Search Results (23)

Mathematical models for infectious diseases, particularly autonomous ODE models, are generally known to possess simple dynamics, often converging to stable disease-free or endemic equilibria. This paper investigates the dynamic consequences of a crucial, yet often overlooked, component of pandemic response: the saturation of public health testing. We extend the standard SIR model to include compartments for ‘Confirmed’ (C) and ‘Monitored’ (M) individuals, resulting in a new SICMR model. By fitting the model to U.S. COVID-19 pandemic data (specifically the Omicron wave of late 2021), we demonstrate that capacity constraints in testing destabilize the testing-free endemic equilibrium ($E_1$). This equilibrium becomes an unstable saddle-focus. The instability is driven by a sociological feedback loop, where the rise in confirmed cases drive testing effort, modeled by a nonlinear Holling Type II functional response. We explicitly verify that the eigenvalues for the best-fit model satisfy the Shilnikov condition (${\lambda }_u>{\lambda }_s$), demonstrating the system possesses the necessary ingredients for complex, chaotic-like dynamics. Furthermore, we employ Stochastic Differential Equations (SDEs) to show that intrinsic noise interacts with this instability to generate ’noise-induced bursting,’ replicating the complex wave-like patterns observed in empirical data. Our results suggest that public health interventions, such as testing, are not merely passive controls but active dynamical variables that can fundamentally alter the qualitative stability of an epidemic. Full article

The recent resurgence of COVID-19 in a Hepatitis B virus some endemic countries could lead to adverse outcomes. In this article, we formulate and analyse a mathematical model to explains the co-infection dynamics of Hepatitis B virus and COVID-19. Our aim is to investigate the effect of Hepatitis B virus prevention, COVID-19 prevention, COVID-19 vaccination, and environmental factors on transmission dynamics, and formulate conditions for extinction and persistence of the diseases. First, we derive the basic reproduction number for HBV only, COVID-19 only, and co-infection stochastic models using the next-generation matrix method. Next, we establish the conditions for stability in the stochastic sense for HBV only, COVID-19 only sub-models, and the co-infection model using suitable Lyapunov functions. Furthermore, we devote our attention to finding sufficient conditions for extinction and persistence. Finally, motivated by Ghana data, we applied the Euler–Murayama scheme to illustrate the dynamics of the co-infection, COVID-19, HBV, and the effect of some parameters on disease transmission dynamics by means of numerical simulations. Full article

This research provides valuable insights into the application of mathematical modeling to real-world scenarios, as exemplified by the COVID-19 pandemic. After data collection, the preparation stage included exploratory analysis, standardization and normalization, computation, and validation. A mathematical model initially developed for COVID-19 dynamics in Romania was subsequently applied to data from Italy and Switzerland during the same time interval. The model is structured as a multiple-input single-output (MISO) system, where the inputs underwent a neural network-based training stage to address inconsistencies in the acquired data. In parallel, an ARMAX model was employed to capture the stochastic nature of the epidemic process. Results demonstrate that the Romanian-based model generalized effectively across the three countries, achieving a strong predictive accuracy (forecast accuracy > 98.59%). Importantly, the model maintained robust performance despite significant cross-country differences in testing strategies, policy measures, timing of initial cases, and imported infections. This work contributes a novel perspective by showing that a unified data-driven modeling framework can be transferable across heterogeneous contexts. More broadly, it underscores the potential of integrating mathematical modeling with predictive analytics to support evidence-based decision-making and strengthen preparedness for future global health crises. Full article

This study investigates the dual dynamics of investment shocks and policy responses in stabilizing South Korea’s macroeconomy during the COVID-19 pandemic, utilizing a Bayesian DSGE framework. The model integrates sophisticated mathematical components, including stochastic differential equations, Bayesian inference, and impulse response functions, to analyze the transmission mechanisms of investment shocks and the relative efficacy of fiscal and monetary interventions. The estimation is conducted through Markov Chain Monte Carlo simulations. Using data from the first quarter of 2020 to the first quarter of 2023, the analysis quantifies the pandemic-induced shocks’ impact on critical macroeconomic indicators, including enterprise output, household consumption, employment, and investment. The findings reveal that heightened investment costs significantly constrained economic performance, with fiscal measures, such as increased government spending and targeted stimulus packages, demonstrating superior stabilization effects compared to monetary interventions. These results emphasize the importance of well-coordinated policy responses in mitigating economic disruptions and enhancing resilience during crises. This study not only provides novel insights into the mathematical modeling of economic stabilization strategies but also offers actionable recommendations for policymakers navigating pandemic-induced challenges. Full article

This paper studies the dynamic behavior of a stochastic SEIRM model of COVID-19 with a standard incidence rate. The existence of global solutions for dynamic system models is proven by integrating stochastic process theory and the concept of stopping times, together with the contradiction method. Moreover, we construct appropriate Lyapunov functions to analyze system stability and apply Dynkin’s formula and Fatou’s lemma to handle stopping times and expectations of stochastic processes. Notably, the extinction study provides mathematical proof that under the given system dynamics, the total population does not grow indefinitely but tends to stabilize over time. The properties of the diffusion matrix are harnessed to guarantee the system’s stationary distribution. Conclusively, numerical simulations confirm the model’s extinction outcomes. Full article

Mathematical models play a crucial role in evaluating real-life processes qualitatively and quantitatively. They have been extensively employed to study the spread of diseases such as hepatitis B, COVID-19, influenza, and other epidemics. Many researchers have discussed various types of epidemiological models, including deterministic, stochastic, and fractional order models, for this purpose. This article presents a comprehensive review and comparative study of the transmission dynamics of fractional order in epidemiological modeling. A significant portion of the paper is dedicated to the graphical simulation of these models, providing a visual representation of their behavior and characteristics. The article further embarks on a comparative analysis of fractional-order models with their integer-order counterparts. This comparison sheds light on the nuances and subtleties that differentiate these models, thereby offering valuable insights into their respective strengths and limitations. The paper also explores time delay models, non-linear incidence rate models, and stochastic models, explaining their use and significance in epidemiology. It includes studies and models that focus on the transmission dynamics of diseases using fractional order models, as well as comparisons with integer-order models. The findings from this study contribute to the broader understanding of epidemiological modeling, paving the way for more accurate and effective strategies in disease control and prevention. Full article

The worldwide data for COVID-19 for active, infected individuals in multiple waves show that traditional epidemic models with constant parameters are not able to capture this kind of disease behavior. We solved this major open mathematical problem in this report. We first consider the disease transmission rate for the stochastic SIRVI epidemic model, which satisfies the mean-reverting Ornstein–Uhlenbeck (OU) process, and we propose a new stochastic SIRVI model. We then showed the existence and uniqueness of the global solution and obtained sufficient conditions for the persistent mean and exponential extinction of infectious disease, which have not been given before. In the second part, we derive a nonlinear system of differential equations for the time-dependent transmission rate from the deterministic SIRVI model and present an algorithm to compute the time-dependent transmission rate directly from the given active, infected individuals’ data. We then show that the time-dependent transmission obtained from and perturbed by the Ornstein–Uhlenbeck process could be represented after using a smoothing technique using a finite linear combination of a Gaussian radial basis function, which was obtained from our algorithm. This novel computer-assisted proof provides a theoretical basis for other epidemic models and epidemic waves. Finally, some numerical solutions of the stochastic SIRVI model are presented using COVID-19 data from Saudi Arabia and Austria. Full article

With retailers increasingly adopting the omnichannel retailing model as a core strategy in their daily operations, this study investigates the impact of random demand on the omnichannel supply chain that employs a combination of the online channel, retail channel, and buy online and pick up in store (BOPS) channel, in light of the more stochastic market after the occurrence of COVID-19. To enhance the sustainable profitability of the omnichannel supply chain, this study considers price and lead time dependent demand with both known and unknown distributions, and establishes mathematical models to maximize profit under centralized situations. The study analyzes the variations in demand with lead time in the three channels and examines the effects of price and lead time on profit. Additionally, it investigates the interactions between price and lead time. Through numerical examples, the study illustrates the effects of the mean and variance of random demand on decision variables and examines the influence of potential demand and the sensitivity of lead time. Overall, this analysis provides valuable insights into the impact of demand randomness on the profitability of an omnichannel supply chain, highlighting the importance of considering price and lead time in the decision-making process. Full article

When an individual with confirmed or suspected COVID-19 is quarantined or isolated, the virus can linger for up to an hour in the air. We developed a mathematical model for COVID-19 by adding the point where a person becomes infectious and begins to show symptoms of COVID-19 after being exposed to an infected environment or the surrounding air. It was proven that the proposed stochastic COVID-19 model is biologically well-justifiable by showing the existence, uniqueness, and positivity of the solution. We also explored the model for a unique global solution and derived the necessary conditions for the persistence and extinction of the COVID-19 epidemic. For the persistence of the disease, we observed that ${\mathfrak{R}}_{\mathfrak{s}}^{\mathfrak{0}}>1$, and it was noticed that, for $R_s<1$, the COVID-19 infection will tend to eliminate itself from the population. Supplementary graphs representing the solutions of the model were produced to justify the obtained results based on the analysis. This study has the potential to establish a strong theoretical basis for the understanding of infectious diseases that re-emerge frequently. Our work was also intended to provide general techniques for developing the Lyapunov functions that will help the readers explore the stationary distribution of stochastic models having perturbations of the nonlinear type in particular. Full article

Human society always wants a safe environment from pollution and infectious diseases, such as COVID-19, etc. To control COVID-19, we have started the big effort for the discovery of a vaccination of COVID-19. Several biological problems have the aspects of symmetry, and this theory has many applications in explaining the dynamics of biological models. In this research article, we developed the stochastic COVID-19 mathematical model, along with the inclusion of a vaccination term, and studied the dynamics of the disease through the theory of symmetric dynamics and ergodic stationary distribution. The basic reproduction number is evaluated using the equilibrium points of the proposed model. For well-posedness, we also test the given problem for the existence and uniqueness of a non-negative solution. The necessary conditions for eradicating the disease are also analyzed along with the stationary distribution of the proposed model. For the verification of the obtained result, simulations of the model are performed. Full article

An environment of turbulence in the market in recent years and increasing inflation, mainly as a result of the post-COVID period and the ongoing military operation in Ukraine, represents a significant financial risk factor for many companies, which has a negative impact on managerial decisions. A lot of enterprises are forced to look for ways to effectively assess the riskiness of the projects that they would like to implement in the future. The aim of the article is to present a new approach for companies with which to assess the riskiness of projects. The basis of this is the use of the new Crystal Ball software tool and the effective application of the Monte Carlo method. The article deals with the current issues of investment and financial planning, which are the basic pillars for effective management decisions with the goal of sustainability. The article has verified a methodology that allows companies to make effective investment decisions based on assessing the level of risk. For practical application, the Monte Carlo method was chosen, as it uses sensitivity analysis and simulations, which were evaluated for two types of projects. Both simulations were primarily carried out based on a deterministic approach through traditional mathematical models. Subsequently, stochastic modeling was performed using the Crystal Ball software tool. As a result of the sensitivity analysis, two tornado graphs were created, which display risk factors according to the degree of their influence on the criterion value. The output of this article is the presentation of these new approaches for financial decision-making within companies. Full article

Natural symmetry exists in several phenomena in physics, chemistry, and biology. Incorporating these symmetries in the differential equations used to characterize these processes is thus a valid modeling assumption. The present study investigates COVID-19 infection through the stochastic model. We consider the real infection data of COVID-19 in Saudi Arabia and present its detailed mathematical results. We first present the existence and uniqueness of the deterministic model and later study the dynamical properties of the deterministic model and determine the global asymptotic stability of the system for ${\mathcal{R}}_0\le 1$. We then study the dynamic properties of the stochastic model and present its global unique solution for the model. We further study the extinction of the stochastic model. Further, we use the nonlinear least-square fitting technique to fit the data to the model for the deterministic and stochastic case and the estimated basic reproduction number is ${\mathcal{R}}_0\approx 1.1367$. We show that the stochastic model provides a good fitting to the real data. We use the numerical approach to solve the stochastic system by presenting the results graphically. The sensitive parameters that significantly impact the model dynamics and reduce the number of infected cases in the future are shown graphically. Full article

The consideration of infectious diseases from a mathematical point of view can reveal possible options for epidemic control and fighting the spread of infection. However, predicting and modeling the spread of a new, previously unexplored virus is still difficult. The present paper examines the possibility of using a new approach to predicting the statistical indicators of the epidemic of a new type of virus based on the example of COVID-19. The important result of the study is the description of the principle of dynamic balance of epidemiological processes, which has not been previously used by other researchers for epidemic modeling. The new approach is also based on solving the problem of predicting the future dynamics of precisely random values of model parameters, which is used for defining the future values of the total number of: cases (C); recovered and dead (R); and active cases (I). Intelligent heuristic algorithms are proposed for calculating the future trajectories of stochastic parameters, which are called the percentage increase in the total number of confirmed cases of the disease and the dynamic characteristics of epidemiological processes. Examples are given of the application of the proposed approach for making forecasts of the considered indicators of the COVID-19 epidemic, in Russia and European countries, during the first wave of the epidemic. Full article

This work aims to study the factors that increase the risk of death of hospitalized patients diagnosed with COVID-19 through the odd log-logistic regression model for censored data with two systematic components, as well as provide new mathematical properties of this distribution. To achieve this, a dataset of individuals residing in the city of Campinas (Brazil) was used and simulations were performed to investigate the accuracy of the maximum likelihood estimators in the proposed regression model. The provided properties, such as stochastic representation, identifiability, and moments, among others, can help future research since they provide important information about the distribution structure. The simulation results revealed the consistency of the estimates for different censoring percentages and show that the empirical distribution of the modified deviance residuals converge to the standard normal distribution. The proposed model proved to be efficient in identifying the determinant variables for the survival of the individuals in this study, which can help to find more opportune treatments and medical interventions. Therefore, the new model can be considered an interesting alternative for future works that evaluate censored lifetimes. Full article

Understanding the factors that increase the transmissibility of the recently emerging variants of SARS-CoV-2 can aid in mitigating the COVID-19 pandemic. Enhanced transmissibility could result from genetic variations that improve how the virus operates within the host or its environmental survival. Variants with enhanced within-host behavior are either more contagious (leading infected individuals to shed more virus copies) or more infective (requiring fewer virus copies to infect). Variants with improved outside-host processes exhibit higher stability on surfaces and in the air. While previous studies focus on a specific attribute, we investigated the contribution of both within-host and outside-host processes to the overall transmission between two individuals. We used a hybrid deterministic-continuous and stochastic-jump mathematical model. The model accounts for two distinct dynamic regimes: fast-discrete actions of the individuals and slow-continuous environmental virus degradation processes. This model produces a detailed description of the transmission mechanisms, in contrast to most-viral transmission models that deal with large populations and are thus compelled to provide an overly simplified description of person-to-person transmission. We based our analysis on the available data of the Alpha, Epsilon, Delta, and Omicron variants on the household secondary attack rate (hSAR). The increased hSAR associated with the recent SARS-CoV-2 variants can only be attributed to within-host processes. Specifically, the Delta variant is more contagious, while the Alpha, Epsilon, and Omicron variants are more infective. The model also predicts that genetic variations have a minimal effect on the serial interval distribution, the distribution of the period between the symptoms’ onset in an infector–infectee pair. Full article