A caputo fractional order epidemic model for evaluating the effectiveness of high-risk quarantine and vaccination strategies on the spread of COVID-19.

The recent global Coronavirus disease (COVID-19) threat to the human race requires research on preventing its reemergence without affecting socio-economic factors. This study proposes a fractional-order mathematical model to analyze the impact of high-risk quarantine and vaccination on COVID-19 transmission. The proposed model is used to analyze real-life COVID-19 data to develop and analyze the solutions and their feasibilities. Numerical simulations study the high-risk quarantine and vaccination strategies and show that both strategies effectively reduce the virus prevalence, but their combined application is more effective. We also demonstrate that their effectiveness varies with the volatile rate of change in the system's distribution. The results are analyzed using Caputo fractional order and presented graphically and extensively analyzed to highlight potent ways of curbing the virus.

Analysis and Simulation of Mathematical Model of COVID-19 Incorporated with Vaccination and Media Induced Fear

COVID-19 pandemic is now increasing concern to authorities and public health officials. The study is aimed to investigate the impact of vaccination in the absence of media induced fear. In this research, analysis and simulation of a mathematical model of COVID-19 incorporated with media induced fear and vaccination was made, the total population is divided into 5 sub-population classes;Susceptible, Exposed, Infected, Quarantine and Recovery. The disease free and the endemic equilibrium of the model were carried out and the basic reproduction number was obtained using the next generation matrix. The stability analysis of the model was done and it was ascertained that the disease free equilibrium of the biological model is stable. Due to its efficiency and accuracy in handling nonlinear coupled ordinary differential equations, the homotopy perturbation method is applied to obtain the approximate solution of the mathematical model and the obtained results was simulated using the computation software Maple 18 to study the impact of vaccination in each compartment of the model when the media induced fear. The outcome of the simulation process were presented graphically and interpreted accordingly and it was discovered that in eradicating the spread of COVID-19 in a society where there is no fear, vaccination is an alternative and better measure. © 2023, Walailak University. All rights reserved.

Conceptual analysis of the combined effects of vaccination, therapeutic actions, and human subjection to physical constraint in reducing the prevalence of COVID-19 using the homotopy perturbation method.

Background: The COVID-19 pandemic has put the world's survival in jeopardy. Although the virus has been contained in certain parts of the world after causing so much grief, the risk of it emerging in the future should not be overlooked because its existence cannot be shown to be completely eradicated. Results: This study investigates the impact of vaccination, therapeutic actions, and compliance rate of individuals to physical limitations in a newly developed SEIQR mathematical model of COVID-19. A qualitative investigation was conducted on the mathematical model, which included validating its positivity, existence, uniqueness, and boundedness. The disease-free and endemic equilibria were found, and the basic reproduction number was derived and utilized to examine the mathematical model's local and global stability. The mathematical model's sensitivity index was calculated equally, and the homotopy perturbation method was utilized to derive the estimated result of each compartment of the model. Numerical simulation carried out using Maple 18 software reveals that the COVID-19 virus's prevalence might be lowered if the actions proposed in this study are applied. Conclusion: It is the collective responsibility of all individuals to fight for the survival of the human race against COVID-19. We urged that all persons, including the government, researchers, and health-care personnel, use the findings of this research to remove the presence of the dangerous COVID-19 virus.

Approximate solution for the nonlinear fractional order mathematical model

Health organizations are working to reduce the outbreak of infectious diseases with the help of several techniques so that exposure to infectious diseases can be minimized. Mathematics is also an important tool in the study of epidemiology. Mathematical modeling presents mathematical expressions and offers a clear view of how variables and interactions between variables affect the results. The objective of this work is to solve the mathematical model of MERS-CoV with the simplest, easiest and most proficient techniques considering the fractional Caputo derivative. To acquire the approximate solution, we apply the Adomian decomposition technique coupled with the Laplace transformation. Also, a convergence analysis of the method is conducted. For the comparison of the obtained results, we apply another semi-analytic technique called the homotopy perturbation method and compare the results. We also investigate the positivity and boundedness of the selected model. The dynamics and solution of the MERS-CoV compartmental mathematical fractional order model and its transmission between the human populace and the camels are investigated graphically for theta = 0.5, 0.7, 0.9, 1.0. It is seen that the recommended schemes are proficient and powerful for the given model considering the fractional Caputo derivative.

Investigation of a time-fractional COVID-19 mathematical model with singular kernel.

We investigate the fractional dynamics of a coronavirus mathematical model under a Caputo derivative. The Laplace-Adomian decomposition and Homotopy perturbation techniques are applied to attain the approximate series solutions of the considered system. The existence and uniqueness solution of the system are presented by using the Banach fixed-point theorem. Ulam-Hyers-type stability is investigated for the proposed model. The obtained approximations are compared with numerical simulations of the proposed model as well as associated real data for numerous fractional-orders. The results reveal a good comparison between the numerical simulations versus approximations of the considered model. Further, one can see good agreements are obtained as compared to the classical integer order.

Stability analysis and optimal control of Covid-19 pandemic SEIQR fractional mathematical model with harmonic mean type incidence rate and treatment.

In the present work, we investigated the transmission dynamics of fractional order SARS-CoV-2 mathematical model with the help of Susceptible S ( t ) , Exposed E ( t ) , Infected I ( t ) , Quarantine Q ( t ) , and Recovered R ( t ) . The aims of this work is to investigate the stability and optimal control of the concerned mathematical model for both local and global stability by third additive compound matrix approach and we also obtained threshold value by the next generation approach. The author's visualized the desired results graphically. We also control each of the population of underlying model with control variables by optimal control strategies with Pontryagin's maximum Principle and obtained the desired numerical results by using the homotopy perturbation method. The proposed model is locally asymptotically unstable, while stable globally asymptotically on endemic equilibrium. We also explored the results graphically in numerical section for better understanding of transmission dynamics.