Mathematical modeling and analysis of the SARS-Cov-2 disease with reinfection

Assessing the impact of disease incidence and immunization on the resilience of complex networks during epidemics

Disease severity through an immunized population ensconced on a physical network topology is a key technique for preventing epidemic spreading. Its influence can be quantified by adjusting the common (basic) methodology for analyzing the percolation and connectivity of contact networks. Stochastic spreading properties are difficult to express, and physical networks significantly influence them. Visualizing physical networks is crucial for studying and intervening in disease transmission. The multi-agent simulation method is useful for measuring randomness, and this study explores stochastic characteristics of epidemic transmission in various homogeneous and heterogeneous networks. This work thoroughly explores stochastic characteristics of epidemic propagation in homogeneous and heterogeneous networks through extensive theoretical analysis (positivity and boundedness of solutions, disease-free equilibrium point, basic reproduction number, endemic equilibrium point, stability analysis) and multi-agent simulation approach using the Gilespie algorithm. Results show that Ring and Lattice networks have small stochastic variations in the ultimate epidemic size, while BA-SF networks have disease transmission starting before the threshold value. The theoretical and deterministic aftermaths strongly agree with multi-agent simulations (MAS) and could shed light on various multi-dynamic spreading process applications. The study also proposes a novel concept of void nodes, Empty nodes and disease severity, which reduces the incidence of contagious diseases through immunization and topologies.

K1K2NN: A novel multi-label classification approach based on neighbors for predicting COVID-19 drug side effects

COVID-19, a novel ailment, has received comparatively fewer drugs for its treatment. Side Effects (SE) of a COVID-19 drug could cause long-term health issues. Hence, SE prediction is essential in COVID-19 drug development. Efficient models are also needed to predict COVID-19 drug SE since most existing research has proposed many classifiers to predict SE for diseases other than COVID-19. This work proposes a novel classifier based on neighbors named K1 K2 Nearest Neighbors (K1K2NN) to predict the SE of the COVID-19 drug from 17 molecules' descriptors and the chemical 1D structure of the drugs. The model is implemented based on the proposition that chemically similar drugs may be assigned similar drug SE, and co-occurring SE may be assigned to chemically similar drugs. The K1K2NN model chooses the first K1 neighbors to the test drug sample by calculating its similarity with the train drug samples. It then assigns the test sample with the SE label having the majority count on the SE labels of these K1 neighbor drugs obtained through a voting mechanism. The model then calculates the SE-SE similarity using the Jaccard similarity measure from the SE co-occurrence values. Finally, the model chooses the most similar K2 SE neighbors for those SE determined by the K1 neighbor drugs and assigns these SE to that test drug sample. The proposed K1K2NN model has showcased promising performance with the highest accuracy of 97.53% on chemical 1D drug structure and outperforms the state-of-the-art multi-label classifiers. In addition, we demonstrate the successful application of the proposed model on gene expression signature datasets, which aided in evaluating its performance and confirming its accuracy and robustness.

[Formula: see text] model for analyzing [Formula: see text]-19 pandemic process via [Formula: see text]-Caputo fractional derivative and numerical simulation

The objective of this study is to develop the [Formula: see text] epidemic model for [Formula: see text]-[Formula: see text] utilizing the [Formula: see text]-Caputo fractional derivative. The reproduction number ([Formula: see text]) is calculated utilizing the next generation matrix method. The equilibrium points of the model are computed, and both the local and global stability of the disease-free equilibrium point are demonstrated. Sensitivity analysis is discussed to describe the importance of the parameters and to demonstrate the existence of a unique solution for the model by applying a fixed point theorem. Utilizing the fractional Euler procedure, an approximate solution to the model is obtained. To study the transmission dynamics of infection, numerical simulations are conducted by using MatLab. Both numerical methods and simulations can provide valuable insights into the behavior of the system and help in understanding the existence and properties of solutions. By placing the values [Formula: see text], [Formula: see text] and [Formula: see text] instead of [Formula: see text], the derivatives of the Caputo and Caputo-Hadamard and Katugampola appear, respectively, to compare the results of each with real data. Besides, these simulations specifically with different fractional orders to examine the transmission dynamics. At the end, we come to the conclusion that the simulation utilizing Caputo derivative with the order of 0.95 shows the prevalence of the disease better. Our results are new which provide a good contribution to the current research on this field of research.

Multi-weight susceptible-infected model for predicting COVID-19 in China

The mutant strains of COVID-19 caused a global explosion of infections, including many cities of China. In 2020, a hybrid AI model was proposed by Zheng et al., which accurately predicted the epidemic in Wuhan. As the main part of the hybrid AI model, ISI method makes two important assumptions to avoid over-fitting. However, the assumptions cannot be effectively applied to new mutant strains. In this paper, a more general method, named the multi-weight susceptible-infected model (MSI) is proposed to predict COVID-19 in Chinese Mainland. First, a Gaussian pre-processing method is proposed to solve the problem of data fluctuation based on the quantity consistency of cumulative infection number and the trend consistency of daily infection number. Then, we improve the model from two aspects: changing the grouped multi-parameter strategy to the multi-weight strategy, and removing the restriction of weight distribution of viral infectivity. Experiments on the outbreaks in many places in China from the end of 2021 to May 2022 show that, in China, an individual infected by Delta or Omicron strains of SARS-CoV-2 can infect others within 3-4 days after he/she got infected. Especially, the proposed method effectively predicts the trend of the epidemics in Xi'an, Tianjin, Henan, and Shanghai from December 2021 to May 2022.

Mathematical Model of COVID-19 Pandemic with Double Dose Vaccination

This paper is concerned with the formulation and analysis of an epidemic model of COVID-19 governed by an eight-dimensional system of ordinary differential equations, by taking into account the first dose and the second dose of vaccinated individuals in the population. The developed model is analyzed and the threshold quantity known as the control reproduction number [Formula: see text] is obtained. We investigate the equilibrium stability of the system, and the COVID-free equilibrium is said to be locally asymptotically stable when the control reproduction number is less than unity, and unstable otherwise. Using the least-squares method, the model is calibrated based on the cumulative number of COVID-19 reported cases and available information about the mass vaccine administration in Malaysia between the 24th of February 2021 and February 2022. Following the model fitting and estimation of the parameter values, a global sensitivity analysis was performed by using the Partial Rank Correlation Coefficient (PRCC) to determine the most influential parameters on the threshold quantities. The result shows that the effective transmission rate [Formula: see text], the rate of first vaccine dose [Formula: see text], the second dose vaccination rate [Formula: see text] and the recovery rate due to the second dose of vaccination [Formula: see text] are the most influential of all the model parameters. We further investigate the impact of these parameters by performing a numerical simulation on the developed COVID-19 model. The result of the study shows that adhering to the preventive measures has a huge impact on reducing the spread of the disease in the population. Particularly, an increase in both the first and second dose vaccination rates reduces the number of infected individuals, thus reducing the disease burden in the population.

Indirect Virus Transmission via Fomites Can Counteract Lock-Down Effectiveness

The spread of severe acute respiratory syndrome-coronavirus-2 (SARS-CoV-2) has raised major health policy questions. Direct transmission via respiratory droplets seems to be the dominant route of its transmission. However, indirect transmission via shared contact of contaminated objects may also occur. The contribution of each transmission route to epidemic spread might change during lock-down scenarios. Here, we simulate viral spread of an abstract epidemic considering both routes of transmission by use of a stochastic, agent-based SEIR model. We show that efficient contact tracing (CT) at a high level of incidence can stabilize daily cases independently of the transmission route long before effects of herd immunity become relevant. CT efficacy depends on the fraction of cases that do not show symptoms. Combining CT with lock-down scenarios that reduce agent mobility lowers the incidence for exclusive direct transmission scenarios and can even eradicate the epidemic. However, even for small fractions of indirect transmission, such lockdowns can impede CT efficacy and increase case numbers. These counterproductive effects can be reduced by applying measures that favor distancing over reduced mobility. In summary, we show that the efficacy of lock-downs depends on the transmission route. Our results point to the particular importance of hygiene measures during mobility lock-downs.

Assessing the potential impact of COVID-19 Omicron variant: Insight through a fractional piecewise model

We consider a new mathematical model for the COVID-19 disease with Omicron variant mutation. We formulate in details the modeling of the problem with omicron variant in classical differential equations. We use the definition of the Atangana-Baleanu derivative and obtain the extended fractional version of the omicron model. We study mathematical results for the fractional model and show the local asymptotical stability of the model for infection-free case ifR 0 < 1 . We show the global asymptotically stable of the model for the disease free case whenR 0 ≤ 1 . We show the existence and uniqueness of solution of the fractional model. We further extend the fractional order model into piecewise differential equation system and give a numerical algorithm for their numerical simulation. We consider the real cases of COVID-19 in South Africa of the third wave March 2021-Sep 2021 and estimate the model parameters and getR 0 ≈ 1 . 4004 . The real parameters values are used to show the graphical results for the fractional and piecewise model.