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

Epidemic propagation risk study with effective fractal dimension

In this article, the risk of epidemic transmission on complex networks is studied from the perspective of effective fractal dimension. First, we introduce the method of calculating the effective fractal dimensionD B ${D}_B$ of the network by taking a scale-free network as an example. Second, we propose the construction method of administrative fractal network and calculate theD B ${D}_B$ . using the classical susceptible exposed infectious removed (SEIR) infectious disease model, we simulate the virus propagation process on the administrative fractal network. The results show that the larger theD B ${D}_B$ is, the higher the risk of virus transmission is. Later, we proposed five parameters P, M, B, F, and D, where P denotes population mobility, M denotes geographical distance, B denotes GDP, F denotesD B ${D}_B$ , and D denotes population density. The new epidemic growth index formulaI = ( P + ( 1 - M ) + B ) ( F + D ) $I = {( {P + ( {1 - M} ) + B} )}^{( {F + D} )}$ was obtained by combining these five parameters, and the validity of I in epidemic transmission risk assessment was demonstrated by parameter sensitivity analysis and reliability analysis. Finally, we also confirmed the reliability of the SEIR dynamic transmission model in simulating early COVID-19 transmission trends and the ability of timely quarantine measures to effectively control the spread of the epidemic.

Exploring the potential of learning methods and recurrent dynamic model with vaccination: A comparative case study of COVID-19 in Austria, Brazil, and China

In order to effectively manage infectious diseases, it is crucial to understand the interplay between disease dynamics and human conduct. Various factors can impact the control of an epidemic, including social interventions, adherence to health protocols, mask-wearing, and vaccination. This article presents the development of an innovative hybrid model, known as the Combined Dynamic-Learning Model, that integrates classical recurrent dynamic models with four different learning methods. The model is composed of two approaches: The first approach introduces a traditional dynamic model that focuses on analyzing the impact of vaccination on the occurrence of an epidemic, and the second approach employs various learning methods to forecast the potential outcomes of an epidemic. Furthermore, our numerical results offer an interesting comparison between the traditional approach and modern learning techniques. Our classic dynamic model is a compartmental model that aims to analyze and forecast the diffusion of epidemics. The model we propose has a recurrent structure with piecewise constant parameters and includes compartments for susceptible, exposed, vaccinated, infected, and recovered individuals. This model can accurately mirror the dynamics of infectious diseases, which enables us to evaluate the impact of restrictive measures on the spread of diseases. We conduct a comprehensive dynamic analysis of our model. Additionally, we suggest an optimal numerical design to determine the parameters of the system. Also, we use regression tree learning, bidirectional long short-term memory, gated recurrent unit, and a combined deep learning method for training and evaluation of an epidemic. In the final section of our paper, we apply these methods to recently published data on COVID-19 in Austria, Brazil, and China from 26 February 2021 to 4 August 2021, which is when vaccination efforts began. To evaluate the numerical results, we utilized various metrics such as RMSE and R-squared. Our findings suggest that the dynamic model is ideal for long-term analysis, data fitting, and identifying parameters that impact epidemics. However, it is not as effective as the supervised learning method for making long-term forecasts. On the other hand, supervised learning techniques, compared to dynamic models, are more effective for predicting the spread of diseases, but not for analyzing the behavior of epidemics.

A data-driven epidemic model with human mobility and vaccination protection for COVID-19 prediction

Epidemiological models allow for quantifying the dynamic characteristics of large-scale outbreaks. However, capturing detailed and accurate epidemiological information often requires consideration of multiple kinetic mechanisms and parameters. Due to the uncertainty of pandemic evolution, such as pathogen variation, host immune response and changes in mitigation strategies, the parameter evaluation and state prediction of complex epidemiological models are challenging. Here, we develop a data-driven epidemic model with a generalized SEIR mechanistic structure that includes new compartments, human mobility and vaccination protection. To address the issue of model complexity, we embed the epidemiological model dynamics into physics-informed neural networks (PINN), taking the observed series of time instances as direct input of the network to simultaneously infer unknown parameters and unobserved dynamics of the underlying model. Using actual data during the COVID-19 outbreak in Australia, Israel, and Switzerland, our model framework demonstrates satisfactory performance in multi-step ahead predictions compared to several benchmark models. Moreover, our model infers time-varying parameters such as transmission rates, hospitalization ratios, and effective reproduction numbers, as well as calculates the latent period and asymptomatic infection count, which are typically unreported in public data. Finally, we employ the proposed data-driven model to analyze the impact of different mitigation strategies on COVID-19.

Attitudinal analysis of vaccination effects to lead endemic phases

To achieve endemic phases, repeated vaccinations are necessary. However, individuals may grapple with whether to get vaccinated due to potential side effects. When an individual is already immune due to previous infections or vaccinations, the perceived risk from vaccination is often less than the risk of infection. Yet, repeated rounds of vaccination can lead to avoidance, impeding the establishment of endemic phases. We explore this phenomenon using an individual-based Monte Carlo simulation, validating our findings with game theory. The Nash equilibrium encapsulates individuals' non-cooperative behavior, while the system's optimal value represents the societal benefits of altruistic cooperation. We define the difference between these as the price of anarchy. Our simulations reveal that the price of anarchy must fall below a threshold of 12.47 for endemic phases to be achieved in a steady state. This suggests that for a basic reproduction number of 10, a consistent vaccination rate greater than 89% is required. These findings offer new insights into vaccination-related decision-making and can inform effective strategies to tackle infectious diseases.