Reactive-diffusion epidemic model on human mobility networks: Analysis and applications to COVID-19 in China

Real-time infectious disease endurance indicator system for scientific decisions using machine learning and rapid data processing

The SARS-CoV-2 virus, which induces an acute respiratory illness commonly referred to as COVID-19, had been designated as a pandemic by the World Health Organization due to its highly infectious nature and the associated public health risks it poses globally. Identifying the critical factors for predicting mortality is essential for improving patient therapy. Unlike other data types, such as computed tomography scans, x-radiation, and ultrasounds, basic blood test results are widely accessible and can aid in predicting mortality. The present research advocates the utilization of machine learning (ML) methodologies for predicting the likelihood of infectious disease like COVID-19 mortality by leveraging blood test data. Age, LDH (lactate dehydrogenase), lymphocytes, neutrophils, and hs-CRP (high-sensitivity C-reactive protein) are five extremely potent characteristics that, when combined, can accurately predict mortality in 96% of cases. By combining XGBoost feature importance with neural network classification, the optimal approach can predict mortality with exceptional accuracy from infectious disease, along with achieving a precision rate of 90% up to 16 days before the event. The studies suggested model's excellent predictive performance and practicality were confirmed through testing with three instances that depended on the days to the outcome. By carefully analyzing and identifying patterns in these significant biomarkers insightful information has been obtained for simple application. This study offers potential remedies that could accelerate decision-making for targeted medical treatments within healthcare systems, utilizing a timely, accurate, and reliable method.

Epidemic spreading on spatial higher-order network

Higher-order interactions exist widely in mobile populations and are extremely important in spreading epidemics, such as influenza. However, research on high-order interaction modeling of mobile crowds and the propagation dynamics above is still insufficient. Therefore, this study attempts to model and simulate higher-order interactions among mobile populations and explore their impact on epidemic transmission. This study simulated the spread of the epidemic in a spatial high-order network based on agent-based model modeling. It explored its propagation dynamics and the impact of spatial characteristics on it. Meanwhile, we construct state-specific rate equations based on the uniform mixing assumption for further analysis. We found that hysteresis loops are an inherent feature of high-order networks in this space under specific scenarios. The evolution curve roughly presents three different states with the initial value change, showing different levels of the endemic balance of low, medium, and high, respectively. Similarly, network snapshots and parameter diagrams also indicate these three types of equilibrium states. Populations in space naturally form components of different sizes and isolations, and higher initial seeds generate higher-order interactions in this spatial network, leading to higher infection densities. This phenomenon emphasizes the impact of high-order interactions and high-order infection rates in propagation. In addition, crowd density and movement speed act as protective and inhibitory factors for epidemic transmission, respectively, and depending on the degree of movement weaken or enhance the effect of hysteresis loops.

Influence of Human Behavior on COVID-19 Dynamics Based on a Reaction-Diffusion Model

To investigate the influence of human behavior on the spread of COVID-19, we propose a reaction-diffusion model that incorporates contact rate functions related to human behavior. The basic reproduction number R 0 is derived and a threshold-type result on its global dynamics in terms of R 0 is established. More precisely, we show that the disease-free equilibrium is globally asymptotically stable if R 0 ≤ 1 ; while there exists a positive stationary solution and the disease is uniformly persistent if R 0 > 1 . By the numerical simulations of the analytic results, we find that human behavior changes may lower infection levels and reduce the number of exposed and infected humans.

Dynamic behavior analysis of an SVIR epidemic model with two time delays associated with the COVID-19 booster vaccination time

Since the outbreak of COVID-19, there has been widespread concern in the community, especially on the recent heated debate about when to get the booster vaccination. In order to explore the optimal time for receiving booster shots, here we construct an SVIR model with two time delays based on temporary immunity. Second, we theoretically analyze the existence and stability of equilibrium and further study the dynamic properties of Hopf bifurcation. Then, the statistical analysis is conducted to obtain two groups of parameters based on the official data, and numerical simulations are carried out to verify the theoretical analysis. As a result, we find that the equilibrium is locally asymptotically stable when the booster vaccination time is within the critical value. Moreover, the results of the simulations also exhibit globally stable properties, which might be more beneficial for controlling the outbreak. Finally, we propose the optimal time of booster vaccination and predict when the outbreak can be effectively controlled.

Mathematical Modelling of the Spatial Distribution of a COVID-19 Outbreak with Vaccination Using Diffusion Equation

The formulation of mathematical models using differential equations has become crucial in predicting the evolution of viral diseases in a population in order to take preventive and curative measures. In December 2019, a novel variety of Coronavirus (SARS-CoV-2) was identified in Wuhan, Hubei Province, China, which causes a severe and potentially fatal respiratory syndrome. Since then, it has been declared a pandemic by the World Health Organization and has spread around the globe. A reaction−diffusion system is a mathematical model that describes the evolution of a phenomenon subjected to two processes: a reaction process, in which different substances are transformed, and a diffusion process, which causes their distribution in space. This article provides a mathematical study of the Susceptible, Exposed, Infected, Recovered, and Vaccinated population model of the COVID-19 pandemic using the bias of reaction−diffusion equations. Both local and global asymptotic stability conditions for the equilibria were determined using a Lyapunov function, and the nature of the stability was determined using the Routh−Hurwitz criterion. Furthermore, we consider the conditions for the existence and uniqueness of the model solution and show the spatial distribution of the model compartments when the basic reproduction rate R0<1 and R0>1. Thereafter, we conducted a sensitivity analysis to determine the most sensitive parameters in the proposed model. We demonstrate the model’s effectiveness by performing numerical simulations and investigating the impact of vaccination, together with the significance of spatial distribution parameters in the spread of COVID-19. The findings indicate that reducing contact with an infected person and increasing the proportion of susceptible people who receive high-efficacy vaccination will lessen the burden of COVID-19 in the population. Therefore, we offer to the public health policymakers a better understanding of COVID-19 management.