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Online digital networks, including social networks, have significantly impacted individuals’ personal and professional lives. Aside from exchanging news and topics of interest, digital networks play an essential role in the diffusion of information, which frequently significantly impacts worldwide societies. In this paper, we present a new mathematical epidemic model for digital networks that considers the sentiment of solitary misinformation in the networks and characteristics of human intelligence that play an important role in judging and spreading misinformation inside the networks. Our mathematical analysis has proved the existence and validity of the system in a real-time environment. Considering the real-world data, our simulation predicts how the misinformation could spread among different global communities and when an intervention mechanism should have to be carried out by the policyholders. Our simulation using the model proves that effective intervention mechanisms by isolating the fake news can effectively control the spread of misinformation among larger populations. The model can analyze the emotional and social intelligence of groups frequently subjected to disinformation and disseminating fake news.

We study a fast–slow version of an SIRS epidemiological model on homogeneous graphs, obtained through the application of the moment closure method. We use GSPT to study the model, taking into account that the infection period is much shorter than the average duration of immunity. We show that the dynamics occurs through a sequence of fast and slow flows, that can be described through 2-dimensional maps that, under some assumptions, can be approximated as 1-dimensional maps. Using this method, together with numerical bifurcation tools, we show that the model can give rise to periodic solutions, differently from the corresponding model based on homogeneous mixing.

Mechanistic infectious disease models are crucial for understanding the forces driving epidemics. Many epidemic models naturally produce equilibrium or stationary behaviors readily seen in epidemiological surveillance. However, respiratory viruses in tropical locations exhibit non-equilibrium behavior without consistent timing. This prevents standard models that commonly produce cycles and equilibria from describing their true dynamics. To evaluate deterministic model structures that can create asynchronous nonannual epidemic patterns seen with tropical influenza, we parameterized 30 variations of a respiratory disease model incorporating three influenza (sub)types and evaluated their abilities to emulate nonannual behaviors. Variations across models included immune-waning dynamics, subpopulations, and periodic case introduction. We defined seven criteria describing irregular epidemic behaviors and conducted parameter-space searches to find parameter sets meeting these criteria. Small parameter perturbations (1%) often led to violations of these criteria, indicating a lack of robustness in the parameter sets’ abilities to predict nonannual influenza dynamics. The models were also unstable to traditional perturbation in state space. We were unable to find evidence of a deterministic epidemic model with a stable parameterization or structure that can robustly produce asynchronous behaviors. It remains unknown whether a canonical deterministic epidemic model exists for the observed asynchronous nonstationary dynamics of tropical influenza.

Newly emerging pandemics like COVID-19 call for predictive models to implement precisely tuned responses to limit their deep impact on society. Standard epidemic models provide a theoretically well-founded dynamical description of disease incidence. For COVID-19 with infectiousness peaking before and at symptom onset, the SEIR model explains the hidden build-up of exposed individuals which creates challenges for containment strategies. However, spatial heterogeneity raises questions about the adequacy of modeling epidemic outbreaks on the level of a whole country. Here, we show that by applying sequential data assimilation to the stochastic SEIR epidemic model, we can capture the dynamic behavior of outbreaks on a regional level. Regional modeling, with relatively low numbers of infected and demographic noise, accounts for both spatial heterogeneity and stochasticity. Based on adapted models, short-term predictions can be achieved. Thus, with the help of these sequential data assimilation methods, more realistic epidemic models are within reach.

In this paper, we are concerned with two SIS epidemic reaction–diffusion models with mass action infection mechanism of the form SI , and study the spatial profile of population distribution as the movement rate of the infected individuals is restricted to be small. For the model with a constant total population number, our results show that the susceptible population always converges to a positive constant which is indeed the minimum of the associated risk function, and the infected population either concentrates at the isolated highest-risk points or aggregates only on the highest-risk intervals once the highest-risk locations contain at least one interval. In sharp contrast, for the model with a varying total population number which is caused by the recruitment of the susceptible individuals and death of the infected individuals, our results reveal that the susceptible population converges to a positive function which is non-constant unless the associated risk function is constant, and the infected population may concentrate only at some isolated highest-risk points, or aggregate at least in a neighborhood of the highest-risk locations or occupy the whole habitat, depending on the behavior of the associated risk function and even its smoothness at the highest-risk locations. Numerical simulations are performed to support and complement our theoretical findings.

Epidemic models can play a major role in understanding the spread of diseases and their control. These mathematical models have plenty of significance in various scientific domains, including public health, to investigate disease propagation and ecology. This article explains the dynamics of SIR epidemic model of arbitrary order with aid of a precise numerical approach called Genocchi wavelet collocation method. The main purpose of this investigation is to explore and discover the results for system of nonlinear ordinary differential equations arising in the considered mathematical model and to investigate the dynamical aspects of SIR model via Caputo fractional derivative which is non-local in behaviour. The projected method depicts rapid algorithms and is extremely precise, reliable, and uses fewer computational resources. Also, this method is simpler than the other traditional numerical methods as it merges the operational matrix with the collocation method in order to transform fractional-order problem into algebraic equations which enables to obtain satisfactory results. The approximate solution obtained using proposed algorithm exposes the nature of their interactions. Furthermore, the numerical outcomes are represented through graphs for different fractional order and compared the results with Runge–Kutta method and residual power series method. The projected technique is very effective, accurate, free from controlling parameters and consume less time to investigate nonlinear complications arising in diverse fields of epidemical and biological models. Ultimately, the current study help to inspect the wild class of models and their performance which are occurring in real world.

This study presents a comprehensive formulation, theoretical analysis, and numerical investigation of a fractional-order SVIR epidemic model employing the normalized Caputo–Fabrizio (NCF) derivative. The NCF operator introduces memory effects through a normalized, non-singular kernel, ensuring physically consistent weighting of past states. Vaccination dynamics are explicitly incorporated, enabling realistic modeling of epidemic control strategies. We establish key mathematical properties of the model, including existence, uniqueness, positivity, boundedness, and conservation of the total population, and propose an efficient numerical scheme for its simulation. The influence of the fractional order and kernel normalization is explored through numerical experiments, highlighting their impact on epidemic peak magnitude, transient dynamics, and vaccination effectiveness. A rigorous equilibrium and bifurcation analysis shows that, for the closed SVIR structure with constant vaccination, neither backward bifurcation nor Hopf bifurcation can occur, even in the presence of saturated incidence. Any oscillatory behavior observed numerically is transient and induced by fractional memory effects rather than sustained periodic solutions. These results clarify the dynamical limitations of the closed NCF–SVIR framework and highlight the role of fractional memory in shaping epidemic trajectories. The proposed model provides a robust foundation for future extensions incorporating demographic turnover or imperfect vaccination, where richer bifurcation phenomena may arise.

The review is devoted to an analysis of mathematical models used for describing epidemic processes. Our main focus is on the models that are based on partial differential equations (PDEs), especially those that were developed and used for the COVID-19 pandemic modeling. Most of our attention is given to the studies in which not only results of numerical simulations are presented but analytical results as well. In particular, traveling fronts (waves), exact solutions, and the estimation of key epidemic parameters of the epidemic models with governing PDEs (typically reaction–diffusion equations) are discussed. The review may serve as a valuable resource for researchers and practitioners in the field of mathematical modeling in epidemiology.

A compartmental epidemiological model with distributed recovery and death rates is proposed. In some particular cases, the model can be reduced to the conventional SIR model. However, in general, the dynamics of epidemic progression in this model is different. Distributed recovery and death rates are evaluated from COVID-19 data. The model is validated by the epidemiological data for different countries, and it shows better agreement with the data than the SIR model. The time-dependent disease transmission rate is estimated.

In this paper, we construct a novel iterative scheme for approximating fixed points of generalized -nonexpansive mappings in the setting of a real Banach space. The proposed scheme not only generalizes but also unifies and extends several well-known fixed point iterative processes available in the literature. We establish both weak and strong convergence results under appropriate conditions. Furthermore, a comparative analysis of the rate of convergence is carried out using a carefully chosen numerical example, with the outcomes demonstrated through both tabular and graphical illustrations.In addition to convergence properties, we derive a data dependence result, offering insights into the stability of the proposed scheme with respect to perturbations in the underlying mapping. We further prove that the scheme satisfies -stability and almost -stability criteria, thereby enhancing its robustness in practical applications. To demonstrate the applicability of our results, we provide significant application of the analysis to a SEIR epidemic model governed by a Caputo-type fractional differential equation, showcasing the utility of the proposed method in the context of real-world dynamical systems. Our findings contribute to the advancement of fixed point theory and its applications in mathematical modeling, offering a flexible and powerful tool for analyzing complex nonlinear problems.