Analysis of novel fractional COVID-19 model with real-life data application

Behavioral game of quarantine during the monkeypox epidemic: Analysis of deterministic and fractional order approach

This work concerns the epidemiology of infectious diseases like monkeypox (mpox) in humans and animals. Our models examine transmission scenarios, including transmission dynamics between humans, animals, and both. We approach this using evolutionary game theory, specifically the intervention game-theoretical (IGT) framework, to study how human behavior can mitigate disease transmission without perfect vaccines and treatments. To do this, we use non-pharmaceutical intervention, namely the quarantine policy, which demonstrates the delayed effect of the epidemic. Additionally, we contemplate quarantine-based behavioral intervention policies in deterministic and fractional-order models to show behavioral impact in the context of the memory effect. Firstly, we extensively analyzed the model's positivity and boundness of the solution, reproduction number, disease-free and endemic equilibrium, possible stability, existence, concavity, and Ulam-Hyers stability for the fractional order. Subsequently, we proceeded to present a numerical analysis that effectively illustrates the repercussions of varying quarantine-related factors, information probability, and protection probability. We aimed to comprehensively examine the effects of non-pharmaceutical interventions on disease control, which we conveyed through line graphs and 2D heat maps. Our findings underscored the significant influence of strict quarantine measures and the protection of both humans and animals in mitigating disease outbreaks. These measures not only significantly curtailed the spread of the disease but also delayed the occurrence of the epidemic's peak. Conversely, when quarantine maintenance policies were implemented at lower rates and protection levels diminished, we observed contrasting outcomes that exacerbated the situation. Eventually, our analysis revealed the emergence of animal reservoirs in cases involving disease transmission between humans and animals.

A Mathematical Modelling and Analysis of COVID-19 Transmission Dynamics with Optimal Control Strategy

We proposed a deterministic compartmental model for the transmission dynamics of COVID-19 disease. We performed qualitative and quantitative analysis of the deterministic model concerning the local and global stability of the disease-free and endemic equilibrium points. We found that the disease-free equilibrium is locally asymptotically stable when the basic reproduction number is less than unity, while the endemic equilibrium point becomes locally asymptotically stable if the basic reproduction number is above unity. Furthermore, we derived the global stability of both the disease-free and endemic equilibriums of the system by constructing some Lyapunov functions. If $R_0\le 1$ , it is found that the disease-free equilibrium is globally asymptotically stable, while the endemic equilibrium point is globally asymptotically stable when $R_0>1$ . The numerical results of the general dynamics are in agreement with the theoretical solutions. We established the optimal control strategy by using Pontryagin’s maximum principle. We performed numerical simulations of the optimal control system to investigate the impact of implementing different combinations of optimal controls in controlling and eradicating COVID-19 disease. From this, a significant difference in the number of cases with and without controls was observed. We observed that the implementation of the combination of the control treatment rate, $u_2$ , and the control treatment rate, $u_3$ , has shown effective and efficient results in eradicating COVID-19 disease in the community relative to the other strategies.

A (2+1)-Dimensional Fractional-Order Epidemic Model with Pulse Jumps for Omicron COVID-19 Transmission and Its Numerical Simulation

In this paper, we would like to propose a (2+1)-dimensional fractional-order epidemic model with pulse jumps to describe the spread of the Omicron variant of COVID-19. The problem of identifying the involved parameters in the proposed model is reduced to a minimization problem of a quadratic objective function, based on the reported data. Moreover, we perform numerical simulation to study the effect of the parameters in diverse fractional-order cases. The number of undiscovered cases can be calculated precisely to assess the severity of the outbreak. The results by numerical simulation show that the degree of accuracy is higher than the classical epidemic models. The regular testing protocol is very important to find the undiscovered cases in the beginning of the outbreak.

Modeling the epidemic control measures in overcoming COVID-19 outbreaks: A fractional-order derivative approach

Novel coronavirus named SARS-CoV-2 is one of the global threads and uncertain challenges worldwide faced at present. It has stroke rapidly around the globe due to viral transmissibility, new variants (strains), and human unconsciousness. Lack of adequate and reliable vaccination and proper treatment, control measures such as self-protection, physical distancing, lockdown, quarantine, and isolation policy plays an essential role in controlling and reducing the pandemic. Decisions on enforcing various control measures should be determined based on a theoretical framework and real-data evidence. We deliberate a general mathematical control measures epidemic model consisting of lockdown, self-protection, physical distancing, quarantine, and isolation compartments. Then, we investigate the proposed model through Caputo fractional order derivative. Fixed point theory has been used to analyze the Caputo fractional-order derivative model's existence and uniqueness solutions, whereas the Adams-Bashforth-Moulton numerical scheme was applied for numerical simulation. Driven by extensive theoretical analysis and numerical simulation, this work further illuminates the substantial impact of various control measures.

A Novel Technique to Control the Accuracy of a Nonlinear Fractional Order Model of COVID-19: Application of the CESTAC Method and the CADNA Library

In this paper, a nonlinear fractional order model of COVID-19 is approximated. For this aim, at first we apply the Caputo–Fabrizio fractional derivative to model the usual form of the phenomenon. In order to show the existence of a solution, the Banach fixed point theorem and the Picard–Lindelof approach are used. Additionally, the stability analysis is discussed using the fixed point theorem. The model is approximated based on Indian data and using the homotopy analysis transform method (HATM), which is among the most famous, flexible and applicable semi-analytical methods. After that, the CESTAC (Controle et Estimation Stochastique des Arrondis de Calculs) method and the CADNA (Control of Accuracy and Debugging for Numerical Applications) library, which are based on discrete stochastic arithmetic (DSA), are applied to validate the numerical results of the HATM. Additionally, the stopping condition in the numerical algorithm is based on two successive approximations and the main theorem of the CESTAC method can aid us analytically to apply the new terminations criterion instead of the usual absolute error that we use in the floating-point arithmetic (FPA). Finding the optimal approximations and the optimal iteration of the HATM to solve the nonlinear fractional order model of COVID-19 are the main novelties of this study.

A new mathematical model of COVID-19 using real data from Pakistan

We propose a new mathematical model to investigate the recent outbreak of the coronavirus disease (COVID-19). The model is studied qualitatively using stability theory of differential equations and the basic reproductive number that represents an epidemic indicator is obtained from the largest eigenvalue of the next-generation matrix. The global asymptotic stability conditions for the disease free equilibrium are obtained. The real COVID-19 incidence data entries from 01 July, 2020 to 14 August, 2020 in the country of Pakistan are used for parameter estimation thereby getting fitted values for the biological parameters. Sensitivity analysis is performed in order to determine the most sensitive parameters in the proposed model. To view more features of the state variables in the proposed model, we perform numerical simulations by using different values of some essential parameters. Moreover, profiles of the reproduction number through contour plots have been biologically explained.