-riding and immunity escaping capacity. Through the mean-field calculation analysis and using a fourth-order Runge-Kutta method with constant step size, we obtain plots from numerical simulations. We found that only when the total number of infectious individuals proves sufficient to reach and exceed a certain level will the individuals face a better trade-off in determining whether to get vaccinated against the diseases based on that information. Besides, authoritative media have a higher decisive influence and efforts should be focused on extending the duration of vaccine protection, which is beneficial to inhibit the outbreaks of epidemics. Our work elucidates that reducing the negative payoff brought about by the free-riding behavior for individuals or improving the positive payoff from the altruistic motivation helps to control the disease in cultures that value social benefits, vaccination willingness is generally stronger. We also note that at a high risk of infection, the decision of vaccination is highly correlated with global epidemic information concerning COVID-19 infection, while at times of lower risk, it depends on the game theoretic vaccine strategy. The findings demonstrate that improving health literacy, ensuring open and transparent information on vaccine safety and efficacy as a public health priority can be an effective strategy for mitigating inequalities in health education, as well as alleviating the phenomenon that immunity escaping abilities is more likely to panic by populations with high levels of education. In addition, prosocial nudges are great ways to bridge these immunity gaps that can contribute to implementing government public health control measures, creating a positive feedback loop.

Assessing the efficacy of health countermeasures on arrival time of infectious diseases

Public health measures to control the international spread of infectious diseases include strengthening quarantines and sealing borders. Although these measures are effective in delaying the importation of infectious diseases, they also have a significant economic impact by stopping the flow of people and goods. The arrival time of infectious diseases is often used to assess quarantine effectiveness. Although the arrival time is highly dependent on the number of infected cases in the endemic country, direct comparisons have not yet been made. Therefore, this study derives an explicit relationship between the number of infected cases and arrival time. Transmission behavior is stochastic, and deterministic models are not always realistic. In this study, random differential equations, which are differential equations with stochastic processes, were used to describe the dynamics of infection in an endemic country. Furthermore, the flow of travelers from the endemic country was described in terms of survival time, and the arrival time in each country was calculated. A scenario in which PCR kits were distributed between endemic and disease-free countries was also considered, and the impact of different distribution rates on arrival time was evaluated. The simulation results showed that increasing the distribution of PCR kits in the endemic country was more effective in delaying arrival times than using PCR kits in quarantine in disease-free countries. It was also found that increasing the proportion of identified infected persons in the endemic country, leading to isolation, was more important and effective in delaying arrival times than increasing the number of PCR tests.

Wastewater-based modeling, reconstruction, and prediction for COVID-19 outbreaks in Hungary caused by highly immune evasive variants

(MOTIVATION)

Wastewater-based epidemiology (WBE) has emerged as a promising approach for monitoring the COVID-19 pandemic, since the measurement process is cost-effective and is exposed to fewer potential errors compared to other indicators like hospitalization data or the number of detected cases. Consequently, WBE was gradually becoming a key tool for epidemic surveillance and often the most reliable data source, as the intensity of clinical testing for COVID-19 drastically decreased by the third year of the pandemic. Recent results suggests that the model-based fusion of wastewater measurements with clinical data and other indicators is essential in future epidemic surveillance.

(METHOD)

In this work, we developed a wastewater-based compartmental epidemic model with a two-phase vaccination dynamics and immune evasion. We proposed a multi-step optimization-based data assimilation method for epidemic state reconstruction, parameter estimation, and prediction. The computations make use of the measured viral load in wastewater, the available clinical data (hospital occupancy, delivered vaccine doses, and deaths), the stringency index of the official social distancing rules, and other measures. The current state assessment and the estimation of the current transmission rate and immunity loss allow a plausible prediction of the future progression of the pandemic.

(RESULTS)

Qualitative and quantitative evaluations revealed that the contribution of wastewater data in our computational epidemiological framework makes predictions more reliable. Predictions suggest that at least half of the Hungarian population has lost immunity during the epidemic outbreak caused by the BA.1 and BA.2 subvariants of Omicron in the first half of 2022. We obtained a similar result for the outbreaks caused by the subvariant BA.5 in the second half of 2022.

(APPLICABILITY)

The proposed approach has been used to support COVID management in Hungary and could be customized for other countries as well.

Multi-weight susceptible-infected model for predicting COVID-19 in China

The mutant strains of COVID-19 caused a global explosion of infections, including many cities of China. In 2020, a hybrid AI model was proposed by Zheng et al., which accurately predicted the epidemic in Wuhan. As the main part of the hybrid AI model, ISI method makes two important assumptions to avoid over-fitting. However, the assumptions cannot be effectively applied to new mutant strains. In this paper, a more general method, named the multi-weight susceptible-infected model (MSI) is proposed to predict COVID-19 in Chinese Mainland. First, a Gaussian pre-processing method is proposed to solve the problem of data fluctuation based on the quantity consistency of cumulative infection number and the trend consistency of daily infection number. Then, we improve the model from two aspects: changing the grouped multi-parameter strategy to the multi-weight strategy, and removing the restriction of weight distribution of viral infectivity. Experiments on the outbreaks in many places in China from the end of 2021 to May 2022 show that, in China, an individual infected by Delta or Omicron strains of SARS-CoV-2 can infect others within 3-4 days after he/she got infected. Especially, the proposed method effectively predicts the trend of the epidemics in Xi'an, Tianjin, Henan, and Shanghai from December 2021 to May 2022.

Global stability of latency-age/stage-structured epidemic models with differential infectivity

In this paper, we first formulate a system of ODEs-PDE to model diseases with latency-age and differential infectivity. Then, based on the ways how latent individuals leave the latent stage, one ODE and two DDE models are derived. We only focus on the global stability of the models. All the models have some similarities in the existence of equilibria. Each model has a threshold dynamics for global stability, which is completely characterized by the basic reproduction number. The approach is the Lyapunov direct method. We propose an idea on constructing Lyapunov functionals for the two DDE and the original ODEs-PDE models. During verifying the negative (semi-)definiteness of derivatives of the Lyapunov functionals along solutions, a novel positive definite function and a new inequality are used. The idea here is also helpful in applying the Lyapunov direct method to prove the global stability of some epidemic models with age structure or delays.

The impact of traffic control measures on the spread of COVID-19 within urban agglomerations based on a modified epidemic model

With the spatial structure of urban agglomerations, well-developed transportation networks and close economic ties can increase the risk of intercity transmission of infectious diseases. To reveal the epidemic transmission mechanism in urban agglomerations and to explore the effectiveness of traffic control measures, this study proposes an Urban-Agglomeration-based Epidemic and Mobility Model (UAEMM) based on the reality of urban transportation networks and population mobility factors. Since the model considers the urban population inflow, along with the active intracity population, it can be used to estimate the composition of urban cases. The model was applied to the Chang-Zhu-Tan urban agglomeration, and the results show that the model can better simulate the transmission process of the urban agglomeration for a certain scale of epidemic. The number of cases within the urban agglomeration is higher than the number of cases imported into the urban agglomeration from external cities. The composition of cases in the core cities of the urban agglomeration changes with the adjustment of prevention and control measures. In contrast, the number of cases imported into the secondary cities is consistently greater than the number of cases transmitted within the cities. A traffic control measures discount factor is introduced to simulate the development of the epidemic in the urban agglomeration under the traffic control measures of the first-level response to major public health emergency, traffic blockades in infected areas, and public transportation shutdowns. If none of those traffic control measures had been taken after the outbreak of COVID-19, the number of cases in the urban agglomeration would theoretically have increased to 3879, which is 11.61 times the actual number of cases that occurred. If only one traffic control measure had been used alone, each of the three measures would have reduced the number of cases in the urban agglomeration to 30.19 %-57.44 % of the theoretical values of infection cases, with the best blocking effect coming from the first-level response to major public health emergency. Traffic control measures have a significant effect in interrupting the spread of COVID-19 in urban agglomerations. The methodology and main findings presented in this paper are of general interest and can also be used in studies in other countries for similar purposes to help understand the spread of COVID-19 in urban agglomerations.

Effectiveness of feedback control and the trade-off between death by COVID-19 and costs of countermeasures

We provided a framework of a mathematical epidemic modeling and a countermeasure against the novel coronavirus disease (COVID-19) under no vaccines and specific medicines. The fact that even asymptomatic cases are infectious plays an important role for disease transmission and control. Some patients recover without developing the disease; therefore, the actual number of infected persons is expected to be greater than the number of confirmed cases of infection. Our study distinguished between cases of confirmed infection and infected persons in public places to investigate the effect of isolation. An epidemic model was established by utilizing a modified extended Susceptible-Exposed-Infectious-Recovered model incorporating three types of infectious and isolated compartments, abbreviated as SEIIIHHHR. Assuming that the intensity of behavioral restrictions can be controlled and be divided into multiple levels, we proposed the feedback controller approach to implement behavioral restrictions based on the active number of hospitalized persons. Numerical simulations were conducted using different detection rates and symptomatic ratios of infected persons. We investigated the appropriate timing for changing the degree of behavioral restrictions and confirmed that early initiating behavioral restrictions is a reasonable measure to reduce the burden on the health care system. We also examined the trade-off between reducing the cumulative number of deaths by the COVID-19 and saving the cost to prevent the spread of the virus. We concluded that a bang-bang control of the behavioral restriction can reduce the socio-economic cost, while a control of the restrictions with multiple levels can reduce the cumulative number of deaths by infection.

A simple SEIR-V model to estimate COVID-19 prevalence and predict SARS-CoV-2 transmission using wastewater-based surveillance data

Wastewater-based surveillance (WBS) has been widely used as a public health tool to monitor SARS-CoV-2 transmission. However, epidemiological inference from WBS data remains understudied and limits its application. In this study, we have established a quantitative framework to estimate COVID-19 prevalence and predict SARS-CoV-2 transmission through integrating WBS data into an SEIR-V model. We conceptually divide the individual-level viral shedding course into exposed, infectious, and recovery phases as an analogy to the compartments in a population-level SEIR model. We demonstrated that the effect of temperature on viral losses in the sewer can be straightforwardly incorporated in our framework. Using WBS data from the second wave of the pandemic (Oct 02, 2020-Jan 25, 2021) in the Greater Boston area, we showed that the SEIR-V model successfully recapitulates the temporal dynamics of viral load in wastewater and predicts the true number of cases peaked earlier and higher than the number of reported cases by 6-16 days and 8.3-10.2 folds (R = 0.93). This work showcases a simple yet effective method to bridge WBS and quantitative epidemiological modeling to estimate the prevalence and transmission of SARS-CoV-2 in the sewershed, which could facilitate the application of wastewater surveillance of infectious diseases for epidemiological inference and inform public health actions.

Twice evasions of Omicron variants explain the temporal patterns in six Asian and Oceanic countries

BACKGROUND

The ongoing coronavirus 2019 (COVID-19) pandemic has emerged and caused multiple pandemic waves in the following six countries: India, Indonesia, Nepal, Malaysia, Bangladesh and Myanmar. Some of the countries have been much less studied in this devastating pandemic. This study aims to assess the impact of the Omicron variant in these six countries and estimate the infection fatality rate (IFR) and the reproduction number [Formula: see text] in these six South Asia, Southeast Asia and Oceania countries.

METHODS

We propose a Susceptible-Vaccinated-Exposed-Infectious-Hospitalized-Death-Recovered model with a time-varying transmission rate [Formula: see text] to fit the multiple waves of the COVID-19 pandemic and to estimate the IFR and [Formula: see text] in the aforementioned six countries. The level of immune evasion and the intrinsic transmissibility advantage of the Omicron variant are also considered in this model.

RESULTS

We fit our model to the reported deaths well. We estimate the IFR (in the range of 0.016 to 0.136%) and the reproduction number [Formula: see text] (in the range of 0 to 9) in the six countries. Multiple pandemic waves in each country were observed in our simulation results.

CONCLUSIONS

The invasion of the Omicron variant caused the new pandemic waves in the six countries. The higher [Formula: see text] suggests the intrinsic transmissibility advantage of the Omicron variant. Our model simulation forecast implies that the Omicron pandemic wave may be mitigated due to the increasing immunized population and vaccine coverage.

Modeling Syphilis and HIV Coinfection: A Case Study in the USA

Syphilis and HIV infections form a dangerous combination. In this paper, we propose an epidemic model of HIV-syphilis coinfection. The model always has a unique disease-free equilibrium, which is stable when both reproduction numbers of syphilis and HIV are less than 1. If the reproduction number of syphilis (HIV) is greater than 1, there exists a unique boundary equilibrium of syphilis (HIV), which is locally stable if the invasion number of HIV (syphilis) is less than 1. Coexistence equilibrium exists and is stable when all reproduction numbers and invasion numbers are greater than 1. Using data of syphilis cases and HIV cases from the US, we estimated that both reproduction numbers for syphilis and HIV are slightly greater than 1, and the boundary equilibrium of syphilis is stable. In addition, we observed competition between the two diseases. Treatment for primary syphilis is more important in mitigating the transmission of syphilis. However, it might lead to increase of HIV cases. The results derived here could be adapted to other multi-disease scenarios in other regions.

Acute threshold dynamics of an epidemic system with quarantine strategy driven by correlated white noises and Lévy jumps associated with infinite measure

Several studies have previously been conducted on the dynamics of probabilistic epidemic models driven by Lévy disorder. All of these works have used the Poisson counting process with finite Lévy measures. However, this scope disregards a considerable category of correlated Lévy jump processes governed by an infinite Lévy measure. In this research, we take into consideration this general framework applied to an epidemic model with a quarantine strategy. Under an appropriate hypothetical setting, we infer the exact threshold value between the ergodicity and the disease disappearance. Our analysis completes the work presented by Privault and Wang (J Nonlinear Sci 31(1):1-28, 2021) and puts forward a novel analytical aspect to deal with other stochastic models in several areas. As a numerical application, we implement the algorithm of Rosinski (Stoch Process Appl 117:677-707, 2007) for tempered stable Lévy processes with an infinite Lévy measure.

Dynamical analysis of a stochastic non-autonomous SVIR model with multiple stages of vaccination

In this paper, we analyze the dynamics of a new proposed stochastic non-autonomous SVIR model, with an emphasis on multiple stages of vaccination, due to the vaccine ineffectiveness. The parameters of the model are allowed to depend on time, to incorporate the seasonal variation. Furthermore, the vaccinated population is divided into three subpopulations, each one representing a different stage. For the proposed model, we prove the mathematical and biological well-posedness. That is, the existence of a unique global almost surely positive solution. Moreover, we establish conditions under which the disease vanishes or persists. Furthermore, based on stochastic stability theory and by constructing a suitable new Lyapunov function, we provide a condition under which the model admits a non-trivial periodic solution. The established theoretical results along with the performed numerical simulations exhibit the effect of the different stages of vaccination along with the stochastic Gaussian noise on the dynamics of the studied population.

Recurrent epidemic waves in a delayed epidemic model with quarantine

In this paper, we are concerned with an epidemic model with quarantine and distributed time delay. We define the basic reproduction number R0 and show that if R0≤1, then the disease-free equilibrium is globally asymptotically stable, whereas if R0>1, then it is unstable and there exists a unique endemic equilibrium. We obtain sufficient conditions for a Hopf bifurcation that induces a nontrivial periodic solution which represents recurrent epidemic waves. By numerical simulations, we illustrate stability and instability parameter regions. Our results suggest that the quarantine and time delay play important roles in the occurrence of recurrent epidemic waves.

Effects of heterogeneous susceptibility on epidemiological models of reinfection

This paper studies an epidemic model with heterogeneous susceptibility which generalizes the SIS (susceptible-infected-susceptible), SIR (susceptible-infected-recovered) and SIRI (susceptible-infected-recovered-infected) models. The proposed model considers the case that some infected people are susceptible again after recovery, some infected people develop immunity after infection, and some infected people are reinfected after recovery. We perform a comprehensive theoretical analysis of the model, showing that under appropriate initial conditions, delayed outbreak phenomenon occurs that can give people false impressions. Moreover, compared with the SIRI model, the proposed model exists the delayed outbreak phenomenon under more probable conditions. Finally, we present a numerical example to illustrate the effectiveness of the theoretical results.

The impact of crowd gatherings on the spread of COVID-19

Crowd gatherings are an important cause of COVID-19 outbreaks. However, how the scale, scene and other factors of gatherings affect the spread of the epidemic remains unclear. A total of 184 gathering events worldwide were collected to construct a database, and 99 of them with a clear gathering scale were used for statistical analysis of the impact of these factors on the disease incidence among the crowd in the study. The results showed that the impact of small-scale (less than 100 people) gathering events on the spread of COVID-19 in the city is also not to be underestimated due to their characteristics of more frequent occurrence and less detection and control. In our dataset, 22.22% of small-scale events have an incidence of more than 0.8. In contrast, the incidence of most large-scale events is less than 0.4. Gathering scenes such as "Meal" and "Family" occur in densely populated private or small public places have the highest incidence. We further designed a model of epidemic transmission triggered by crowd gathering events and simulated the impact of crowd gathering events on the overall epidemic situation in the city. The simulation results showed that the number of patients will be drastically reduced if the scale and the density of crowds gathering are halved. It indicated that crowd gatherings should be strictly controlled on a small scale. In addition, it showed that the model well reproduce the epidemic spread after crowd gathering events better than does the original SIER model and could be applied to epidemic prediction after sudden gathering events.

Investigation of vaccination game approach in spreading covid-19 epidemic model with considering the birth and death rates

In this study, an epidemic model for spreading COVID-19 is presented. This model considers the birth and death rates in the dynamics of spreading COVID-19. The birth and death rates are assumed to be the same, so the population remains constant. The dynamics of the model are explained in two phases. The first is the epidemic phase, which spreads during a season based on the proposed SIR/V model and reaches a stable state at the end of the season. The other one is the "vaccination campaign", which takes place between two seasons based on the rules of the vaccination game. In this stage, each individual in the population decides whether to be vaccinated or not. Investigating the dynamics of the studied model during a single epidemic season without consideration of the vaccination game shows waves in the model as experimental knowledge. In addition, the impact of the parameters is studied via the rules of the vaccination game using three update strategies. The result shows that the pandemic speeding can be changed by varying parameters such as efficiency and cost of vaccination, defense against contagious, and birth and death rates. The final epidemic size decreases when the vaccination coverage increases and the average social payoff is modified.

Impact of optimal vaccination and social distancing on COVID-19 pandemic

The first COVID-19 case was reported at Wuhan in China at the end of December 2019 but till today the virus has caused millions of deaths worldwide. Governments of each country, observing the severity, took non-pharmaceutical interventions from the very beginning to break the chain of higher transmission. Fortunately, vaccines are available now in most countries and people are asked to take recommended vaccines as precautionary measures. In this work, an epidemiological model on COVID-19 is proposed where people from the susceptible and asymptomatically infected phase move to the vaccinated class after a full two-dose vaccination. The overall analysis says that the disease transmission rate from symptomatically infected people is most sensitive on the disease prevalence. Moreover, better disease control can be achieved by vaccination of the susceptible class. In the later part of the work, a corresponding optimal control problem is considered where maintaining social distancing and vaccination procedure change with time. The result says that even in absence of social distancing, only the vaccination to people can significantly reduce the overall infected population. From the analysis, it is observed that maintaining physical distancing and taking vaccines at an early stage decreases the infection level significantly in the environment by reducing the probability of becoming infected.

Analysing the Effect of Test-and-Trace Strategy in an SIR Epidemic Model

Consider a Markovian SIR epidemic model in a homogeneous community. To this model we add a rate at which individuals are tested, and once an infectious individual tests positive it is isolated and each of their contacts are traced and tested independently with some fixed probability. If such a traced individual tests positive it is isolated, and the contact tracing is iterated. This model is analysed using large population approximations, both for the early stage of the epidemic when the "to-be-traced components" of the epidemic behaves like a branching process, and for the main stage of the epidemic where the process of to-be-traced components converges to a deterministic process defined by a system of differential equations. These approximations are used to quantify the effect of testing and of contact tracing on the effective reproduction numbers (for the components as well as for the individuals), the probability of a major outbreak, and the final fraction getting infected. Using numerical illustrations when rates of infection and natural recovery are fixed, it is shown that Test-and-Trace strategy is effective in reducing the reproduction number. Surprisingly, the reproduction number for the branching process of components is not monotonically decreasing in the tracing probability, but the individual reproduction number is conjectured to be monotonic as expected. Further, in the situation where individuals also self-report for testing, the tracing probability is more influential than the screening rate (measured by the fraction infected being screened).

A phenomenological approach to predicting tuberculosis cases with an assessment of measurement errors

BACKGROUND

Measurement errors produce bias and uncertainty. They affect the outcomes of data-fitted models. Unfortunately, tuberculosis incidence data providers do not appear to be interested in this topic.

METHOD

We use a phenomenological approach to describe and forecast tuberculosis incidence numbers in the US, and England and Wales as a function of time. We use a heuristic method to evaluate if the lack of fit of our descriptive models to the data could be explained by measurement errors.

FINDINGS

We find that if the lack of fit of our proposed models to the data is due to measurement errors, these are not so large as to make the models useless. We find numerical regularities that provide trustworthy tools to make a description and forecast the tuberculosis incidence trends.

INTERPRETATION

Measurement errors of epidemiological data collected "in the field" are probably large and could justify the lack of fit of an epidemic model to the data. Thus, to choose an appropriate model to describe an epidemic, we propose to assess the magnitude of measurement errors and apply the epidemic theory.

An Epidemic Model with Pro and Anti-vaccine Groups

Here, an epidemiological model considering pro and anti-vaccination groups is proposed and analyzed. In this model, susceptible individuals can migrate between these two groups due to the influence of false and true news about safety and efficacy of vaccines. From this model, written as a set of three ordinary differential equations, analytical expressions for the disease-free steady state, the endemic steady state, and the basic reproduction number are derived. It is analytically shown that low vaccination rate and no influx to the pro-vaccination group have similar impacts on the long-term amount of infected individuals. Numerical simulations are performed with parameter values of the COVID-19 pandemic to illustrate the analytical results. The possible relevance of this work is discussed from a public health perspective.

Transmission dynamics of COVID-19 pandemic with combined effects of relapse, reinfection and environmental contribution: A modeling analysis

Reinfection and reactivation of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) have recently raised public health pressing concerns in the fight against the current pandemic globally. In this study, we propose a new dynamic model to study the transmission of the coronavirus disease 2019 (COVID-19) pandemic. The model incorporates possible relapse, reinfection and environmental contribution to assess the combined effects on the overall transmission dynamics of SARS-CoV-2. The model's local asymptotic stability is analyzed qualitatively. We derive the formula for the basic reproduction number ( R 0 ) and final size epidemic relation, which are vital epidemiological quantities that are used to reveal disease transmission status and guide control strategies. Furthermore, the model is validated using the COVID-19 reported situations in Saudi Arabia. Moreover, sensitivity analysis is examined by implementing a partial rank correlation coefficient technique to obtain the ultimate rank model parameters to control or mitigate the pandemic effectively. Finally, we employ a standard Euler technique for numerical simulations of the model to elucidate the influence of some crucial parameters on the overall transmission dynamics. Our results highlight that contact rate, hospitalization rate, and reactivation rate are the fundamental parameters that need particular emphasis for the prevention, mitigation and control.

Bistability in deterministic and stochastic SLIAR-type models with imperfect and waning vaccine protection

Various vaccines have been approved for use to combat COVID-19 that offer imperfect immunity and could furthermore wane over time. We analyze the effect of vaccination in an SLIARS model with demography by adding a compartment for vaccinated individuals and considering disease-induced death, imperfect and waning vaccination protection as well as waning infections-acquired immunity. When analyzed as systems of ordinary differential equations, the model is proven to admit a backward bifurcation. A continuous time Markov chain (CTMC) version of the model is simulated numerically and compared to the results of branching process approximations. While the CTMC model detects the presence of the backward bifurcation, the branching process approximation does not. The special case of an SVIRS model is shown to have the same properties.

Compartmental structures used in modeling COVID-19: a scoping review

Background

The coronavirus disease 2019 (COVID-19) epidemic, considered as the worst global public health event in nearly a century, has severely affected more than 200 countries and regions around the world. To effectively prevent and control the epidemic, researchers have widely employed dynamic models to predict and simulate the epidemic’s development, understand the spread rule, evaluate the effects of intervention measures, inform vaccination strategies, and assist in the formulation of prevention and control measures. In this review, we aimed to sort out the compartmental structures used in COVID-19 dynamic models and provide reference for the dynamic modeling for COVID-19 and other infectious diseases in the future.

Main text

A scoping review on the compartmental structures used in modeling COVID-19 was conducted. In this scoping review, 241 research articles published before May 14, 2021 were analyzed to better understand the model types and compartmental structures used in modeling COVID-19. Three types of dynamics models were analyzed: compartment models expanded based on susceptible-exposed-infected-recovered (SEIR) model, meta-population models, and agent-based models. The expanded compartments based on SEIR model are mainly according to the COVID-19 transmission characteristics, public health interventions, and age structure. The meta-population models and the agent-based models, as a trade-off for more complex model structures, basic susceptible-exposed-infected-recovered or simply expanded compartmental structures were generally adopted.

Conclusion

There has been a great deal of models to understand the spread of COVID-19, and to help prevention and control strategies. Researchers build compartments according to actual situation, research objectives and complexity of models used. As the COVID-19 epidemic remains uncertain and poses a major challenge to humans, researchers still need dynamic models as the main tool to predict dynamics, evaluate intervention effects, and provide scientific evidence for the development of prevention and control strategies. The compartmental structures reviewed in this study provide guidance for future modeling for COVID-19, and also offer recommendations for the dynamic modeling of other infectious diseases.

Graphical Abstract

Supplementary Information

The online version contains supplementary material available at 10.1186/s40249-022-01001-y.

Controlling COVID-19 transmission with isolation of influential nodes

To understand the transmission dynamics of any infectious disease outbreak, identification of influential nodes plays a crucial role in a complex network. In most infectious disease outbreaks, activities of some key nodes can trigger rapid disease transmission in the population. Identification and immediate isolation of those influential nodes can impede the disease transmission effectively. In this paper, the technique for order of preference by similarity to ideal solution (TOPSIS) method with a novel formula has been proposed to detect the influential and top ranked nodes in a complex social network, which involves analyzing and studying of structural organization of a network. In the proposed TOPSIS method, several centrality measures have been used as multi-attributes of a complex social network. A new formula has been designed for calculating the transmission probability of an epidemic disease to identify the impact of isolating influential nodes. To verify the robustness of the proposed method, we present a comprehensive comparison with five node-ranking methods, which are being used currently for assessing the importance of nodes. The key nodes can be considered as a person, community, cluster or a particular area. The Susceptible-infected-recovered (SIR) epidemic model is exploited in two real networks to examine the spreading ability of the nodes, and the results illustrate the effectiveness of the proposed method. Our findings have unearthed that quarantine or isolation of influential nodes following proper health protocols can play a pivotal role in curbing the transmission rate of COVID-19.

A wastewater-based epidemic model for SARS-CoV-2 with application to three Canadian cities

The COVID-19 pandemic has stimulated wastewater-based surveillance, allowing public health to track the epidemic by monitoring the concentration of the genetic fingerprints of SARS-CoV-2 shed in wastewater by infected individuals. Wastewater-based surveillance for COVID-19 is still in its infancy. In particular, the quantitative link between clinical cases observed through traditional surveillance and the signals from viral concentrations in wastewater is still developing and hampers interpretation of the data and actionable public-health decisions. We present a modelling framework that includes both SARS-CoV-2 transmission at the population level and the fate of SARS-CoV-2 RNA particles in the sewage system after faecal shedding by infected persons in the population. Using our mechanistic representation of the combined clinical/wastewater system, we perform exploratory simulations to quantify the effect of surveillance effectiveness, public-health interventions and vaccination on the discordance between clinical and wastewater signals. We also apply our model to surveillance data from three Canadian cities to provide wastewater-informed estimates for the actual prevalence, the effective reproduction number and incidence forecasts. We find that wastewater-based surveillance, paired with this model, can complement clinical surveillance by supporting the estimation of key epidemiological metrics and hence better triangulate the state of an epidemic using this alternative data source.

Prediction of COVID-19 Infected Population for Indian States through a State Interaction Network-based SEIR Epidemic Model

Objective of this present study is to predict the COVID-19 trajectories in terms of infected population of Indian states. In this work, a state interaction network of sixteen Indian states with highest number of infected caseload is considered, based on networked Susceptible-Exposed-Infected-Recovered (SEIR) epidemic model. An intervention term has been introduced in order to capture the effect of lockdown with different stringencies at different periods of time. The model has been fitted using least absolute shrinkage and selection operator (LASSO). Machine learning methods have been used to train the parameters of the model, cross-validate the data, and predict the parameters. The predictions of infected population for each of the sixteen states have been shown using data considered from January 1, 2021 till writing this manuscript on June 25, 2021. Finally, the effectiveness of the model is manifested by the calculated mean error and confidence interval.

Individual variation in susceptibility or exposure to SARS-CoV-2 lowers the herd immunity threshold

Individual variation in susceptibility and exposure is subject to selection by natural infection, accelerating the acquisition of immunity, and reducing herd immunity thresholds and epidemic final sizes. This is a manifestation of a wider population phenomenon known as "frailty variation". Despite theoretical understanding, public health policies continue to be guided by mathematical models that leave out considerable variation and as a result inflate projected disease burdens and overestimate the impact of interventions. Here we focus on trajectories of the coronavirus disease (COVID-19) pandemic in England and Scotland until November 2021. We fit models to series of daily deaths and infer relevant epidemiological parameters, including coefficients of variation and effects of non-pharmaceutical interventions which we find in agreement with independent empirical estimates based on contact surveys. Our estimates are robust to whether the analysed data series encompass one or two pandemic waves and enable projections compatible with subsequent dynamics. We conclude that vaccination programmes may have contributed modestly to the acquisition of herd immunity in populations with high levels of pre-existing naturally acquired immunity, while being crucial to protect vulnerable individuals from severe outcomes as the virus becomes endemic.

Infection fatality rate and infection attack rate of COVID-19 in South American countries

BACKGROUND

The ongoing COVID-19 pandemic hit South America badly with multiple waves. Different COVID-19 variants have been storming across the region, leading to more severe infections and deaths even in places with high vaccination coverage. This study aims to assess the spatiotemporal variability of the COVID-19 pandemic and estimate the infection fatality rate (IFR), infection attack rate (IAR) and reproduction number ([Formula: see text]) for twelve most affected South American countries.

METHODS

We fit a susceptible-exposed-infectious-recovered (SEIR)-based model with a time-varying transmission rate to the reported COVID-19 deaths for the twelve South American countries with the highest mortalities. Most of the epidemiological datasets analysed in this work are retrieved from the disease surveillance systems by the World Health Organization, Johns Hopkins Coronavirus Resource Center and Our World in Data. We investigate the COVID-19 mortalities in these countries, which could represent the situation  for the overall South American region. We employ COVID-19 dynamic model with-and-without vaccination considering time-varying flexible transmission rate to estimate IFR, IAR and [Formula: see text] of COVID-19 for the South American countries.

RESULTS

We simulate the model in each scenario under suitable parameter settings and yield biologically reasonable estimates for IFR (varies between 0.303% and 0.723%), IAR (varies between 0.03 and 0.784) and [Formula: see text] (varies between 0.7 and 2.5) for the 12 South American countries. We observe that the severity, dynamical patterns of deaths and time-varying transmission rates among the countries are highly heterogeneous. Further analysis of the model with the effect of vaccination highlights that increasing the vaccination rate could help suppress the pandemic in South America.

CONCLUSIONS

This study reveals possible reasons for the two waves of COVID-19 outbreaks in South America. We observed reductions in the transmission rate corresponding to each wave plausibly due to improvement in nonpharmaceutical interventions measures and human protective behavioral reaction to recent deaths. Thus, strategies coupling social distancing and vaccination could substantially suppress the mortality rate of COVID-19 in South America.

Infection fatality rate and infection attack rate of COVID-19 in South American countries

BACKGROUND

The ongoing COVID-19 pandemic hit South America badly with multiple waves. Different COVID-19 variants have been storming across the region, leading to more severe infections and deaths even in places with high vaccination coverage. This study aims to assess the spatiotemporal variability of the COVID-19 pandemic and estimate the infection fatality rate (IFR), infection attack rate (IAR) and reproduction number ([Formula: see text]) for twelve most affected South American countries.

METHODS

We fit a susceptible-exposed-infectious-recovered (SEIR)-based model with a time-varying transmission rate to the reported COVID-19 deaths for the twelve South American countries with the highest mortalities. Most of the epidemiological datasets analysed in this work are retrieved from the disease surveillance systems by the World Health Organization, Johns Hopkins Coronavirus Resource Center and Our World in Data. We investigate the COVID-19 mortalities in these countries, which could represent the situation  for the overall South American region. We employ COVID-19 dynamic model with-and-without vaccination considering time-varying flexible transmission rate to estimate IFR, IAR and [Formula: see text] of COVID-19 for the South American countries.

RESULTS

We simulate the model in each scenario under suitable parameter settings and yield biologically reasonable estimates for IFR (varies between 0.303% and 0.723%), IAR (varies between 0.03 and 0.784) and [Formula: see text] (varies between 0.7 and 2.5) for the 12 South American countries. We observe that the severity, dynamical patterns of deaths and time-varying transmission rates among the countries are highly heterogeneous. Further analysis of the model with the effect of vaccination highlights that increasing the vaccination rate could help suppress the pandemic in South America.

CONCLUSIONS

This study reveals possible reasons for the two waves of COVID-19 outbreaks in South America. We observed reductions in the transmission rate corresponding to each wave plausibly due to improvement in nonpharmaceutical interventions measures and human protective behavioral reaction to recent deaths. Thus, strategies coupling social distancing and vaccination could substantially suppress the mortality rate of COVID-19 in South America.

Analyzing the COVID-19 vaccination behavior based on epidemic model with awareness-information

Background

The widespread use of effective COVID-19 vaccines could prevent substantial morbidity and mortality. Individual decision behavior about whether or not to be vaccinated plays an important role in achieving adequate vaccination coverage and herd immunity.

Methods

This research proposes a new susceptible–vaccinated–exposed–infected–recovered with awareness-information (SEIR/V-AI) model to study the interaction between vaccination and information dissemination. Information creation rate and information sensitivity are introduced to understand the individual decision behavior of COVID-19 vaccination. We then analyze the dynamical evolution of the system and validate the analysis by numerical simulation.

Results

The decision behavior of COVID-19 vaccination in China and the United States are analyzed. The results showed the coefficient of information creation and the information sensitivity affect vaccination behavior of individuals.

Conclusions

The information-driven vaccination is an effective way to curb the COVID-19 spreading. Besides, to solve vaccine hesitancy and free-ride, the government needs to disseminate accurate information about vaccines safety to alleviate public concerns, and provide the widespread public educational campaigns and communication to guide individuals to act in group interests rather than self-interest and reduce the temptation to free-riding, which often results from individuals who are inadequately informed about vaccines and thus blindly imitate free-riding behavior.

Individual variation in susceptibility or exposure to SARS-CoV-2 lowers the herd immunity threshold

Individual variation in susceptibility and exposure is subject to selection by natural infection, accelerating the acquisition of immunity, and reducing herd immunity thresholds and epidemic final sizes. This is a manifestation of a wider population phenomenon known as "frailty variation". Despite theoretical understanding, public health policies continue to be guided by mathematical models that leave out considerable variation and as a result inflate projected disease burdens and overestimate the impact of interventions. Here we focus on trajectories of the coronavirus disease (COVID-19) pandemic in England and Scotland until November 2021. We fit models to series of daily deaths and infer relevant epidemiological parameters, including coefficients of variation and effects of non-pharmaceutical interventions which we find in agreement with independent empirical estimates based on contact surveys. Our estimates are robust to whether the analysed data series encompass one or two pandemic waves and enable projections compatible with subsequent dynamics. We conclude that vaccination programmes may have contributed modestly to the acquisition of herd immunity in populations with high levels of pre-existing naturally acquired immunity, while being critical to protect vulnerable individuals from severe outcomes as the virus becomes endemic.

Optimal control of pattern formations for an SIR reaction-diffusion epidemic model

Patterns arising from the reaction-diffusion epidemic model provide insightful aspects into the transmission of infectious diseases. For a classic SIR reaction-diffusion epidemic model, we review its Turing pattern formations with different transmission rates. A quantitative indicator, "normal serious prevalent area (NSPA)", is introduced to characterize the relationship between patterns and the extent of the epidemic. The extent of epidemic is positively correlated to NSPA. To effectively reduce NSPA of patterns under the large transmission rates, taken removed (recovery or isolation) rate as a control parameter, we consider the mathematical formulation and numerical solution of an optimal control problem for the SIR reaction-diffusion model. Numerical experiments demonstrate the effectiveness of our method in terms of control effect, control precision and control cost.

Novel approaches to fake news and fake account detection in OSNs: user social engagement and visual content centric model

With an increase in the number of active users on OSNs (Online Social Networks), the propagation of fake news became obvious. OSNs provide a platform for users to interact with others by expressing their opinions, resharing content into different networks, etc. In addition to these, interactions with posts are also collected, termed as social engagement patterns. By taking these social engagement patterns (by analyzing infectious disease spread analogy), SENAD(Social Engagement-based News Authenticity Detection) model is proposed, which detects the authenticity of news articles shared on Twitter based on the authenticity and bias of the users who are engaging with these articles. The proposed SENAD model incorporates the novel idea of authenticity score and factors in user social engagement centric measures such as Following-followers ratio, account age, bias, etc. The proposed model significantly improves fake news and fake account detection, as highlighted by classification accuracy of 93.7%. Images embedded with textual data catch more attention than textual messages and play a vital role in quickly propagating fake news. Images published have distinctive features which need special attention for detecting whether it is real or fake. Images get altered or misused to spread fake news. The framework Credibility Neural Network (CredNN) is proposed to assess the credibility of images on OSNs, by utilizing the spatial properties of CNNs to look for physical alterations in an image as well as analyze if the image reflects a negative sentiment since fake images often exhibit either one or both characteristics. The proposed hybrid idea of combining ELA and Sentiment analysis plays a prominent role in detecting fake images with an accuracy of around 76%.

Impact of social media advertisements on the transmission dynamics of COVID-19 pandemic in India

In this paper, we propose a mathematical model to assess the impact of social media advertisements in combating the coronavirus pandemic in India. We assume that dissemination of awareness among susceptible individuals modifies public attitudes and behaviours towards this contagious disease which results in reducing the chance of contact with the coronavirus and hence decreasing the disease transmission. Moreover, the individual's behavioral response in the presence of global information campaigns accelerate the rate of hospitalization of symptomatic individuals and also encourage the asymptomatic individuals for conducting health protocols, such as self-isolation, social distancing, etc. We calibrate the proposed model with the cumulative confirmed COVID-19 cases for the Republic of India. We estimate eight epidemiologically important parameters, and also the size of basic reproduction number for India. We find that the basic reproduction number for India is greater than unity, which represents the substantial outbreak of COVID-19 in the country. Sophisticated techniques of sensitivity analysis are employed to determine the impacts of model parameters on basic reproduction number and symptomatic infected population. Our results reveal that to reduce disease burden in India, non-pharmaceutical interventions strategies should be implemented effectively to decrease basic reproduction number below unity. Continuous propagation of awareness through the internet and social media platforms should be regularly circulated by the health authorities/government officials for hospitalization of symptomatic individuals and quarantine of asymptomatic individuals to control the prevalence of disease in India.

A nonlinear model predictive control model aimed at the epidemic spread with quarantine strategy

Allocating limit medicine resources by mathematical modeling to control spreading of epidemic diseases is a very promising approach. Especially, how to use the existing partial data to efficiently control epidemic diseases is a interesting problem. When an epidemic disease is spreading, it is very urgent and essential to build a prediction and control model based on the real-time and partial data in order that decision makers find and implement the optimal strategy timely. In this paper, we developed a new framework for solving the problem. Our nonlinear model predictive control (NMPC) based on a discrete time susceptible-infected-removed dynamics (SIR) gave an attempt that aims at timely dealing with the condition. Our NMPC model minimizes the total number of infectious cases and the total cost, with the treatment beds capacity constraints and other constraints, especially, with a state observer based on the system output which can be sampled more easily and more accurately. Our control policy can be updated timely according to the current statistical data because our NMPC is a kind of closed-loop control algorithm based on our observer. We also presented some theoretical results on the state observer. Finally, we gave a numerical example to illustrate our algorithm.

Approximating Quasi-Stationary Behaviour in Network-Based SIS Dynamics

Deterministic approximations to stochastic Susceptible-Infectious-Susceptible models typically predict a stable endemic steady-state when above threshold. This can be hard to relate to the underlying stochastic dynamics, which has no endemic steady-state but can exhibit approximately stable behaviour. Here, we relate the approximate models to the stochastic dynamics via the definition of the quasi-stationary distribution (QSD), which captures this approximately stable behaviour. We develop a system of ordinary differential equations that approximate the number of infected individuals in the QSD for arbitrary contact networks and parameter values. When the epidemic level is high, these QSD approximations coincide with the existing approximation methods. However, as we approach the epidemic threshold, the models deviate, with these models following the QSD and the existing methods approaching the all susceptible state. Through consistently approximating the QSD, the proposed methods provide a more robust link to the stochastic models.

Robust trend estimation for COVID-19 in Brazil

Estimating patterns of occurrence of cases and deaths related to the COVID-19 pandemic is a complex problem. The incidence of cases presents a great spatial and temporal heterogeneity, and the mechanisms of accounting for occurrences adopted by health departments induce a process of measurement error that alters the dependence structure of the process. In this work we propose methods to estimate the trend in the cases of COVID-19, controlling for the presence of measurement error. This decomposition is presented in Bayesian time series and spatio-temporal models for counting processes with latent components, and compared to the empirical analysis based on moving averages. We applied time series decompositions for the total number of deaths in Brazil and for the states of São Paulo and Amazonas, and a spatio-temporal analysis for all occurrences of deaths at the state level in Brazil, using two alternative specifications with global and regional components.

A simple statistical physics model for the epidemic with incubation period

Based on the classical SIR model, we derive a simple modification for the dynamics of epidemics with a known incubation period of infection. The model is described by a system of integro-differential equations. Parameters of our model are directly related to epidemiological data. We derive some analytical results, as well as perform numerical simulations. We use the proposed model to analyze COVID-19 epidemic data in Armenia.

A fractional-order model for CoViD-19 dynamics with reinfection and the importance of quarantine

Coronavirus disease 2019 (CoViD-19) is an infectious disease caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Among many symptoms, cough, fever and tiredness are the most common. People over 60 years old and with associated comorbidities are most likely to develop a worsening health condition. This paper proposes a non-integer order model to describe the dynamics of CoViD-19 in a standard population. The model incorporates the reinfection rate in the individuals recovered from the disease. Numerical simulations are performed for different values of the order of the fractional derivative and of reinfection rate. The results are discussed from a biological point of view.

A geometric analysis of the SIRS epidemiological model on a homogeneous network

We study a fast–slow version of an SIRS epidemiological model on homogeneous graphs, obtained through the application of the moment closure method. We use GSPT to study the model, taking into account that the infection period is much shorter than the average duration of immunity. We show that the dynamics occurs through a sequence of fast and slow flows, that can be described through 2-dimensional maps that, under some assumptions, can be approximated as 1-dimensional maps. Using this method, together with numerical bifurcation tools, we show that the model can give rise to periodic solutions, differently from the corresponding model based on homogeneous mixing.

Dengue models based on machine learning techniques: A systematic literature review

BACKGROUND

Dengue modeling is a research topic that has increased in recent years. Early prediction and decision-making are key factors to control dengue. This Systematic Literature Review (SLR) analyzes three modeling approaches of dengue: diagnostic, epidemic, intervention. These approaches require models of prediction, prescription and optimization. This SLR establishes the state-of-the-art in dengue modeling, using machine learning, in the last years.

METHODS

Several databases were selected to search the articles. The selection was made based on Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) methodology. Sixty-four articles were obtained and analyzed to describe their strengths and limitations. Finally, challenges and opportunities for research on machine-learning for dengue modeling were identified.

RESULTS

Logistic regression was the most used modeling approach for the diagnosis of dengue (59.1%). The analysis of the epidemic approach showed that linear regression (17.4%) is the most used technique within the spatial analysis. Finally, the most used intervention modeling is General Linear Model with 70%.

CONCLUSIONS

We conclude that cause-effect models may improve diagnosis and understanding of dengue. Models that manage uncertainty can also be helpful, because of low data-quality in healthcare. Finally, decentralization of data, using federated learning, may decrease computational costs and allow model building without compromising data security.

Continuous-time stochastic processes for the spread of COVID-19 disease simulated via a Monte Carlo approach and comparison with deterministic models

Two stochastic models are proposed to describe the evolution of the COVID-19 pandemic. In the first model the population is partitioned into four compartments: susceptible S, infected I, removed R and dead people D. In order to have a cross validation, a deterministic version of such a model is also devised which is represented by a system of ordinary differential equations with delays. In the second stochastic model two further compartments are added: the class A of asymptomatic individuals and the class L of isolated infected people. Effects such as social distancing measures are easily included and the consequences are analyzed. Numerical solutions are obtained with Monte Carlo simulations. Quantitative predictions are provided which can be useful for the evaluation of political measures, e.g. the obtained results suggest that strategies based on herd immunity are too risky. Finally, the models are calibrated on data referring to the second wave of infection in Italy.