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Seasonal influenza is a serious public health and societal problem due to its consequences resulting from absenteeism, hospitalizations, and deaths. The overall burden of influenza is captured by the Centers for Disease Control and Prevention's influenza-like illness network, which provides invaluable information about the current incidence. This information is used to provide decision support regarding prevention and response efforts. Despite the relatively rich surveillance data and the recurrent nature of seasonal influenza, forecasting the timing and intensity of seasonal influenza in the U.S. remains challenging because the form of the disease transmission process is uncertain, the disease dynamics are only partially observed, and the public health observations are noisy. Fitting a probabilistic state-space model motivated by a deterministic mathematical model [a susceptible-infectious-recovered (SIR) model] is a promising approach for forecasting seasonal influenza while simultaneously accounting for multiple sources of uncertainty. A significant finding of this work is the importance of thoughtfully specifying the prior, as results critically depend on its specification. Our conditionally specified prior allows us to exploit known relationships between latent SIR initial conditions and parameters and functions of surveillance data. We demonstrate advantages of our approach relative to alternatives via a forecasting comparison using several forecast accuracy metrics.

The health organizations around the world are currently facing one of the greatest challenges, to overcome the current global pandemic, COVID-19. It erupted in December 2019, in Wuhan City, China. It spreads rapidly throughout the world within couple of months. In this paper, the data of the COVID-19 have been collected, organized, analyzed and interpreted using the discrete-time model of SIR epidemic model. Moreover, results for several countries from different regions of the world have been obtained. Furthermore, comparative study has been carried out for the countries under consideration. The comparison was performed for the data of different countries on same dates of each month. However, the calculations are carried out for thirteen consecutive weeks, to investigate the rate of spread and the control of the disease in these countries. This guides us to some important concepts like factors favoring the spread of virus and those resisting the spread. Different regions are studied and their data have been evaluated to know which regions are the most effected. This study helps to know the important factors about the behavior of the coronavirus in different environments, such as lockdowns, temperatures, humidity and other restrictions. The proposed concepts and equations can be used to project the upcoming behavior of the pandemic.

The COVID-19 pandemic caused by the SARS-CoV-2 virus has inflicted significant mortality and morbidity worldwide. Continuous virus mutations have led to the emergence of new variants. The Omicron BA.1 sub-lineage prevailed as the dominant variant globally at the beginning of 2022 but was subsequently replaced by BA.2 in numerous countries. Wastewater-based epidemiology (WBE) offers an efficient tool for capturing viral shedding from infected individuals, enabling early detection of potential pandemic outbreaks without relying solely on community cooperation and clinical testing resources. This study integrated RT-qPCR assays for detecting general SARS-CoV-2 and its variants levels in wastewater into a modified triple susceptible-infected-recovered-susceptible (SIRS) model. The emergence of the Omicron BA.1 variant was observed, replacing the presence of its predecessor, the Delta variant. Comparative analysis between the wastewater data and the modified SIRS model effectively described the BA.1 and subsequent BA.2 waves, with the decline of the Delta variant aligning with its diminished presence below the detection threshold in wastewater. This study demonstrates the potential of WBE as a valuable tool for future pandemics. Furthermore, by analyzing the sensitivity of different variants to model parameters, we are able to deduce real-life values of cross-variant immunity probabilities, emphasizing the asymmetry in their strength.

According to the World Health Organization updates, the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) caused a pandemic between 2019 and 2022, with millions of confirmed cases and deaths worldwide. There are various approaches to predicting the suspected, infected, and recovered (SIR) cases with different factual or epidemiological models. Some of the recent approaches to predicting the COVID-19 outbreak have had positive impacts in specific nations. Results show that the SIR model is a significant tool to cast the dynamics and predictions of the COVID-19 outbreak compared to other epidemic models. In this paper, we employ the Monte Carlo simulation to predict the spread of COVID-19 in the United Arab Emirates. We study traditional SIR models in general and focus on a time-dependent SIR model, which has been proven more adaptive and robust in predicting the COVID-19 outbreak. We evaluate the time-dependent SIR model. Then, we implement a Monte Carlo model. The Monte Carlo model uses the parameters extracted from the Time-Dependent SIR Model. The Monte Carlo model exhibited a better prediction accuracy and resembles the data collected from the Ministry of Cabinet Affairs, United Arab Emirates, between April and July 2020.

This study presents Bayesian analysis and discrimination for the structured two levels of mixing stochastic susceptible–infective–removed (SIR) epidemic model of infectious disease spread in a closed population, given temporal epidemic data. We focus on estimating key parameters, the global and local transmission rates ( β G and β L ), with a view to understanding their influence on disease dynamics. Utilizing Bayesian inference, we derive the joint posterior distribution of these parameters for both complete and incomplete outbreak data scenarios. In addition, we establish a simulation‐based method for discriminating between the two levels of mixing SIR models from other stochastic models and evaluate its performance through simulation experiments. Our methodologies provide valuable insights into disease transmission dynamics within and between households and can be extended to more complex models.

A healthy, latently infected, diseased (HLD) plant model for botanical epidemics was defined for tomato bacterial canker (TBC) caused by the pathogenic plant bacteria, Clavibacter michiganensis subsp. michiganensis (Cmm). To estimate the infection probability parameter, inoculation experiments were conducted in which it was assumed that infection is transferred to healthy plants through contaminated scissors used to cut symptomless infected plants. The approximate concentration of Cmm in symptomless infected plants was 1 × 106 cells/mL, and the probability of infection of healthy tomato plants was approximately 0.75 due to cutting with scissors soaked in a cell suspension of Cmm at 1 × 106 cells/mL. Three different HLD models were developed by changing some parameters, and the D curve calculated by the developed HLD model A was quite similar to the curve of the proportion of diseased plants observed in fields that had a severe disease incidence. Under a simulation of disease incidence using this model, the basic reproduction number (R0) was 2.6. However, if the infected scissors were disinfected using ethanol, R0 was estimated as 0.3. The HLD model for TBC can be used to simulate the increasing number of diseased plants and the term of disease incidence.

The Sars-Cov-2 pandemic certainly represents an unprecedented challenge not only for medical researchers fighting against its worldwide diffusion but also for statisticians involved in proposing models to estimate the crucial epidemic parameters and monitor and control its future evolution. The traditional epidemiological SIR model (Brauer, Castillo-Chavez and Feng, 2019) is usually specified in a deterministic way and fitted to empirical data by numerical optimization, neglecting the error component’s role so that its performances cannot be statistically tested. This paper introduces uncertainty explicitly in the estimation process (Bailey, 1955; Kendall, 1956). We start providing a finite difference representation of the model. We then introduce stochastic components in the model in the form of a measurement error and a random error. We finally apply the model to the case of the Italian 2020-2021 Sars-Cov-2 pandemic diffusion showing its relative advantages with respect to the deterministic specification.

Predicting the outbreak of a pandemic is an important measure in order to help saving people lives threatened by Covid-19. Having information about the possible spread of the pandemic, authorities and people can make better decisions. For example, such analyses help developing better strategies for distributing vaccines and medicines. This paper has modified the original Susceptible-Infectious-Recovered (SIR) model to Susceptible-Immune-Infected-Recovered (SIRM) which includes the Immunity ratio as a parameter to enhance the prediction of the pandemic. SIR is a widely used model to predict the spread of a pandemic. Many types of pandemics imply many variants of the SIR models which make it very difficult to find out the best model that matches the running pandemic. The simulation of this paper used the published data about the spread of the pandemic in order to examine our new SIRM. The results showed clearly that our new SIRM covering the aspects of vaccine and medicine is an appropriate model to predict the behavior of the pandemic.

To show the potential of non-commensurable fractional-order dynamical systems in modeling epidemiological phenomena, we will adjust the parameters of a fractional generalization of the SIR model to describe the population distributions generated by SARS-CoV-2 in France and Colombia. Despite the completely different contexts of both countries, we will see how the system presented here manages to adequately model them thanks to the flexibility provided by the fractional-order differential equations. The data for Colombia were obtained from the records published by the Colombian Ministry of Information Technology and Communications from March 24 to July 10, 2020. Those for France were taken from the information published by the Ministry of Solidarity and Health from May 1 to September 6, 2020. As for the methodology implemented in this study, we conducted an exploratory analysis focused on solving the fractional SIR model by means of the fractional transformation method. In addition, the model parameters were adjusted using a sophisticated optimization method known as the Bound Optimization BY Quadratic Approximation (BOBYQA) algorithm. According to the results, the maximum error percentage for the evolution of the susceptible, infected, and recovered populations in France was 0.05%, 19%, and 6%, respectively, while that for the evolution of the susceptible, infected, and recovered populations in Colombia was 0.003%, 19%, and 38%, respectively. This was considered for data in which the disease began to spread and human intervention did not imply a substantial change in the community.

Many of the models used nowadays in mathematical epidemiology, in particular in COVID-19 research, belong to a certain subclass of compartmental models whose classes may be divided into three “(x,y,z)” groups, which we will call respectively “susceptible/entrance, diseased, and output” (in the classic SIR case, there is only one class of each type). Roughly, the ODE dynamics of these models contains only linear terms, with the exception of products between x and y terms. It has long been noticed that the reproduction number R has a very simple Formula in terms of the matrices which define the model, and an explicit first integral Formula is also available. These results can be traced back at least to Arino, Brauer, van den Driessche, Watmough, and Wu (2007) and to Feng (2007), respectively, and may be viewed as the “basic laws of SIR-type epidemics”. However, many papers continue to reprove them in particular instances. This motivated us to redraw attention to these basic laws and provide a self-contained reference of related formulas for (x,y,z) models. For the case of one susceptible class, we propose to use the name SIR-PH, due to a simple probabilistic interpretation as SIR models where the exponential infection time has been replaced by a PH-type distribution. Note that to each SIR-PH model, one may associate a scalar quantity Y(t) which satisfies “classic SIR relations”,which may be useful to obtain approximate control policies.