Fractional modeling and optimal control strategies for mutated COVID‐19 pandemic

As the COVID‐19 continues to mutate, the number of infected people is increasing dramatically, and the vaccine is not enough to fight the mutated strain. In this paper, a SEIR‐type fractional model with reinfection and vaccine inefficacy is proposed, which can successfully capture the mutated COVID‐19 pandemic. The existence, uniqueness, boundedness, and nonnegativeness of the fractional model are derived. Based on the basic reproduction number R0$$ {R}_0 $$, locally stability and globally stability are analyzed. The sensitivity analysis evaluate the influence of each parameter on the R0$$ {R}_0 $$ and rank key epidemiological parameters. Finally, the necessary conditions for implementing fractional optimal control are obtained by Pontryagin's maximum principle, and the corresponding optimal solutions are derived for mitigation COVID‐19 transmission. The numerical results show that humans will coexist with COVID‐19 for a long time under the current control strategy. Furthermore, it is particularly important to develop new vaccines with higher protection rates. [ FROM AUTHOR] Copyright of Mathematical Methods in the Applied Sciences is the property of John Wiley & Sons, Inc. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)

Multiple models for outbreak decision support in the face of uncertainty.

Policymakers must make management decisions despite incomplete knowledge and conflicting model projections. Little guidance exists for the rapid, representative, and unbiased collection of policy-relevant scientific input from independent modeling teams. Integrating approaches from decision analysis, expert judgment, and model aggregation, we convened multiple modeling teams to evaluate COVID-19 reopening strategies for a mid-sized United States county early in the pandemic. Projections from seventeen distinct models were inconsistent in magnitude but highly consistent in ranking interventions. The 6-mo-ahead aggregate projections were well in line with observed outbreaks in mid-sized US counties. The aggregate results showed that up to half the population could be infected with full workplace reopening, while workplace restrictions reduced median cumulative infections by 82%. Rankings of interventions were consistent across public health objectives, but there was a strong trade-off between public health outcomes and duration of workplace closures, and no win-win intermediate reopening strategies were identified. Between-model variation was high; the aggregate results thus provide valuable risk quantification for decision making. This approach can be applied to the evaluation of management interventions in any setting where models are used to inform decision making. This case study demonstrated the utility of our approach and was one of several multimodel efforts that laid the groundwork for the COVID-19 Scenario Modeling Hub, which has provided multiple rounds of real-time scenario projections for situational awareness and decision making to the Centers for Disease Control and Prevention since December 2020.

The effect mitigation measures for COVID-19 by a fractional-order SEIHRDP model with individuals migration.

In this paper, the generalized SEIHRDP (susceptible-exposed-infective-hospitalized-recovered-death-insusceptible) fractional-order epidemic model is established with individual migration. Firstly, the global properties of the proposed system are studied. Particularly, the sensitivity of parameters to the basic reproduction number are analyzed both theoretically and numerically. Secondly, according to the real data in India and Brazil, it can all be concluded that the bilinear incidence rate has a better description of COVID-19 transmission. Meanwhile, multi-peak situation is considered in China, and it is shown that the proposed system can better predict the next peak. Finally, taking individual migration between Los Angeles and New York as an example, the spread of COVID-19 between cities can be effectively controlled by limiting individual movement, enhancing nucleic acid testing and reducing individual contact.

Is fractional-order chaos theory the new tool to model chaotic pandemics as Covid-19?

The deadly outbreak of the second wave of Covid-19, especially in worst hit lower-middle-income countries like India, and the drastic rise of another growing epidemic of Mucormycosis, call for an efficient mathematical tool to model pandemics, analyse their course of outbreak and help in adopting quicker control strategies to converge to an infection-free equilibrium. This review paper on prominent pandemics reveals that their dispersion is chaotic in nature having long-range memory effects and features which the existing integer-order models fail to capture. This paper thus puts forward the use of fractional-order (FO) chaos theory that has memory capacity and hereditary properties, as a potential tool to model the pandemics with more accuracy and closeness to their real physical dynamics. We investigate eight FO models of Bombay plague, Cancer and Covid-19 pandemics through phase portraits, time series, Lyapunov exponents and bifurcation analysis. FO controllers (FOCs) on the concepts of fuzzy logic, adaptive sliding mode and active backstepping control are designed to stabilise chaos. Also, FOCs based on adaptive sliding mode and active backstepping synchronisation are designed to synchronise a chaotic epidemic with a non-chaotic one, to mitigate the unpredictability due to chaos during transmission. It is found that severity and complexity of the models increase as the memory fades, indicating that FO can be used as a crucial parameter to analyse the progression of a pandemic. To sum it up, this paper will help researchers to have an overview of using fractional calculus in modelling pandemics more precisely and also to approximate, choose, stabilise and synchronise the chaos control parameter that will eliminate the extreme sensitivity and irregularity of the models.

Stability analysis of a nonlocal SIHRDP epidemic model with memory effects.

The prediction and control of COVID-19 is critical for ending this pandemic. In this paper, a nonlocal SIHRDP (S-susceptible class, I-infective class (infected but not hospitalized), H-hospitalized class, R-recovered class, D-death class and P-isolated class) epidemic model with long memory is proposed to describe the multi-wave peaks for the spread of COVID-19. Based on the basic reproduction number R 0 , which is completely controlled by fractional order, the stability of the proposed system is studied. Furthermore, the numerical simulation is conducted to gauge the performance of the proposed model. The results on Hunan, China, reveal that R 0 < 1 suggests that the disease-free equilibrium point is globally asymptotically stable. Likewise, the situation of the multi-peak case in China is presented, and it is clear that the nonlocal epidemic system has a superior fitting effect than the classical model. Finally an adaptive impulsive vaccination is introduced based on the proposed system. Then employing the real data of France, India, the USA and Argentina, parameters identification and short-term forecasts are carried out to verify the effectiveness of the proposed model in describing the case of multiple peaks. Moreover, the implementation of vaccine control is expected once the hospitalized population exceeds 20 % of the total population. Numerical results of France, Indian, the USA and Argentina shed light on the varied effect of vaccine control in different countries. According to the vaccine control imposed on France, no obvious effect is observed even consider reducing human contact. As for India, although there will be a temporary increase in hospitalized admissions after execution of vaccination control, COVID-19 will eventually disappear. Results on the USA have seen most significant effect of vaccine control, the number of hospitalized individuals drops off and the disease is eventually eradicated. In contrast to the USA, vaccine control in Argentina has also been very effective, but COVID-19 cannot be completely eradicated.

Stability analysis of a nonlocal SIHRDP epidemic model with memory effects

The prediction and control of COVID-19 is critical for ending this pandemic. In this paper, a nonlocal SIHRDP (S-susceptible class, I-infective class (infected but not hospitalized), H-hospitalized class, R-recovered class, D-death class and P-isolated class) epidemic model with long memory is proposed to describe the multi-wave peaks for the spread of COVID-19. Based on the basic reproduction number

Qualitative and quantitative analysis of the COVID-19 pandemic by a two-side fractional-order compartmental model☆

Global efforts are focused on discussing effective measures for minimizing the impact of COVID-19 on global community. It is clear that the ongoing pandemic of this virus caused an immense threat to public health and economic development. Mathematical models with real data simulations are powerful tools that can identify key factors of pandemic and improve control or mitigation strategies. Compared with integer-order and left-hand side fractional models, two-side fractional models can better capture the state of pandemic spreading. In this paper, two-side fractional models are first proposed to qualitative and quantitative analysis of the COVID-19 pandemic. A basic framework are given for the prediction and analysis of infectious diseases by these types of models. By means of asymptotic stability analysis of disease-free and endemic equilibrium points, basic reproduction number

RLIM: a recursive and latent infection model for the prediction of US COVID-19 infections and turning points.

Initially found in Hubei, Wuhan, and identified as a novel virus of the coronavirus family by the WHO, COVID-19 has spread worldwide at exponential speed, causing millions of deaths and public fear. Currently, the USA, India, Brazil, and other parts of the world are experiencing a secondary wave of COVID-19. However, the medical, mathematical, and pharmaceutical aspects of its transmission, incubation, and recovery processes are still unclear. The classical susceptible-infected-recovered model has limitations in describing the dynamic behavior of COVID-19. Hence, it is necessary to introduce a recursive, latent model to predict the number of future COVID-19 infection cases in the USA. In this article, a dynamic recursive and latent infection model (RLIM) based on the classical SEIR model is proposed to predict the number of COVID-19 infections. Given COVID-19 infection and recovery data for a certain period, the RLIM is able to fit current values and produce an optimal set of parameters with a minimum error rate according to actual reported numbers. With these optimal parameters assigned, the RLIM model then becomes able to produce predictions of infection numbers within a certain period. To locate the turning point of COVID-19 transmission, an initial value for the secondary infection rate is given to the RLIM algorithm for calculation. RLIM will then calculate the secondary infection rates of a continuous time series with an iterative search strategy to speed up the convergence of the prediction outcomes and minimize the maximum square errors. Compared with other forecast algorithms, RLIM is able to adapt the COVID-19 infection curve faster and more accurately and, more importantly, provides a way to identify the turning point in virus transmission by searching for the equilibrium between recoveries and new infections. Simulations of four US states show that with the secondary infection rate ω initially set to 0.5 within the selected latent period of 14 days, RLIM is able to minimize this value at 0.07 and reach an equilibrium condition. A successful forecast is generated using New York state's COVID-19 transmission, in which a turning point is predicted to emerge on January 31, 2021. Supplementary Information: The online version contains supplementary material available at 10.1007/s11071-021-06520-1.

Forecast analysis of the epidemics trend of COVID-19 in the USA by a generalized fractional-order SEIR model.

In this paper, a generalized fractional-order SEIR model is proposed, denoted by SEIQRP model, which divided the population into susceptible, exposed, infectious, quarantined, recovered and insusceptible individuals and has a basic guiding significance for the prediction of the possible outbreak of infectious diseases like the coronavirus disease in 2019 (COVID-19) and other insect diseases in the future. Firstly, some qualitative properties of the model are analyzed. The basic reproduction number R 0 is derived. When R 0 < 1 , the disease-free equilibrium point is unique and locally asymptotically stable. When R 0 > 1 , the endemic equilibrium point is also unique. Furthermore, some conditions are established to ensure the local asymptotic stability of disease-free and endemic equilibrium points. The trend of COVID-19 spread in the USA is predicted. Considering the influence of the individual behavior and government mitigation measurement, a modified SEIQRP model is proposed, defined as SEIQRPD model, which is divided the population into susceptible, exposed, infectious, quarantined, recovered, insusceptible and dead individuals. According to the real data of the USA, it is found that our improved model has a better prediction ability for the epidemic trend in the next two weeks. Hence, the epidemic trend of the USA in the next two weeks is investigated, and the peak of isolated cases is predicted. The modified SEIQRP model successfully capture the development process of COVID-19, which provides an important reference for understanding the trend of the outbreak.

A fractional-order SEIHDR model for COVID-19 with inter-city networked coupling effects.

In the end of 2019, a new type of coronavirus first appeared in Wuhan. Through the real-data of COVID-19 from January 23 to March 18, 2020, this paper proposes a fractional SEIHDR model based on the coupling effect of inter-city networks. At the same time, the proposed model considers the mortality rates (exposure, infection and hospitalization) and the infectivity of individuals during the incubation period. By applying the least squares method and prediction-correction method, the proposed system is fitted and predicted based on the real-data from January 23 to March 18 - m where m represents predict days. Compared with the integer system, the non-network fractional model has been verified and can better fit the data of Beijing, Shanghai, Wuhan and Huanggang. Compared with the no-network case, results show that the proposed system with inter-city network may not be able to better describe the spread of disease in China due to the lock and isolation measures, but this may have a significant impact on countries that has no closure measures. Meanwhile, the proposed model is more suitable for the data of Japan, the USA from January 22 and February 1 to April 16 and Italy from February 24 to March 31. Then, the proposed fractional model can also predict the peak of diagnosis. Furthermore, the existence, uniqueness and boundedness of a nonnegative solution are considered in the proposed system. Afterward, the disease-free equilibrium point is locally asymptotically stable when the basic reproduction number R 0 ≤ 1 , which provide a theoretical basis for the future control of COVID-19.