Mathematical analysis of an extended SEIR model of COVID-19 using the ABC-fractional operator

Estimation of the size of the COVID-19 pandemic using the epidemiological wavelength model: results from OECD countries

OBJECTIVES

This study aimed to simplify the previously developed epidemiological wavelength model and to expand the scope of the model with additional variables to estimate the magnitude of the COVID-19 pandemic. The applicability of the extended wavelength model was tested in Organisation for Economic Cooperation and Development (OECD) member countries.

STUDY DESIGN

The epidemiological wavelengths of OECD member countries for the years 2020, 2021 and 2022 were estimated comparatively, considering the cumulative number of COVID-19 cases.

METHODS

The size of the COVID-19 pandemic was estimated using the wavelength model. The scope of the wavelength model was expanded to include additional variables. The extended estimation model was improved by adding population density and human development index variables, in addition to the number of COVID-19 cases and number of days since the first case reported from the previous estimation model.

RESULTS

According to the findings obtained from the wavelength model, the country with the highest epidemiological wavelength for the years 2020, 2021 and 2022 was the United States (W_e = 29.96, W_e = 28.63 and W_e = 28.86, respectively), and the country with the lowest wavelength was Australia (W_e = 10.50, W_e = 13.14 and W_e = 18.44, respectively). The average wavelength score of OECD member countries was highest in 2022 (W_e = 24.32) and lowest in 2020 (W_e = 22.84). The differences in the periodic wavelengths of OECD countries were analysed with the dependent t-test for paired samples in two periods, 2020-2021 and 2021-2022. There was a statistically significant difference between wavelengths in the 2020-2021 and 2021-2022 groups (t(36) = -3.670; P < 0.001).

CONCLUSIONS

Decision-makers can use the extended wavelength model to easily follow the progress of the epidemic and to make quicker and more reliable decisions.

Modelling the impact of vaccination and environmental transmission on the dynamics of monkeypox virus under Caputo operator

In this study, we examine the impact of vaccination and environmental transmission on the dynamics of the monkeypox. We formulate and analyze a mathematical model for the dynamics of monkeypox virus transmission under Caputo fractional order. We obtain the basic reproduction number, the conditions for the local and global asymptotic stability for the disease-free equilibrium of the model. Under the Caputo fractional order, existence and uniqueness solutions have been determined using fixed point theorem. Numerical trajectories are obtained. Furthermore, we explored some of the sensitive parameters impact. Based on the trajectories, we hypothesised that the memory index or fractional order could use to control the Monkeypox virus transmission dynamics. We observed that if the proper vaccination is administrated, public health education is given, and practice like personal hygiene and proper disinfection spray, the infected individuals decreases.

Mathematical epidemiological modeling and analysis of monkeypox dynamism with non-pharmaceutical intervention using real data from United Kingdom

In this study, a mathematical model for studying the dynamics of monkeypox virus transmission with non-pharmaceutical intervention is created, examined, and simulated using real-time data. Positiveness, invariance, and boundedness of the solutions are thus examined as fundamental features of mathematical models. The equilibrium points and the prerequisites for their stability are achieved. The basic reproduction number and thus the virus transmission coefficient ℜ0 were determined and quantitatively used to study the global stability of the model's steady state. Furthermore, this study considered the sensitivity analysis of the parameters according to ℜ0. The most sensitive variables that are important for infection control are determined using the normalized forward sensitivity index. Data from the United Kingdom collected between May and August 2022, which also aid in demonstrating the usefulness and practical application of the model to the spread of the disease in the United Kingdom, were used. In addition, using the Caputo-Fabrizio operator, Krasnoselskii's fixed point theorem has been used to analyze the existence and uniqueness of the solutions to the suggested model. The numerical simulations are presented to assess the system dynamic behavior. More vulnerability was observed when monkeypox virus cases first appeared recently as a result of numerical calculations. We advise the policymakers to consider these elements to control monkeypox transmission. Based on these findings, we hypothesized that another control parameter could be the memory index or fractional order.

Global stability and analysing the sensitivity of parameters of a multiple-susceptible population model of SARS-CoV-2 emphasising vaccination drive

The study explores the dynamics of a COVID-19 epidemic in multiple susceptible populations, including the various stages of vaccination administration. In the model, there are eight human compartments: completely susceptible; susceptible with dose-1 vaccination; susceptible with dose-2 vaccination; susceptible with booster dose vaccination; exposed; infected with and without symptoms, and recovered compartments. The biological feasibility of the model is analysed. The threshold value, R 0 , is derived using the next-generation matrix. The stability analysis of the equilibrium points was performed locally and globally using the threshold parameter of the model. The conditions determining disease persistence is obtained. The model is subjected to sensitivity analysis, and the most sensitive parameters are identified. Also, MATLAB is used to verify the mathematical outcomes of the system's dynamic behaviour and suggests that necessary steps should be taken to keep the spread of the omicron variant infectious disease under control. The findings of this study could aid health officials in their efforts to combat the spread of COVID-19.

Analytical Study of Fractional Epidemic Model via Natural Transform Homotopy Analysis Method

In this study, we present a new general solution to a rational epidemiological mathematical model via a recent intelligent method called the natural transform homotopy analysis method (NTHAM), which combines two methods: the natural transform method (NTM) and homotopy analysis method (HAM). To assess the precision and the reliability of the present method, we compared the obtained results with those of the Laplace homotopy perturbation method (LHPM) as well as the q-homotopy analysis Sumudu transform method (q-HASTM), which revealed that the NTHAM is more reliable. The Caputo fractional derivative is employed. It not only gives initial conditions with obvious natural interpretation but is also bounded, meaning that there is no derivative of a constant. The results show that the proposed technique is superior in terms of simplicity, quality, accuracy, and stability and demonstrate the effectiveness of the rational technique under consideration.

A unified fixed point approach to study the existence of solutions for a class of fractional boundary value problems arising in a chemical graph theory

A theory of chemical graphs is a part of mathematical chemistry concerned with the effects of connectedness in chemical graphs. Several researchers have studied the solutions of fractional differential equations using the concept of star graphs. They employed star graphs because their technique requires a central node with links to adjacent vertices but no edges between nodes. The purpose of this paper is to extend the method’s range by introducing the concept of an octane graph, which is an essential organic compound having the formula C8H18. In this manner, we analyze a graph with vertices annotated by 0 or 1, which is influenced by the structure of the chemical substance octane, and formulate a fractional boundary value problem on each of the graph’s edges. We use the Schaefer and Krasnoselskii fixed point theorems to investigate the existence of solutions to the presented boundary value problems in the framework of the Caputo fractional derivative. Finally, two examples are provided to highlight the importance of our results in this area of study.

Comparative Dynamics of Delta and Omicron SARS-CoV-2 Variants across and between California and Mexico

Evolutionary analysis using viral sequence data can elucidate the epidemiology of transmission. Using publicly available SARS-CoV-2 sequence and epidemiological data, we developed discrete phylogeographic models to interrogate the emergence and dispersal of the Delta and Omicron variants in 2021 between and across California and Mexico. External introductions of Delta and Omicron in the region peaked in early July (2021-07-10 [95% CI: 2021-04-20, 2021-11-01]) and mid-December (2021-12-15 [95% CI: 2021-11-14, 2022-01-09]), respectively, 3 months and 2 weeks after first detection. These repeated introductions coincided with domestic migration events with no evidence of a unique transmission hub. The spread of Omicron was most consistent with gravity centric patterns within Mexico. While cross-border events accounted for only 5.1% [95% CI: 4.3-6] of all Delta migration events, they accounted for 20.6% [95% CI: 12.4-29] of Omicron movements, paralleling the increase in international travel observed in late 2021. Our investigations of the Delta and Omicron epidemics in the California/Mexico region illustrate the complex interplay and the multiplicity of viral and structural factors that need to be considered to limit viral spread, even as vaccination is reducing disease burden. Understanding viral transmission patterns may help intra-governmental responses to viral epidemics.

On Caputo–Katugampola Fractional Stochastic Differential Equation

We consider the following stochastic fractional differential equation CD0+α,ρφ(t)=κϑ(t,φ(t))w˙(t), 0<t≤T, where φ(0)=φ0 is the initial function, CD0+α,ρ is the Caputo–Katugampola fractional differential operator of orders 0<α≤1,ρ>0, the function ϑ:[0,T]×R→R is Lipschitz continuous on the second variable, w˙(t) denotes the generalized derivative of the Wiener process w(t) and κ>0 represents the noise level. The main result of the paper focuses on the energy growth bound and the asymptotic behaviour of the random solution. Furthermore, we employ Banach fixed point theorem to establish the existence and uniqueness result of the mild solution.