Search Results (31)

The outbreaks of large-scale epidemics, such as COVID-19 in 2019–2022, challenge modelers. Beside the effect of the incubation period of the virus, the delay property of detection should be also stressed. This kind of memory effect affects the entire change rate, which cannot be reflected by the conventional instantaneous derivative. The fractional derivative (FD) meets this request to some extent. Yet the shortcoming of it limits its usage. Through a strict modeling approach, a new susceptible–infective–removed (SIR) model with the memory-dependent derivative (MDD) has been constructed. The numerical simulations indicate that (1) the neglecting of the incubation period may underestimate the number of susceptible individuals and overestimate the infected ones; (2) the neglecting of the treatment period may badly overestimate the removed individuals; (3) the consequence of tardy detection intervention may be very serious, and the infectious rate may increase rapidly with a postponed peak time; and (4) the SIR model with the FD yields bad estimations, not only in the primary stage but also in the subsequent evolution. Due to the reasonability of the new SIR model with the MDD, it is suggested to epidemic researchers. Full article

The phenomenological universalities (PU) approach is employed to derive the Richards growth function in the unknown hyperbolic representation. The formula derived can be applied in theoretical modeling of sigmoid and involuted growth of biological systems. In the model proposed, the exponent in the Richards function has the following clear biological meaning: it describes the number of cells doubling, leading to an increase in a biomass of the system from $m_0$ (birth or hatching mass) to the limiting value $m_{\infty }$ (mass at maturity). The generalized form of the universal growth function is derived. It can be employed in fitting the weight–age data for a variety of biological systems, including copepods, tumors, fish, birds, mammals and dinosaurs. Both the PU methodology and the Richards model can be effectively applied in the theoretical modeling of infectious disease outbreaks. To substantiate this assertion, the simplest PU-SIR (Susceptible–Infective–Removed) epidemiological model is considered. In this approach, it is assumed that the number of births is approximately equal to the number of deaths, while the impact of recovered (quarantined) individuals on the dynamics of the infection is negligible. Full article

In the post-COVID-19 era, the dynamic spread of COVID-19 poses new challenges to epidemiological modelling, particularly due to the absence of large-scale screening and the growing complexity introduced by immune failure and reinfections. This paper proposes an AEIHD (antibody-acquired, exposed, infected, hospitalised, and deceased) model to analyse and predict COVID-19 transmission dynamics in the post-COVID-19 era. This model removes the susceptible compartment and combines the recovered and vaccinated compartments into an “antibody-acquired” compartment. It also introduces a new hospitalised compartment to monitor severe cases. The model incorporates an antibody-acquired infection rate to account for immune failure. The Extended Kalman Filter based on the AEIHD model is proposed for real-time state and parameter estimation, overcoming the limitations of fixed-parameter approaches and enhancing adaptability to nonlinear dynamics. Simulation studies based on reported data from Australia validate the AEIHD model, demonstrating its capability to accurately capture COVID-19 transmission dynamics with limited statistical information. The proposed approach addresses the key limitations of traditional SIR and SEIR models by integrating hospitalisation data and time-varying parameters, offering a robust framework for monitoring and predicting epidemic behaviours in the post-COVID-19 era. It also provides a valuable tool for public health decision-making and resource allocation to handle rapidly evolving epidemiology. Full article

In this paper, we propose a novel normalized time-fractional susceptible–infected–removed (SIR) model that incorporates memory effects into epidemiological dynamics. The proposed model is based on a newly developed normalized time-fractional derivative, which is similar to the well-known Caputo fractional derivative but is characterized by the property that the sum of its weight function equals one. This unity property is crucial because it helps with evaluating how the fractional order influences the behavior of time-fractional differential equations over time. The normalized time-fractional derivative, with its unity property, provides an intuitive understanding of how fractional orders influence the SIR model’s dynamics and enables systematic exploration of how changes in the fractional order affect the model’s behavior. We numerically investigate how these variations impact the epidemiological dynamics of our normalized time-fractional SIR model and highlight the role of fractional order in improving the accuracy of infectious disease predictions. The appendix provides the program code for the model. Full article

The deterministic SIR model for disease spread in a closed population is extended to allow infected individuals to recover to the susceptible state. This extension preserves the second constant of motion, i.e., a functional relationship of susceptible and removed numbers, $S\left(t\right)$ and $R\left(t\right)$, respectively. This feature allows a substantially complete elucidation of qualitative properties. The model exhibits three modes of behaviour classified in terms of the sign of $-S^{\prime }\left(0\right)$, the initial value of the epidemic curve. Model behaviour is similar to that of the SIS model if $S^{\prime }\left(0\right)>0$ and to the SIR model if $S^{\prime }\left(0\right)<0$. The separating case is completely soluble and $S\left(t\right)$ is constant-valued. Long-term outcomes are determined for all cases, together with determination of the rate of convergence. Determining the shape of the epidemic curve motivates an investigation of curvature properties of all three state functions and quite complete results are obtained that are new, even for the SIR model. Finally, the second threshold theorem for the SIR model is extended in refined and generalised forms. Full article

Identifying influential nodes, with pivotal roles in practical domains like epidemic management, social information dissemination optimization, and transportation network security enhancement, is a critical research focus in complex network analysis. Researchers have long strived for rapid and precise identification approaches for these influential nodes that are significantly shaping network structures and functions. The recently developed SPON (sum of proportion of neighbors) method integrates information from the three-hop neighborhood of each node, proving more efficient and accurate in identifying influential nodes than traditional methods. However, SPON overlooks the heterogeneity of neighbor information, derived from the asymmetry properties of natural networks, leading to its lower accuracy in identifying essential nodes. To sustain the efficiency of the SPON method pertaining to the local method, as opposed to global approaches, we propose an improved local approach, called the SSPN (sum of the structural proportion of neighbors), adapted from the SPON method. The SSPN method classifies neighbors based on the h-index values of nodes, emphasizing the diversity of asymmetric neighbor structure information by considering the local clustering coefficient and addressing the accuracy limitations of the SPON method. To test the performance of the SSPN, we conducted simulation experiments on six real networks using the Susceptible–Infected–Removed (SIR) model. Our method demonstrates superior monotonicity, ranking accuracy, and robustness compared to seven benchmarks. These findings are valuable for developing effective methods to discover and safeguard influential nodes within complex networked systems. Full article

The susceptible–infected–recovered/removed–vaccinated (SIRV) epidemic model is an important generalization of the SIR epidemic model, as it accounts quantitatively for the effects of vaccination campaigns on the temporal evolution of epidemic outbreaks. Additional to the time-dependent infection ($a\left(t\right)$) and recovery ($\mathit{\mu }\left(t\right)$) rates, regulating the transitions between the compartments $S\to I$ and $I\to R$, respectively, the time-dependent vaccination rate $v\left(t\right)$ accounts for the transition between the compartments $S\to V$ of susceptible to vaccinated fractions. An accurate analytical approximation is derived for arbitrary and different temporal dependencies of the rates, which is valid for all times after the start of the epidemics for which the cumulative fraction of new infections $J\left(t\right)\ll 1$. As vaccination campaigns automatically reduce the rate of new infections by transferring persons from susceptible to vaccinated, the limit $J\left(t\right)\ll 1$ is even better fulfilled than in the SIR-epidemic model. The comparison of the analytical approximation for the temporal dependence of the rate of new infections $\mathring{J}\left(t\right)=a\left(t\right)S\left(t\right)I\left(t\right)$, the corresponding cumulative fraction $J\left(t\right)$, and $V\left(t\right)$, respectively, with the exact numerical solution of the SIRV-equations for different illustrative examples proves the accuracy of our approach. The considered illustrative examples include the cases of stationary ratios with a delayed start of vaccinations, and an oscillating ratio of recovery to infection rate with a delayed vaccination at constant rate. The proposed analytical approximation is self-regulating as the final analytical expression for the cumulative fraction $J_{\infty }$ after infinite time allows us to check the validity of the original assumption $J\left(t\right)\le J_{\infty }\ll 1$. Full article

The dynamical equations of the susceptible-infected-recovered/removed (SIR) epidemics model play an important role in predicting and/or analyzing the temporal evolution of epidemic outbreaks. Crucial input quantities are the time-dependent infection ($a\left(t\right)$) and recovery ($\mu \left(t\right)$) rates regulating the transitions between the compartments $S\to I$ and $I\to R$, respectively. Accurate analytical approximations for the temporal dependence of the rate of new infections $\mathring{J}\left(t\right)=a\left(t\right)S\left(t\right)I\left(t\right)$ and the corresponding cumulative fraction of new infections $J\left(t\right)=J\left(t_0\right)+{\int }_{t_0}^{t}dx\mathring{J}\left(x\right)$ are available in the literature for either stationary infection and recovery rates or for a stationary value of the ratio $k\left(t\right)=\mu \left(t\right)/a\left(t\right)$. Here, a new and original accurate analytical approximation is derived for general, arbitrary, and different temporal dependencies of the infection and recovery rates, which is valid for not-too-late times after the start of the infection when the cumulative fraction $J\left(t\right)\ll 1$ is much less than unity. The comparison of the analytical approximation with the exact numerical solution of the SIR equations for different illustrative examples proves the accuracy of the analytical approach. Full article

As the main methods of the coronavirus disease (COVID-19) transmission are air and physical contact, actions to mitigate and suppress its spread must be developed in order to change population dynamics and provide efficient control strategies. Here, these actions are described as a simple heuristic framework to establish public policies. Two control systems were studied: the first organized in the form of an algorithm stratified into three levels and the second as a minimization problem similar to optimal control strategies, applied to both social distancing and vaccination. The possible effects of these actions are modeled and applied to an extension of the Susceptible - Infected - Removed (SIR) compartmental model. The control system is developed, which is organized in the form of an algorithm stratified into three levels. These levels intend to represent social distancing strategies implemented by sanitary authorities around the globe, representing stronger or weaker grades of isolation intensity according to the ability of the healthcare system to cope with symptomatic individuals. The algorithm control is applied in a simulation, and the results give evidence of the effectiveness of the procedures adopted against the coronavirus. The model dynamics are analyzed and validated with simulations considering parameters obtained from epidemiological data from Brazil and Uruguay and in a more detailed way for three Brazilian states: São Paulo, Minas Gerais and Rio de Janeiro. The model was validated using cumulative data on cases and deaths. For cases of death, the results were satisfactory, while for case data, the response was reasonable, considering the possibility of adding delays or variations in parameters in the model. In addition, the effective reproduction number was proposed for the cities studied in Brazil, the result being relevant because it has a qualitative behavior similar to that published by official centers. This paper also discusses the implementation and optimization of social distancing and vaccination control strategies, considering different parameters and their effects on reducing the number of cases and deaths. Model simulations present promising results for developing strategies to attack COVID-19 dissemination. Full article

Monitored differential infection rates of past corona waves are used to infer, a posteriori, the real time variation of the ratio of recovery to infection rate as a key parameter of the SIR (susceptible-infected-recovered/removed) epidemic model. From monitored corona waves in five different countries, it is found that this ratio exhibits a linear increase at early times below the first maximum of the differential infection rate, before the ratios approach a nearly constant value close to unity at the time of the first maximum with small amplitude oscillations at later times. The observed time dependencies at early times and at times near the first maximum agree favorably well with the behavior of the calculated ratio for the Gaussian temporal evolution of the rate of new infections, although the predicted linear increase of the Gaussian ratio at late times is not observed. Full article

The spatio-temporal course of an epidemic (such as COVID-19) can be significantly affected by non-pharmaceutical interventions (NPIs) such as full or partial lockdowns. Bayesian Susceptible-Infected-Removed (SIR) models can be applied to the spatio-temporal spread of infectious diseases (STIFs) (such as COVID-19). In causal inference, it is classically of interest to investigate the counterfactuals. In the context of STIF, it is possible to use nowcasting to assess the possible counterfactual realization of disease in an incidence that would have been evidenced with no NPI. Classic lagged dependency spatio-temporal IF models are discussed, and the importance of the ST component in nowcasting is assessed. Real examples of lockdowns for COVID-19 in two US states during 2020 and 2021 are provided. The degeneracy in prediction over longer time periods is highlighted, and the wide confidence intervals characterize the forecasts. For SC, the early and short lockdown contrasted with the longer NJ intervention. The approach here demonstrated marked differences in spatio-temporal disparities across counties with respect to an adherence to counterfactual predictions. Full article

In the present work, a fractional temporal SIR model is considered. The total population is divided into three compartments—susceptible, infected and removed individuals. It generalizes the classical SIR model and consists of three coupled time-fractional ordinary differential equations (ODEs). The fractional derivative is introduced to account for the subdiffusion process of confirmed, cured and deceased people dynamics. Although relatively basic, the model is robust and captures the real dynamics, helped by the memory property of the fractional system. In the paper, the issue of an adequate model reconstruction is addressed, and a coefficient identification inverse problem is solved; in particular, the transition and recovering rates, varying in time, are recovered. A least-squares cost functional is minimized for solving the problem. The time-dependent parameters are reconstructed with an iterative predictor–corrector algorithm. Its application is demonstrated via tests with synthetic and real data. What is more, an approach for economic impact assessment is proposed. Full article

This paper proposes an impulsive control scheme for a complex network that helps reduce the spread of two epidemic diseases: influenza type A and COVID-19. Both are respiratory infections; thus, they have a similar form of transmission, and it is possible to use the same control scheme in both study cases. The objective of this work is to use neural impulsive inverse optimal pinning control for complex networks to reduce the effects of propagation. The dynamic model is considered unknown, for which we design a neural identifier that, through training using the extended Kalman filter algorithm, provides the appropriate nonlinear model for this complex network. The dynamics of the network nodes are represented by the Susceptible-Infected-Removed (SIR) compartmental model in their discrete form. The results of the simulations are presented and addressed, applying the same control scheme but with different parameter values for each case study. Full article

As communication continues to develop, the high freedom and low cost of the communication network environment also make rumors spread more rapidly. If rumors are not clarified and controlled in time, it is very easy to trigger mass panic and undermine social stability. Therefore, it is important to establish an efficient model for rumor propagation. In this paper, the impact of rumor clarifiers on the spread of rumors is considered and fractional order differentiation is introduced to solve the problem that traditional models do not take into account the “anomalous propagation” characteristics of information. A fractional-order Susceptible-Infected-Removal-Clarify (SIR-C) rumor propagation prediction model featuring the clarification mechanism is proposed. The existence and asymptotic stability conditions of the rumor-free equilibrium point (RFEP) $E_0$; the boundary equilibrium points (BEPs) $E_1$ and $E_2$ are also given. Finally, the stability conditions and practical cases are verified by numerical simulations. The experimental results confirm the analysis of the theoretical study and the model fits well with the real-world case data with just minor deviations. As a result, the model can play a positive and effective role in rumor propagation prediction. Full article

Using the recently proposed Susceptible–Asymptomatic–Infected–Vaccinated–Removed (SAIVR) model, we study the impact of key factors affecting COVID-19 vaccine rollout effectiveness and the susceptibility to resurgent epidemics. The SAIVR model expands the widely used Susceptible–Infectious–Removed (SIR) model for describing epidemics by adding compartments to include the asymptomatic infected (A) and the vaccinated (V) populations. We solve the model numerically to make predictions on the susceptibility to resurgent COVID-19 epidemics depending on initial vaccination coverage, importation loads, continuing vaccination, and more contagious SARS-CoV-2 variants, under persistent immunity and immunity waning conditions. The parameters of the model represent reported epidemiological characteristics of the SARS-CoV-2 virus such as the disease spread in countries with high levels of vaccination coverage. Our findings help explain how the combined effects of different vaccination coverage levels and waning immunity lead to distinct patterns of resurgent COVID-19 epidemics (either surges or endemic), which are observed in countries that implemented different COVID-19 health policies and achieved different vaccinated population plateaus after the vaccine rollouts in the first half of 2021. Full article