ABSTRACT
In this paper, we propose and investigate the SIQR epidemic model with a generalized incidence rate function, a general treatment function and vaccination term. We firstly consider the existence and uniqueness of the global nonnegative solution to the deterministic model. Further, we show the locally asymptotic stability of the disease-free equilibrium and endemic equilibrium of the deterministic model, and obtain the basic reproduction number R0. Then we study the existence and uniqueness of the global positive solution to the stochastic model with any positive initial value. Meanwhile, we obtain sufficient conditions for the extinction of the disease in the stochastic epidemic model, and find that the large noise can make the disease die out exponentially. Finally, we make an empirical analysis by the COVID-19 data of Russia and Serbia. By the performance comparison of different models, it shows that the model with vaccination and treatment we proposed is better for the real situation, which is also verified by different estimation methods. Especially, that shows the recovery rate of the infected increases by 0.042 and the death rate of the recovered is 1.525 times that of normal human in Russia. Through statistical analysis, the short-term trend of epidemic transmission is predicted: under the condition of unchanged prevention and control policies, it may reach a stable endemic equilibrium state in Russia and the epidemic will eventually extinct in Serbia. © 2023 Elsevier Inc.
ABSTRACT
The revise is given as follows: The rapid emergence of the super-spreader COVID-19 with severe economic calamities with devastating social impact worldwide created the demand for effective research on the spread dynamics of the disease to combat and create surveillance systems on a global scale. In this study, a novel hybrid Deterministic Autoregressive Fractional Integral Moving Average (ARFIMA) model is presented to forecast the bimodal COVID-19 transmission dynamics. The heterogeneity of multimodal behavior of the COVID-19 pandemic in Pakistan is modeled by a hybrid paradigm, in which a deterministic pattern is combined with the ARFIMA model to absorb the inherent chaotic pattern of the pandemic spread. The fractional fluctuation of the real epidemic system is effectively taken as a paradigm by stochastic type improved the deterministic model and ARFIMA process. Special transformations are also introduced to enhance the convergent rate of the bimodal paradigm in deterministic modeling. The outcome of the improved deterministic model is combined with the ARFIMA model is evaluated on the spread pattern of pandemic data in Pakistan for the next 30 days. The performance-indices of the hybrid-model based on Relative-Errors and RMSE statistics confirmed the effectiveness of the proposed paradigm for long-term epidemic modeling compared to other classical and machine learning algorithms. © 2023 Informa UK Limited, trading as Taylor & Francis Group.
ABSTRACT
The world experienced the life-threatening COVID-19 disease worldwide since its inversion. The whole world experienced difficult moments during the COVID-19 period, whereby most individual lives were affected by the disease socially and economically. The disease caused millions of illnesses and hundreds of thousands of deaths worldwide. To fight and control the COVID-19 disease intensity, mathematical modeling was an essential tool used to determine the potentiality and seriousness of the disease. Due to the effects of the COVID-19 disease, scientists observed that vaccination was the main option to fight against the disease for the betterment of human lives and the world economy. Unvaccinated individuals are more stressed with the disease, hence their body's immune system are affected by the disease. In this study, the SVEIHR deterministic model of COVID-19 with six compartments was proposed and analyzed. Analytically, the next-generation matrix method was used to determine the basic reproduction number (R0). Detailed stability analysis of the no-disease equilibrium (E0) of the proposed model to observe the dynamics of the system was carried out and the results showed that E0 is stable if R0<1 and unstable when R0>1. The Bayesian Markov Chain Monte Carlo (MCMC) method for the parameter identifiability was discussed. Moreover, the sensitivity analysis of R0 showed that vaccination was an essential method to control the disease. With the presence of a vaccine in our SVEIHR model, the results showed that R0=0.208, which means COVID-19 is fading out of the community and hence minimizes the transmission. Moreover, in the absence of a vaccine in our model, R0=1.7214, which means the disease is in the community and spread very fast. The numerical simulations demonstrated the importance of the proposed model because the numerical results agree with the sensitivity results of the system. The numerical simulations also focused on preventing the disease to spread in the community. © 2022 The Authors
ABSTRACT
The efficient natural ventilation in indoor environments is extremely important especially this period with the appearance of new hazardous viruses such as COVID-19. It is well known that the maximum wind speed causes the lowest individual exposure to hazardous substances in an environment (either indoor or outdoor) and as a result its reliable prediction by a numerical model (either simple or complex) becomes of utmost importance. In this study a deterministic model, that was developed for the outdoor environment, is examined as a possible candidate to predict the maximum wind speed in indoor environments. For the needs of the study a wind tunnel experiment is simulated by the LES methodology in order to acquire the maximum wind speed at various locations in an indoor environment. Then the deterministic model, without any change in its parameters, is validated successfully with the LES maximum wind speeds. The present deterministic model can be incorporated in simple methodologies (e.g. RANS) provided that the latest are able to predict the mean speed, the turbulent intensity and a hydrodynamic time scale. © British Crown Copyright (2022)
ABSTRACT
The aim of this paper is the derivation of an robust formalism that calculates the so-called social distancing as already determined in the ongoing Corona Virus Disease 2019 (Covid-19 in short) being established in various places in the world between 1.5 m and 2.5 m. This would constitutes a critic space of separation among people in the which aerosols might not be effective to infect healthy people. In addition to wearing masks and face protection, the social distancing appears to be critic to keep people far of infections and consequences produced from it. In this way, the paper has opted by the incorporation of a full deterministic model inside the equation of Weiss, by the which it fits well to the action of outdoor infection when wind manages the direction and displacement of aerosols in space. Thus, while a deterministic approach targets to propose a risk’s probability, a probabilistic scenario established by Weiss in conjunction to the deterministic events would yield an approximated model of outdoor infection when there is a continuous source of infected aerosols that are moving through air in according to a wind velocity. The simulations have shown that the present approach is valid to some extent in the sense that only the 1D case is considered. The model can be extended with the implementation of physical variables that can attenuate the presence of disturbs and random noise that minimizes the effectiveness of present proposal. © 2021, ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering.
ABSTRACT
We begin with a simple model for the COVID-19 epidemic and add face mask usages and testing and quarantine of infectives. We estimate the effect on the reproduction number and discuss the question of whether the epidemic can be controlled by increased use of face masks.