Review of fractional epidemic models

Nonlocal models in biology and life sciences: Sources, developments, and applications

Mathematical modeling is one of the fundamental techniques for understanding biophysical mechanisms in developmental biology. It helps researchers to analyze complex physiological processes and connect like a bridge between theoretical and experimental observations. Various groups of mathematical models have been studied to analyze these processes, and the nonlocal models are one of them. Nonlocality is important in realistic mathematical models of physical and biological systems when local models fail to capture the essential dynamics and interactions that occur over a range of distances (e.g., cell-cell, cell-tissue adhesions, neural networks, the spread of diseases, intra-specific competition, nanobeams, etc.). This review illustrates different nonlocal mathematical models applied to biology and life sciences. The major focus has been given to sources, developments, and applications of such models. Among other things, a systematic discussion has been provided for the conditions of pattern formations in biological systems of population dynamics. Special attention has also been given to nonlocal interactions on networks, network coupling and integration, including brain dynamics models that provide an important tool to understand neurodegenerative diseases better. In addition, we have discussed nonlocal modeling approaches for cancer stem cells and tumor cells that are widely applied in the cell migration processes, growth, and avascular tumors in any organ. Furthermore, the discussed nonlocal continuum models can go sufficiently smaller scales, including nanotechnology, where classical local models often fail to capture the complexities of nanoscale interactions, applied to build biosensors to sense biomaterial and its concentration. Piezoelectric and other smart materials are among them, and these devices are becoming increasingly important in the digital and physical world that is intrinsically interconnected with biological systems. Additionally, we have reviewed a nonlocal theory of peridynamics, which deals with continuous and discrete media and applies to model the relationship between fracture and healing in cortical bone, tissue growth and shrinkage, and other areas increasingly important in biomedical and bioengineering applications. Finally, we provided a comprehensive summary of emerging trends and highlighted future directions in this rapidly expanding field.

Global infectious disease early warning models: An updated review and lessons from the COVID-19 pandemic

An early warning model for infectious diseases is a crucial tool for timely monitoring, prevention, and control of disease outbreaks. The integration of diverse multi-source data using big data and artificial intelligence techniques has emerged as a key approach in advancing these early warning models. This paper presents a comprehensive review of widely utilized early warning models for infectious diseases around the globe. Unlike previous review studies, this review encompasses newly developed approaches such as the combined model and Hawkes model after the COVID-19 pandemic, providing a thorough evaluation of their current application status and development prospects for the first time. These models not only rely on conventional surveillance data but also incorporate information from various sources. We aim to provide valuable insights for enhancing global infectious disease surveillance and early warning systems, as well as informing future research in this field, by summarizing the underlying modeling concepts, algorithms, and application scenarios of each model.

Dynamic analysis of a Caputo fractional-order SEIR model with a general incidence rate

This study develops a fractional-order SEIR model with asymptomatic infections and memory effects, introducing a generalized incidence rate to better reflect the nonlinear characteristics of transmission. The Caputo fractional derivative is used to capture memory effects and non-locality, dynamically adjusting the order to adapt to complex processes, improving accuracy and fitting. Based on Lyapunov functions, we rigorously prove that the disease-free equilibrium is globally asymptotically stable whenR 0 < 1 , and the endemic equilibrium is globally stable whenR 0 > 1 . Sensitivity analysis identifies key factors influencing disease spread and control. Numerical simulations validate the theoretical results and demonstrate the advantages of the fractional-order model in capturing epidemic dynamics, which traditional integer-order models fail to capture such dynamics. This study contributes to more accurate disease modeling and provides insights for optimizing control strategies for complex infectious diseases.

Global dynamics of a fractional order SIRS epidemic model by the way of generalized continuous time random walk

In this paper, we propose a novel fractional-order SIRS (frSIRS) model incorporating infection forces under intervention strategies, developed through the framework of generalized continuous-time random walks. The model is first transformed into a system of Volterra integral equations to identify the disease-free equilibrium (DFE) state and the endemic equilibrium (EE) state. Additionally, we introduce a new F V - 1 method for calculating the basic reproduction number R 0 . Through several examples, we demonstrate the broad applicability of this F V - 1 method in determining R 0 for fractional-order epidemic models. Next, we establish that R 0 serves as a critical threshold governing the model's dynamics: ifR 0 < 1 , the unique DFE is globally asymptotically stable; while ifR 0 > 1 , the unique EE is globally asymptotically stable. Furthermore, we apply our findings to two fractional-order SIRS (frSIRS) models incorporating infection forces under various intervention strategies, thereby substantiating our results. From an epidemiological perspective, our analysis reveals several key insights for controlling disease spread: (i) when the death rate is high, it is essential to increase the memory index; (ii) when the recovery rate is high, decreasing the memory index is advisable; and (iii) enhancing psychological or inhibitory effects-factors independent of the death rate, recovery rate, or memory index-can also play a critical role in mitigating disease transmission. These findings offer valuable insights into how the memory index influences disease outbreaks and the overall severity of epidemics.

Significance of supervision sampling in control of communicable respiratory disease simulated by a new model during different stages of the disease

The coronavirus disease 2019 (COVID-19) interventions in interrupting transmission have paid heavy losses politically and economically. The Chinese government has replaced scaling up testing with monitoring focus groups and randomly supervising sampling, encouraging scientific research on the COVID-19 transmission curve to be confirmed by constructing epidemiological models, which include statistical models, computer simulations, mathematical illustrations of the pathogen and its effects, and several other methodologies. Although predicting and forecasting the propagation of COVID-19 are valuable, they nevertheless present an enormous challenge. This paper emphasis on pandemic simulation models by introduced respiratory-specific transmission to extend and complement the classical Susceptible-Exposed-(Asymptomatic)-Infected-Recovered SE(A)IR model to assess the significance of the COVID-19 transmission control features to provide an explanation of the rationale for the government policy. A novel epidemiological model is developed using mean-field theory. Utilizing the SE(A)IR extended framework, which is a suitable method for describing the progression of epidemics over actual or genuine landscapes, we have developed a novel model named SEIAPUFR. This model effectively detects the connections between various stages of infection. Subsequently, we formulated eight ordinary differential equations that precisely depict the population's temporal development inside each segment. Furthermore, we calibrated the transmission and clearance rates by considering the impact of various control strategies on the epidemiological dynamics, which we used to project the future course of COVID-19. Based on these parameter values, our emphasis was on determining the criteria for stabilizing the disease-free equilibrium (DEF). We also developed model parameters that are appropriate for COVID-19 outbreaks, taking into account varied population sizes. Ultimately, we conducted simulations and predictions for other prominent cities in China, such as Wuhan, Shanghai, Guangzhou, and Shenzhen, that have recently been affected by the COVID-19 outbreak. By integrating different control measures, respiratory-specific modeling, and disease supervision sampling into an expanded SEI (A) R epidemic model, we found that supervision sampling can improve early warning of viral activity levels and superspreading events, and explained the significance of containments in controlling COVID-19 transmission and the rationality of policy by the influence of different containment measures on the transmission rate. These results indicate that the control measures during the pandemic interrupted the transmission chain mainly by inhibiting respiratory transmission, and the proportion of supervision sampling should be proportional to the transmission rate, especially only aimed at preventing a resurgence of SARS-CoV-2 transmission in low-prevalence areas. Furthermore, The incidence hazard of Males and Females was 1.39(1.23-1.58), and 1.43(1.26-1.63), respectively. Our investigation found that the ratio of peak sampling is directly related to the transmission rate, and both decrease when control measures are implemented. Consequently, the control measures during the pandemic interrupted the transmission chain mainly by inhibiting respiratory transmission. Reasonable and effective interventions during the early stage can flatten the transmission curve, which will slow the momentum of the outbreak to reduce medical pressure.

Perpetuation of Avian Influenza from Molt to Fall Migration in Wild Swan Geese (Anser cygnoides): An Agent-Based Modeling Approach

Wild waterfowl are considered to be the reservoir of avian influenza, but their distinct annual life cycle stages and their contribution to disease dynamics are not well understood. Studies of the highly pathogenic avian influenza (HPAI) virus have primarily focused on wintering grounds, where human and poultry densities are high year-round, compared with breeding grounds, where migratory waterfowl are more isolated. Few if any studies of avian influenza have focused on the molting stage where wild waterfowl congregate in a few selected wetlands and undergo the simultaneous molt of wing and tail feathers during a vulnerable flightless period. The molting stage may be one of the most important periods for the perpetuation of the disease in waterfowl, since during this stage, immunologically naïve young birds and adults freely intermix prior to the fall migration. Our study incorporated empirical data from virological field samplings and markings of Swan Geese (Anser cygnoides) on their breeding grounds in Mongolia in an integrated agent-based model (ABM) that included susceptible-exposed-infectious-recovered (SEIR) states. Our ABM results provided unique insights and indicated that individual movements between different molting wetlands and the transmission rate were the key predictors of HPAI perpetuation. While wetland extent was not a significant predictor of HPAI perpetuation, it had a large effect on the number of infections and associated death toll. Our results indicate that conserving undisturbed habitats for wild waterfowl during the molting stage of the breeding season could reduce the risk of HPAI transmission.

Autonomous and policy-induced behavior change during the COVID-19 pandemic: Towards understanding and modeling the interplay of behavioral adaptation

Changes in human behaviors, such as reductions of physical contacts and the adoption of preventive measures, impact the transmission of infectious diseases considerably. Behavioral adaptations may be the result of individuals aiming to protect themselves or mere responses to public containment measures, or a combination of both. What drives autonomous and policy-induced adaptation, how they are related and change over time is insufficiently understood. Here, we develop a framework for more precise analysis of behavioral adaptation, focusing on confluence, interactions and time variance of autonomous and policy-induced adaptation. We carry out an empirical analysis of Germany during the fall of 2020 and beyond. Subsequently, we discuss how behavioral adaptation processes can be better represented in behavioral-epidemiological models. We find that our framework is useful to understand the interplay of autonomous and policy-induced adaptation as a "moving target". Our empirical analysis suggests that mobility patterns in Germany changed significantly due to both autonomous and policy-induced adaption, with potentially weaker effects over time due to decreasing risk signals, diminishing risk perceptions and an erosion of trust in the government. We find that while a number of simulation and prediction models have made great efforts to represent behavioral adaptation, the interplay of autonomous and policy-induced adaption needs to be better understood to construct convincing counterfactual scenarios for policy analysis. The insights presented here are of interest to modelers and policy makers aiming to understand and account for behaviors during a pandemic response more accurately.

Assessing the potential impact of livestock immunisation and acaricide use on controlling the spread of East Coast fever

Immunisation of livestock with high-quality vaccines and the use of acaricides are highly ranked tick control strategies worldwide. However, the effects of coupling livestock immunisation and acaricide control on mitigating the spread of East Coast Fever (ECF) is not well understood. Effective strategies to curb the disease require an understanding of the influence of control strategies on ECF dynamics. This paper presents a new mathematical model for ECF in ticks and livestock to analyze the effect of livestock immunisation and acaricide control on preventing ECF spread. Our research is focused on examining how vaccine efficacy, inoculation rate, and acaricide efficacy affect disease progression. Our finding is that acaricide control alone may not be sufficient to stop the spread of ECF, even if it has an 80% effectiveness all the time. However, by pairing acaricide control with livestock vaccination, disease transmission is significantly reduced and elimination is possible under certain circumstances. Overall, results show that it is crucial to understand the influence of combining control strategies to mitigate the spread of this devastating livestock disease and enhance decision making among policymakers and livestock keepers.

Large-deviations of disease spreading dynamics with vaccination

We numerically simulated the spread of disease for a Susceptible-Infected-Recovered (SIR) model on contact networks drawn from a small-world ensemble. We investigated the impact of two types of vaccination strategies, namely random vaccination and high-degree heuristics, on the probability density function (pdf) of the cumulative number C of infected people over a large range of its support. To obtain the pdf even in the range of probabilities as small as 10-80, we applied a large-deviation approach, in particular the 1/t Wang-Landau algorithm. To study the size-dependence of the pdfs within the framework of large-deviation theory, we analyzed the empirical rate function. To find out how typical as well as extreme mild or extreme severe infection courses arise, we investigated the structures of the time series conditioned to the observed values of C.

A fractional-order mathematical model based on vaccinated and infected compartments of SARS-CoV-2 with a real case study during the last stages of the epidemiological event

In 2020 the world faced with a pandemic spread that affected almost everything of humans' social and health life. Regulations to decrease the epidemiological spread and studies to produce the vaccine of SARS-CoV-2 were on one side a hope to return back to the regular life, but on the other side there were also notable criticism about the vaccines itself. In this study, we established a fractional order differential equations system incorporating the vaccinated and re-infected compartments to a S I R frame to consider the expanded and detailed form as an S V I I v R model. We considered in the model some essential parameters, such as the protection rate of the vaccines, the vaccination rate, and the vaccine's lost efficacy after a certain period. We obtained the local stability of the disease-free and co-existing equilibrium points under specific conditions using the Routh-Hurwitz Criterion and the global stability in using a suitable Lyapunov function. For the numerical solutions we applied the Euler's method. The data for the simulations were taken from the World Health Organization (WHO) to illustrate numerically some scenarios that happened.

Analysis of mathematical model involving nonlinear systems of Caputo-Fabrizio fractional differential equation

In this paper, we consider a mathematical model of a coronavirus disease involving the Caputo-Fabrizio fractional derivative by dividing the total population into the susceptible population S ( t ) , the vaccinated population V ( t ) , the infected population I ( t ) , the recovered population R ( t ) , and the death class D ( t ) . A core goal of this study is the analysis of the solution of a proposed mathematical model involving nonlinear systems of Caputo-Fabrizio fractional differential equations. With the help of Lipschitz hypotheses, we have built sufficient conditions and inequalities to analyze the solutions to the model. Eventually, we analyze the solution for the formed mathematical model by employing Krasnoselskii's fixed point theorem, Schauder's fixed point theorem, the Banach contraction principle, and Ulam-Hyers stability theorem.

Fractional derivative based weighted skip connections for satellite image road segmentation

Segmentation of a road portion from a satellite image is challenging due to its complex background, occlusion, shadows, clouds, and other optical artifacts. One must combine both local and global cues for an accurate and continuous/connected road network extraction. This paper proposes a model using fractional derivative-based weighted skip connections on a densely connected convolutional neural network for road segmentation. Weights corresponding to the skip connections are determined using Grunwald-Letnikov fractional derivative. Fractional derivatives being non-local in nature incorporates memory into the system and thereby combine both local and global features. Experiments have been performed on two open source widely used benchmark databases viz. Massachusetts Road database (MRD) and Ottawa Road database (ORD). Both these datasets represent different road topography and network structure including varying road widths and complexities. Result reveals that the proposed system demonstrated better performance than the other state-of-the-art methods by achieving an F1-score of 0.748 and the mIoU of 0.787 at fractional order 0.4 on the MRD and a mIoU of 0.9062 at fractional order 0.5 on the ORD.

LMI-Based Delayed Output Feedback Controller Design for a Class of Fractional-Order Neutral-Type Delay Systems Using Guaranteed Cost Control Approach

In this research work, we deal with the stabilization of uncertain fractional-order neutral systems with delayed input. To tackle this problem, the guaranteed cost control method is considered. The purpose is to design a proportional-differential output feedback controller to obtain a satisfactory performance. The stability of the overall system is described in terms of matrix inequalities, and the corresponding analysis is performed in the perspective of Lyapunov's theory. Two application examples verify the analytic findings.

Fractional-Order Ebola-Malaria Coinfection Model with a Focus on Detection and Treatment Rate

Coinfection of Ebola virus and malaria is widespread, particularly in impoverished areas where malaria is already ubiquitous. Epidemics of Ebola virus disease arise on a sporadic basis in African nations with a high malaria burden. An observational study discovered that patients in Sierra Leone's Ebola treatment centers were routinely infected with malaria parasites, increasing the risk of death. In this paper, we study Ebola-malaria coinfections under the generalized Mittag-Leffler kernel fractional derivative. The Banach fixed point theorem and the Krasnoselskii type are used to analyse the model's existence and uniqueness. We discuss the model stability using the Hyers-Ulam functional analysis. The numerical scheme for the Ebola-malaria coinfections using Lagrange interpolation is presented. The numerical trajectories show that the prevalence of Ebola-malaria coinfections ranged from low to moderate depending on memory. This means that controlling the disease requires adequate knowledge of the past history of the dynamics of both malaria and Ebola. The graphical dynamics of the detection rate indicate that a variation in the detection rate only affects the following compartments: individuals that are latently infected with the Ebola, Ebola virus afflicted people who went unnoticed, individuals who have been infected with the Ebola virus and have been diagnosed with the disease, and persons undergoing Ebola virus therapy.

A Class of Deterministic and Stochastic Fractional Epidemic Models with Vaccination

In this paper, a class of fractional deterministic and stochastic susceptible-infected-removed- susceptible (SIRS) epidemic models with vaccination is proposed. For the fractional deterministic SIRS epidemic model, the existence of solution and the stability of equilibrium points are analyzed by using dynamic method. Then, the appropriate controls are established to effectively control the disease and eliminate it. On this basis, the fractional stochastic SIRS epidemic model with vaccination is further considered, and a numerical approximation method is proposed. The correctness of the conclusion is verified by numerical simulation.

COVID-19 and H1N1-09: A Systematic Review of Two Pandemics with a Focus on the Lung at Autopsy

BACKGROUND

The purpose of this manuscript is to provide a comparative overview of the two global pandemics: the first on June 11th 2009 due to influenza A H1N1 (H1N1-09); the second and current pandemic caused by coronavirus 2019 (COVID-19) on March 11th 2020, focusing on how autopsy can contribute to the definition of cellular pathology, to clinical pathology and, more generally, to public health.

METHODS

A systematic literature search selection was conducted on PubMed database on June 5, 2021, with this search strategy: (COVID-19) AND (H1N1 influenza) showing 101 results. The following inclusion criteria were selected: English language; published in a scholarly peer-reviewed journal; full-length articles were further elected. To further refine the research was to focus on the type of manuscript: review, systematic review, and meta-analysis. A critical appraisal of the collected studies was conducted, analyzing titles and abstracts, excluding the following topics: treatment, public health measures and perception of the general population or healthcare personnel about their quality of life. According to these procedures, 54 eligible studies were included in the present review.

RESULTS

Histopathological findings play a key role in understanding the pathophysiological mechanisms of diseases and, thus possible therapeutic approaches. The evidence on the thrombo-inflammatory mechanism underlying COVID-19 is growing to a much greater magnitude than the diffuse alveolar damage in common with H1N1-09; our study appears to be in line with these results. The prevailing scientific thinking to explain the morbidity and mortality of COVID-19 patients is that it elicits an exuberant immune reaction characterized by dysregulated cytokine production, known as a "cytokine storm".

CONCLUSIONS

The histological and immunohistochemical pattern demonstrated similarities and differences between the infectious manifestations of the two pathogens, which justify empirical therapeutic approaches, in the first phase of the COVID-19 pandemic. Therefore, the previous pandemic should have taught us to promote a culture of clinical and forensic autopsies in order to provide timely evidence from integration among autopsy and clinical data for early adopting adequate therapies.

Long-term predictions of current confirmed and dead cases of COVID-19 in China by the non-autonomous delayed epidemic models

In this paper, we make long-term predictions based on numbers of current confirmed cases, accumulative dead cases of COVID-19 in different regions in China by modeling approach. Firstly, we use the SIRD epidemic model (S-Susceptible, I-Infected, R-Recovered, D-Dead) which is a non-autonomous dynamic system with incubation time delay to study the evolution of the COVID-19 in Wuhan City, Hubei Province and China Mainland. According to the data in the early stage issued by the National Health Commission of China, we can accurately estimate the parameters of the model, and then accurately predict the evolution of the COVID-19 there. From the analysis of the issued data, we find that the cure rates in Wuhan City, Hubei Province and China Mainland are the approximately linear increasing functions of time t and their death rates are the piecewisely decreasing functions. These can be estimated by finite difference method. Secondly, we use the delayed SIRD epidemic model to study the evolution of the COVID-19 in the Hubei Province outside Wuhan City. We find that its cure rate is an approximately linear increasing function and its death rate is nearly a constant. Thirdly, we use the delayed SIR epidemic model (S-Susceptible, I-Infected, R-Removed) to predict those of Beijing, Shanghai, Zhejiang and Anhui Provinces. We find that their cure rates are the approximately linear increasing functions and their death rates are the small constants. The results indicate that it is possible to make accurate long-term predictions for numbers of current confirmed, accumulative dead cases of COVID-19 by modeling. In this paper the results indicate we can accurately obtain and predict the turning points, the end time and the maximum numbers of the current infected and dead cases of the COVID-19 in China. In spite of our simple method and small data, it is rather effective in the long-term prediction of the COVID-19.

Modelling the impact of travel restrictions on COVID-19 cases in Hong Kong in early 2020

BACKGROUND

Coronavirus Disease 2019 (COVID-19) led to pandemic that affected almost all countries in the world. Many countries have implemented border restriction as a public health measure to limit local outbreak. However, there is inadequate scientific data to support such a practice, especially in the presence of an established local transmission of the disease.

OBJECTIVE

To apply a metapopulation Susceptible-Exposed-Infectious-Recovered (SEIR) model with inspected migration to investigate the effect of border restriction as a public health measure to limit outbreak of coronavirus disease 2019.

METHODS

We apply a modified metapopulation SEIR model with inspected migration with simulating population migration, and incorporating parameters such as efficiency of custom inspection in blocking infected travelers in the model. The population sizes were retrieved from government reports, while the number of COVID-19 patients were retrieved from Hong Kong Department of Health and China Centre for Disease Control (CDC) data. The R₀ was obtained from previous clinical studies.

RESULTS

Complete border closure can help to reduce the cumulative COVID-19 case number and mortality in Hong Kong by 13.99% and 13.98% respectively. To prevent full occupancy of isolation facilities in Hong Kong; effective public health measures to reduce local R₀ to below 1.6 was necessary, apart from having complete border closure.

CONCLUSIONS

Early complete travel restriction is effective in reducing cumulative cases and mortality. However, additional anti-COVID-19 measures to reduce local R₀ to below 1.6 are necessary to prevent COVID-19 cases from overwhelming hospital isolation facilities.

A Review of Recent Advances in Fractional-Order Sensing and Filtering Techniques

The present manuscript aims at raising awareness of the endless possibilities of fractional calculus applied not only to system identification and control engineering, but also into sensing and filtering domains. The creation of the fractance device has enabled the physical realization of a new array of sensors capable of gathering more information. The same fractional-order electronic component has led to the possibility of exploring analog filtering techniques from a practical perspective, enlarging the horizon to a wider frequency range, with increased robustness to component variation, stability and noise reduction. Furthermore, fractional-order digital filters have developed to provide an alternative solution to higher-order integer-order filters, with increased design flexibility and better performance. The present study is a comprehensive review of the latest advances in fractional-order sensors and filters, with a focus on design methodologies and their real-life applicability reported in the last decade. The potential enhancements brought by the use of fractional calculus have been exploited as well in sensing and filtering techniques. Several extensions of the classical sensing and filtering methods have been proposed to date. The basics of fractional-order filters are reviewed, with a focus on the popular fractional-order Kalman filter, as well as those related to sensing. A detailed presentation of fractional-order filters is included in applications such as data transmission and networking, electrical and chemical engineering, biomedicine and various industrial fields.

An Operator-Based Scheme for the Numerical Integration of FDEs

An operator-based scheme for the numerical integration of fractional differential equations is presented in this paper. The generalized differential operator is used to construct the analytic solution to the corresponding characteristic ordinary differential equation in the form of an infinite power series. The approximate numerical solution is constructed by truncating the power series, and by changing the point of the expansion. The developed adaptive integration step selection strategy is based on the controlled error of approximation induced by the truncation. Computational experiments are used to demonstrate the efficacy of the proposed scheme.