Mathematical Modeling and backward bifurcation in monkeypox disease under real observed data.

We propose a mathematical model to analyze the monkeypox disease in the context of the known cases of the USA epidemic. We formulate the model and obtain their essential properties. The equilibrium points are found and their stability is demonstrated. We prove that the model is locally asymptotical stable (LAS) at disease free equilibrium (DFE) under R0<1. The presence of an endemic equilibrium is demonstrated, and the phenomena of backward bifurcation is discovered in the monkeypox disease model. In the monkeypox infectious disease model, the parameters that lead to backward bifurcation are θr, τ1, and ξr. When R0>1, we determine the model's global asymptotical stability (GAS). To parameterize the model using real data, we obtain the real value of the model parameters and compute R1=0.5905. Additionally, we do a sensitivity analysis on the parameters in R0. We conclude by presenting specific numerical findings.

A Mathematical Model of Vaccinations Using New Fractional Order Derivative.

Purpose: This paper studies a simple SVIR (susceptible, vaccinated, infected, recovered) type of model to investigate the coronavirus's dynamics in Saudi Arabia with the recent cases of the coronavirus. Our purpose is to investigate coronavirus cases in Saudi Arabia and to predict the early eliminations as well as future case predictions. The impact of vaccinations on COVID-19 is also analyzed. Methods: We consider the recently introduced fractional derivative known as the generalized Hattaf fractional derivative to extend our COVID-19 model. To obtain the fitted and estimated values of the parameters, we consider the nonlinear least square fitting method. We present the numerical scheme using the newly introduced fractional operator for the graphical solution of the generalized fractional differential equation in the sense of the Hattaf fractional derivative. Mathematical as well as numerical aspects of the model are investigated. Results: The local stability of the model at disease-free equilibrium is shown. Further, we consider real cases from Saudi Arabia since 1 May−4 August 2022, to parameterize the model and obtain the basic reproduction number R0v≈2.92. Further, we find the equilibrium point of the endemic state and observe the possibility of the backward bifurcation for the model and present their results. We present the global stability of the model at the endemic case, which we found to be globally asymptotically stable when R0v>1. Conclusion: The simulation results using the recently introduced scheme are obtained and discussed in detail. We present graphical results with different fractional orders and found that when the order is decreased, the number of cases decreases. The sensitive parameters indicate that future infected cases decrease faster if face masks, social distancing, vaccination, etc., are effective.

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 if R 0 < 1 . We show the global asymptotically stable of the model for the disease free case when R 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 get R 0 ≈ 1 . 4004 . The real parameters values are used to show the graphical results for the fractional and piecewise model.

A mathematical model for SARS-CoV-2 in variable-order fractional derivative.

A new coronavirus mathematical with hospitalization is considered with the consideration of the real cases from March 06, 2021 till the end of April 30, 2021. The essential mathematical results for the model are presented. We show the model stability when R 0 < 1 in the absence of infection. We show that the system is stable locally asymptotically when R 0 < 1 at infection free state. We also show that the system is globally asymptotically stable in the disease absence when R 0 < 1 . Data have been used to fit accurately to the model and found the estimated basic reproduction number to be R 0 = 1.2036 . Some graphical results for the effective parameters are drawn for the disease elimination. In addition, a variable-order model is introduced, and so as to handle the outbreak effectively and efficiently, a genetic algorithm is used to produce high-quality control. Numerical simulations clearly show that decision-makers may develop helpful and practical strategies to manage future waves by implementing optimum policies.