Communication in Biomathematical Sciences

Fractional-Order Epidemiological Modeling and Optimal Control of Circulating Vaccine-Derived Poliovirus Type 2(cVDPV2)

2026-11-06T14:35:07+07:00

This paper advocates an intriguing fractional-order mathematical model (FOMM) to assess the dissemination volatility of (cVDPV2), a re-emerging public health threat linked to insufficient immunization coverage. The model incorporates key epidemiological compartments, including vaccinated individuals and those susceptible to vaccine reversion, using Caputo fractional derivatives(CFD) for logging the ripples of reminiscence and long-term immunity responses. We derive and analyze the disease-free(DFE) and endemic equilibrium points(EE), compute the fractional basic reproduction number R0, and conduct local stability(LS) analysis using the Mittag-Leffler function(MLF) approach. A sensitivity analysis identifies critical parameters influencing virus persistence, such as the reversion rate and vaccine efficacy. Furthermore, plausible coefficients are used in numerical simulations (NS) and fractional orders α ∈ (0, 1], highlighting the role of memory in disease progression. Optimal control(OC) theory is applied to evaluate intervention strategies, including vaccination scale-up and awareness programs, with simulations demonstrating the effectiveness of these controls in reducing infection prevalence. This work enhances the theoretical understanding of cVDPV2 dynamics, emphasizes the advantages of fractional-order models in epidemiology, and provides a robust framework for guiding public health responses in regions at risk of vaccine-derived poliovirus outbreaks.

CNN-based Fast Computation of the Determinism Towards Its Application to Neurofeedback

2026-10-28T16:27:36+07:00

Recurrence quantification analysis provides the nonlinear measure, called determinism (DET), to characterize the deterministic process of given signals. However, the calculation of DET is computationally demanding, limiting its real-time application. This study proposes a convolutional neural network (CNN)-based method for computing the DET fast. The method was validated using the multi-channel electroencephalography (EEG) data recorded at rest, and was tested with the occipital-lobe EEG data recorded during the neurofeedback, where alpha and beta powers were controlled to improve the relaxedness. Then, the CNN-predicted DET showed significantly high correlation with the explicitly calculated DET (r = 0.9281 in the validation and r = 0.9873 in the testing, p < 0.0001), yielding the approximately tenfold improvement in speed. Further, the pre- and post-training analysis underpinned a phenomenon, where the DET can change upward or downward when the alpha/beta ratio increases. These results demonstrated the potential use of the CNN-based DET computation in neurofeedback, suggesting that the combined use of the alpha/beta ratio and DET could be an effective way for capturing both linear features and nonlinear dynamics in the brain.

Transmitted and Acquired HIV Drug Resistance in South Africa: A Caputo Fractional-Order Two-Strain Model with a Data-Based Test of the Fractional Order

2026-10-19T17:19:32+07:00

Succeeding in the world's largest antiretroviral therapy (ART) programme in South Africa is threatened by the emergence of drug-resistant virus. A lot of time fractional-order epidemic models are suggested to include memory effects, but the fractional order is not usually evaluated with data. To construct a 2 strain model of HIV with both transmitted and acquired drug resistance, analyse it in its Caputo fractional form, calibrate it to South African estimates, and see if the data support a fractional order below one. The model consists of five classes: susceptible, untreated with drug-sensitive virus, untreated with drug-resistant virus, suppressed on ART, and failure on ART with drug-resistant virus. Strain-specific reproduction numbers are calculated, existence, nonnegativity and boundedness of solutions are proven, local stability of the disease-free equilibrium is verified by Matignon's criterion, and the global extinction with a Mittag-Leffler bound is shown. We fit the model to UNAIDS estimates for 2010--2024 and 2017 resistance survey data with an Adams--Bashforth--Moulton scheme, and profile the fit over the fractional order $q$. The best fit occurs at $q=1$ and orders with $q<0.96$ are significantly poorer fits of the estimates. The reproduction number of the drug-sensitive strain is $\mathcal{R}_{0s}=0.88$. An assumed mean of 2 years for switching patients with failure yields $\mathcal{R}_{0r}=1.24$ and the proportion of new infections due to resistance increases from 37\% in 2024 to 60\% in 2040. Switching four times faster brings $\mathcal{R}_{0r}$ below one and prevents 24\% of infections in 2024--2040, and with faster ART initiation and lower failure, 48\% are averted. Results for resistance will vary by assumed switching delay and fitness cost and resistance data are prior to dolutegravir-based first-line therapy. The estimates are not compatible with appreciable memory effects. In the model, early intervention to detect treatment failure and switch to second-line treatment is the best agent against resistance; a quicker ART initiation reduces the incidence but raises the proportion of resistant cases.

A Mathematical Framework for Smoking-Driven Lung Cancer Progression Incorporating Treatment and Recovery Pathways

2026-10-18T22:08:29+07:00

In this work a deterministic compartmental model is presented to investigate the progression of smoking induced infection to cancer when treated and cured. The total population is structured into seven interacting classes that account for susceptible, latent exposure, chronic infection, untreated and treated individuals, cancer cases and recovered. A nonlinear incidence rate (based on a log function) is used to model disease transmission, taking into account saturation effects. The well-posedness of the model is verified by analytical results, which include existence, uniqueness, positivity and boundedness of the solutions. The next generation matrix approach is used to calculate the basic reproduction number $\mathcal{R}_0$ and use it as a critical threshold for the dynamics of the disease. It is demonstrated that the disease-free equilibrium is globally asymptotically stable if $\mathcal{R}_0 \leq 1$ and it is shown that a disease-free equilibrium is locally stable if and only if $\mathcal{R}_0 > 1$. A sensitivity analysis identifies the fact that the primary factors influencing the value of $\mathcal{R}_0$ are transmission intensity and natural mortality. Analytical results are supported by numerical experiments, using the fourth-order Runge-Kutta method, and are used to demonstrate the action of the treatment strategies for reducing the burden of smoking-related cancer.