Search Results (214)

In recent years, fractional HIV models have received increasing attention. This study derives a fractional HIV model using the continuous-time random walk (CTRW) method, endowing the mathematical model with physical significance. Based on the transmission characteristics of HIV, the proposed model considers extrinsic infectivity, intrinsic infectivity, and drug control, specifically as follows: the extrinsic infectivity is a constant independent of the infection time; the intrinsic infectivity is a power-law function that depends on drug efficacy and infection time; the drug efficacy rate follows a Mittag–Leffler distribution with a long-term effect. Based on these considerations, a fractional HIV model with drug control is established in this paper. In addition, the global asymptotic stability of the equilibrium and the sensitivity analysis of the basic reproduction number $R_0$ are studied, and the theoretical results are verified by numerical simulations. The results show that reducing extrinsic infectivity, controlling intrinsic infectivity, and the drug efficacy rate are crucial in controlling the spread of HIV. Full article

This study develops an integrated mathematical model to investigate the interaction between tuberculosis (TB) transmission and childhood stunting, which is aligned with the United Nations Sustainable Development Goals (SDG 3). The population is structured into two age groups (0–5 years and ≥5 years), with stunting explicitly incorporated into the pediatric population to capture its potential influence on TB dynamics. The model is formulated as a system of ordinary differential equations and analyzed using equilibrium and stability analysis, with the basic reproduction number, $R_0$. The disease-free equilibrium is locally asymptotically stable when $R_0<1$, while an endemic equilibrium exists when $R_0>1$. Sensitivity analysis indicates that the transmission rate ($\beta$), progression rate from latent to active infection ($\sigma$), and recovery rate ($\gamma$) are the most influential parameters affecting $R_0$. These parameters are therefore selected as control variables in an optimal control framework to design effective intervention strategies. Numerical simulations show that the combined control strategy significantly reduces TB transmission, resulting in a reduction of more than $80\%$ in active TB cases within a relatively short intervention period. The results suggest that integrated interventions targeting transmission, disease progression, and recovery are substantially more effective than single-measure strategies. This study provides a quantitative framework to support integrated public health policies addressing TB and childhood stunting simultaneously. Full article

In this study, we propose a compartmental mathematical model that considers two interacting populations (citrus plants and insect vectors) and investigate the transmission dynamics of Huanglongbing in citrus crops. This disease is caused by the bacterium Candidatus Liberibacter asiaticus and is vectored by the psyllid Diaphorina citri. The disease is modeled under the following three main assumptions: there is vital dynamics with constant recruitment rates of citrus plants, the force of infection in both populations is a spatially dependent function varying with geographic location, and there is a spatial displacement of the vectors. In the main results of the paper, we formulate a coupled ordinary and partial differential equation system with initial and zero flux boundary conditions, establish the existence and uniqueness of solutions to the proposed model by applying semigroup theory, and introduce a numerical approximation of the system. Moreover, we develop a stability and persistence analysis. From the analytical point of view, we calculate the basic reproduction number $R_0$ and prove three facts: the disease-free equilibrium is globally asymptotically stable when $R_0<1$; the disease-free equilibrium is globally asymptotically stable when $R_0>1$; and the hybrid system exhibits uniform persistence of infection when $R_0>1$. In addition, we present some numerical examples. Full article

This paper presents a novel mathematical framework for anthrax transmission by integrating Caputo fractional derivatives, distributed delays, and a Beddington–DeAngelis incidence function. The proposed model captures memory effects in disease progression, temporal heterogeneities in pathogen release, and saturation phenomena in host–pathogen interactions. We establish the well-posedness of the system and derive the basic reproduction number ${\mathcal{R}}_0$, which serves as a sharp threshold for disease dynamics: when ${\mathcal{R}}_0\le 1$, the disease-free equilibrium is globally asymptotically stable; when ${\mathcal{R}}_0>1$, a unique endemic equilibrium emerges and is globally stable. Theoretical analysis demonstrates that the fractional order modulates convergence rates through memory effects, while distributed delays influence oscillatory behaviors and time to equilibrium. Numerical simulations validate these findings and illustrate the impacts of key parameters on disease transmission. The results provide a scientific foundation for designing targeted public health interventions in anthrax control. Full article

The aim of this research is to formulate and analyze a modified $S{I}_{p}IVR$ mathematical model to study the transmission dynamics of poliovirus and assess the impact of vaccination on disease control. The proposed model extends classical SEIV-type frameworks by incorporating a recovered compartment with long-term immunity and by replacing the traditional exposed class with a pre-infectious compartment ($I_p$) that captures silent viral shedding during the incubation phase of poliovirus. This modification addresses the critical epidemiological feature that individuals can transmit the virus before showing symptoms while maintaining biological accuracy in compartment definition. Several fundamental analytical properties are rigorously established, including positivity, boundedness, and the existence of a biologically meaningful invariant region. The basic reproduction number $R_0$ is derived using the next-generation matrix approach, and comprehensive stability analysis is carried out. The analysis shows that the DFE is locally and globally asymptotically stable whenever $R_0<1$. Using center manifold theory, a forward bifurcation is rigorously demonstrated, indicating that disease persistence emerges smoothly as $R_0$ crosses unity. Local and global sensitivity analyses of the basic reproduction number $R_0$ identify critical epidemiological parameters, and points to vaccination coverage and transmission rates as key drivers of outbreak dynamics. Numerical simulations confirm the analytical results and illustrates two different epidemiological scenarios, one with $R_0<1$, and another with $R_0>1$ along with neural network analysis by using the same data from both cases in a built-in function package in MATLAB-2020 software. It utilizes all of its hidden layers to check the data used by the model for validation performance and training and to find the absolute and mean squared errors. It also shows how vaccination suppresses the spread of infection. These findings provide a strong mathematical basis for public health policy, offering strategic insight into how vaccination campaigns might be optimized to accelerate progress toward global polio eradication. Full article

Dental caries is an example of an oral infectious disease that affects many people worldwide, but it is not well studied in deterministic mathematical modeling. Therefore, we are interested in studying the dynamics of tooth cavity disease using a deterministic modeling approach. We propose a delay differential equation system (DDEs) to describe the phenomenon. The breakthrough of the constructed model is the formulation of the recovery rate as a saturation function constrained by healthcare capacity and the plausibility of caries reformation. In addition, we consider two controls, such as a health campaign and a post-treatment intervention. The mathematical analysis yields equilibrium solutions and their stability, which is determined by the basic reproduction number $\left({\mathfrak{R}}_0\right)$. Furthermore, backward bifurcation occurs as the medical facility’s capacity decreases, driven by an increasing infectious population. The sensitivity analysis results indicate that both considered controls are the most influential parameters. The optimal control problem is formulated using the Pontryagin Maximum Principle to obtain an optimal solution in suppressing the number of caries formation cases. At the end, a numerical simulation shows that interventions reduce the risk of transmission and suppress the number of infectious individuals. The constructed model has excellent future potential, such as generating a function for relapse cases or other preventive actions into an optimal control problem. Full article

In this study, we developed an SIR-like mathematical model of disease transmission dynamics. Hantavirus is a neglected tropical disease, and this paper presents a mathematical model of hantavirus transmission among rodents and its effect on the number of hantavirus-infected humans. We review an existing SIR-SIR model of hantavirus transmission and analyze it in a standard mathematical epidemiology framework. The original SIR-SIR model is summarized, with emphasis on its structural assumptions, epidemiological interpretation, and analytical results, including the derivation of the basic reproduction number and the characterization of the stability of the disease-free and endemic equilibria. A critical evaluation of the original SIR-SIR model highlights several biological limitations of the baseline model, notably, the unrealistic assumption of homogeneous transmission and the absence of ecological seasonality. To address these gaps, an improved model incorporating periodic forcing in rodent recruitment and disease transmission is proposed. The use of sine and cosine functions introduces a biologically motivated phase shift between rodent recruitment and transmission, reflecting the fact that birth pulses and peak contact rates rarely occur simultaneously in natural rodent populations. The reproduction number for the extended system is constructed using a Floquet-style argument for DFE stability. A theorem connecting the stability of the DFE with the seasonal component is presented, resembling the well-known rule for non-seasonal hantavirus transmission but with more realistic assumptions. Numerical simulations demonstrate that seasonal variation can generate oscillatory outbreak patterns that more closely reflect empirical rodent population dynamics and human risk profiles. Overall, the results underscore the importance of ecological realism in zoonotic disease modeling and provide a foundation for more accurate prediction and control of the disease, especially in NTD elimination programs. Full article

Plant-parasitic nematodes (PPNs) cause big crop losses globally. Safe/reliable methods for their durable management strategies can harness various beneficial relationships among the plant immune system and related microbiomes. Molecular mechanisms basic to these relations reveal wide arrays of significant roles for plant-healthy growth. This review focuses on such relations of microbiomes to prime and immunize plants against PPNs. It also highlights molecular issues facing PPN-resistant varieties with possible solutions such as genetic breeding/engineering, grafting, PPN-antagonistic root exudates, and novel resistant cultivars. These issues call for optimal uses of various widespread groups of microbiomes. Related plant signaling hormones and transcription factors that regulate gene expression and modulate nematode-responsive genes to ease positive/negative adaptation are presented. Exploring PPN-resistance genes, their activation mechanisms, and signaling networks offers a holistic grasp of plant defense related to biotic/abiotic factors. Such factors relevant to systemic acquired resistance (SAR) via plant–microbe interactions to manage PPNs are stressed. The microbiomes can be added as inoculants and/or steering the indigenous rhizosphere ones. Consequently, SAR is mediated by the accumulation of salicylic acid and the subsequent expression of pathogenesis-related genes. To activate SAR, adequate priming and induction of plant defense against PPNs would rely on closely linked factors. They mainly include the engaged microbiome species/strains, plant genotypes, existing fauna/flora, compatibility with other involved biologicals, and methods/rates of the inoculants. To operationalize improved plant resistance and the microbiome’s usage, novel actionable insights for research and field applications are necessary. Synthesis of adequate screening techniques in plant breeding would better use multiple parameters (molecular and classical ones)-based ratings for PPN-host suitability designation. Sound statistical analyses and interpretation approaches can better identify genotypes with high-level, stable resistance to PPNs than the commonly used ones. Linking molecular mechanisms to consistent field relevance can be progressed via dissemination of many advanced techniques. The CRISPR/Cas9 system has been effective in knocking out both the OsHPP04 gene in rice to confer resistance against Meloidogyne graminicola and the GhiMLO3 gene in cotton to minimize the Rotylenchulus reniformis reproduction. Its genetic modifications in crops synthesized “transgene-free” PPN-resistant plants without decreased growth/yield. Characterizing microbiome species/strains needed to prime and immunize plants requires better molecular tools for fine-scale taxonomic resolution than the common ones used. The former can distinguish closely related ones that exhibit divergent phenotypes for key attributes like stability and production of enzymes and secondary metabolites. As PPN-control strategies via tritrophic interactions are more sensitive to the relevant settings than chemical nematicides, it is suggested herein to test these settings on a case-by-case basis to avoid erratic/contradictory results. Moreover, expanding the use of automated systems to expedite detection/count processes of PPN and related microbes with objectivity/accuracy is discussed. When PPNs and their related microbial distribution patterns were modeled, more aspects of their field distributions were discovered in order to optimize their integrated management. Hence, the feasibility of site-specific microbiome application in PPN–hotspot infections can be evaluated. The main technical challenges and controversies in the field are also addressed herein. Their conceptual revision based on harnessing novel techniques/tools is direly needed for future clear trends. This review also engages raising growers’ awareness to leverage such strategies for enhancing plant resistance and advancing the microbiome role. Microbiomes enjoy wide spectrum efficacy, low fitness cost, and inheritance to next generations in durable agriculture. Full article

Tick-borne diseases (TBDs) pose a significant global threat to both canine and public health, largely attributable to the extensive geographic distribution of ticks and their ability to harbor diverse pathogens. To evaluate regional risk, this study examined the developmental biology of a prevalent tick species in Xinjiang, China, and performed molecular surveillance for key pathogens in both tick vectors and canine hosts. Observations of reproductive biology revealed that Riphicephalus turanicus ticks could complete their development from egg to adult in approximately 50 days on laboratory rabbits, indicating a rapid lifecycle and high reproductive potential. Polymerase chain reaction (PCR)-based screening of 379 canine blood samples detected infection rates of 14.25% for Anaplasma spp., 2.64% for Hepatozoon spp., 21.64% for Rickettsia spp., and 21.90% for Babesia spp. Concurrently, screening of 184 tick samples revealed detection rates of 15.22% for Anaplasma ovis, 8.15% for Hepatozoon spp., and 21.74% for Rickettsia spp. Statistical analysis identified significant regional variation in pathogen prevalence across the surveyed locations. The BLASTn (BLAST: Basic Local Alignment Search Tool) alignment revealed high sequence identity (99.30–100%) with known strains of Babesia, Rickettsia, and Anaplasma circulating in Asia and Europe. confirming the presence of these pathogens in the local ecosystem and evolutionary linkage to global lineages. Collectively, these findings provide valuable epidemiological insight into the endemic nature of TBDs in Xinjiang and emphasize the importance of integrated tick management and sustained disease surveillance programs. Full article

Objective: Dynamic allocation of emergency medical resources is a critical task in the prevention and control of respiratory infectious diseases (RIDs). This study aims to address the challenge of a “run on the healthcare system” by proposing an effective resource allocation strategy to curb the spread of RIDs. Methods: Considering the infection severity of RIDs, the capacity of emergency medical resources (hospitalization rate), and vaccination status, we construct an S_VIⁿR dynamic model of RIDs that considers vaccine failure. Under the constraint of emergency medical resources and with the goal of minimizing the basic reproduction number, we propose a dynamic allocation strategy for distributing emergency medical resources among different types of infected individuals. Results: Simulation results demonstrate that improving the hospitalization efficiency of emergency medical resources significantly contributes to the effective control of RIDs. The model shows that targeted dynamic allocation helps reduce disease transmission. Conclusions: Validation using real-world data confirms that the model is effective and practical. It offers theoretical guidance for dynamically allocating emergency medical resources and supports informed decision-making in response to major emerging RIDs. Full article

Background and objectives: During an outbreak, measles cases tend to aggregate into increasingly bigger clusters that show specific characteristics, different from the non-cluster cases. As the measles threat continues throughout Europe in 2025 with a high notification rate in Romania as well, exploring how clustering affects the disease propagation can provide additional insights into how to improve measles surveillance and control. Methods: National measles cases from 2020 to 2024 have been split into cluster (at least three related cases) and non-cluster-related cases and analyzed comparatively based on vaccination status, disease-related data (hospitalization) and patient-related data (age, location). Large outbreaks with at least 150 cases, allowing for more comprehensive R₀ analysis, have been described and the basic reproduction numbers computed for each of them. Results: There are statistically significant differences in vaccination status, age, and hospital stay between outbreak and non-outbreak cases. Large outbreaks (≥150 cases) show a high degree of variability, with R₀ values varying from as low to 1 to as high as 3.92, indicating limited measles transmission control. Conclusions: The findings in this research highlight the critical impact of clustering on measles transmission dynamics during outbreaks. Significant differences in vaccination status, age, and hospitalization rates between cluster and non-cluster cases underscore the importance of targeted surveillance and intervention strategies while the wide range of R₀ values observed in large outbreaks points to inconsistent control measures and emphasizes the need for strengthened vaccination campaigns and improved outbreak response protocols to better contain measles spread. Full article

Background/Objectives: Female tubal factor infertility is a major clinical challenge. While surgical repair of the fallopian tubes remains the traditional standard, biological fibrin sealants have been proposed to reduce tissue trauma and improve reproductive outcomes. Methods: We conducted database searches of PubMed/MEDLINE, EMBASE and Google Scholar until 31 August 2025, using the keywords “tubal anastomosis”, “tubal reanastomosis,” “tubal reanastomosis”, “uterine horn anastomosis”, “fibrin glue”, “fibrin sealant”, “biological sealant”, “tissue adhesive”, “rabbit”, “rat” and “sterilization reversal.” Reference lists of retrieved articles have been examined to find studies which tested end-to-end tubal (or small-animal uterine horn) anastomosis through biological adhesives with or without additional components to evaluate patency success, fertility results and adhesion formation. Results: Thirteen studies met the inclusion criteria (eleven animal; two human). Rat and rabbit models demonstrated that fibrin sealants with intraluminal splints and one-to-two anchoring sutures produced results comparable to microsutures for patency (tubal patency rates of 75–100%) and pregnancy success (pregnancy rates of 60–83%) while reducing surgical time and decreasing peritubal adhesions. The success rates of the procedures depended on the anastomosis locations. Isthmic–isthmic anastomosis produced better results than ampullary repairs which tended to fail or develop stenosis. Fibrin sealant-only repairs without splinting were associated with lower patency (almost 60%) despite acceptable histologic healing. Human data showed similar pregnancy rates (intrauterine pregnancy in about 40–50% of women) and tubal patency but no consistent decrease in adhesions. Ectopic pregnancy rates ranged from 9 to 11%. Conclusions: Fibrin sealants are useful adjuncts to microsurgical tubal repair, but they should not replace the basic repair procedures. The effectiveness of this procedure is dependent on three critical factors: precise segment alignment, proper use of splints and stents, and selection of segments with comparable caliber. In a personalized-medicine framework, fibrin-assisted reanastomosis may offer a tailored option for selected women who desire natural pregnancy. Modern standardized research is required to define indications and analyze how the adaptation of fibrin sealants in minimally invasive procedures affect reproductive outcomes, ectopic pregnancy rates, and adhesion development. Full article

This paper presents a comprehensive mathematical analysis of a novel compartmental model describing the dynamics of dispersed water pollutants and their interaction with two distinct host populations. The model is formulated as a system of integro-differential equations that incorporates multiple distributed delays to realistically account for time lags in the infection process and pollutant transport. We rigorously establish the biological well-posedness of the model by proving the non-negativity and ultimate boundedness of solutions, confirming the existence of a positively invariant feasible region. The analysis characterizes the long-term behavior of the system through the derivation of the basic reproduction number ${\mathcal{R}}_0^d$, which serves as a sharp threshold determining the system’s fate. For the model without delays, we prove the global asymptotic stability of the infection-free equilibrium (IFE) when ${\mathcal{R}}_0\le 1$ and of the endemic equilibrium (EE) when ${\mathcal{R}}_0>1$. These stability results are extended to the distributed-delay model by using sophisticated Lyapunov functionals, demonstrating that ${\mathcal{R}}_0^d$ universally governs the global dynamics: the IFE (${\mathcal{E}}_0^d$) is globally asymptotically stable (GAS) if ${\mathcal{R}}_0^d\le 1$, while the EE (${\mathcal{E}}_d^{\ast }$) is GAS if ${\mathcal{R}}_0^d>1$. Numerical simulations validate the theoretical findings and provide further insights. Sensitivity analysis identifies the most influential parameters on ${\mathcal{R}}_0^d$, highlighting the recruitment rate of susceptible individuals, exposure rate, and pollutant shedding rate as key intervention targets. Furthermore, we investigate the impact of control measures, showing that treatment efficacy exceeding a critical value is sufficient for disease eradication. The analysis also reveals the inherent mitigating effect of the maturation delay, demonstrating that a delay longer than a critical duration can naturally suppress the outbreak. This work provides a robust mathematical framework for understanding and managing dispersed water pollution, emphasizing the critical roles of multi-source contributions, time delays, and targeted interventions for environmental sustainability. Full article

We present a comprehensive mathematical analysis of a within-host dual-target HIV dynamics model, which explicitly incorporates the virus’s interactions with its two primary cellular targets: CD4⁺ T cells and macrophages. The model is formulated as a system of five nonlinear delay differential equations, integrating three distinct discrete time delays to account for critical intracellular processes such as the development of productively infected cells and the maturation of new virions. We first establish the model’s biological well-posedness by proving the non-negativity and boundedness of solutions, ensuring all trajectories remain within a feasible region. The basic reproduction number, ${\mathcal{R}}_0^d$, is derived using the next-generation matrix method and serves as a sharp threshold for disease dynamics. Analytical results demonstrate that the infection-free equilibrium is globally asymptotically stable (GAS) when ${\mathcal{R}}_0^d\le 1$, guaranteeing viral eradication from any initial state. Conversely, when ${\mathcal{R}}_0^d>1$, a unique endemic equilibrium emerges and is proven to be GAS, representing a state of chronic infection. These global stability properties are rigorously established for both the non-delayed and delayed systems using carefully constructed Lyapunov functions and functionals, coupled with LaSalle’s invariance principle. A sensitivity analysis identifies viral production rates ($p_1,p_2$) and infection rates (${\beta }_1,{\beta }_2$) as the most influential parameters on ${\mathcal{R}}_0^d$, while the viral clearance rate (m) and maturation delay (${\tau }_3$) have a suppressive effect. The model is extended to evaluate antiretroviral therapy (ART), revealing a critical treatment efficacy threshold ${ϵ}^{cr}$ required to suppress the virus. Numerical simulations validate all theoretical findings and further investigate the dynamics under varying treatment efficacies and maturation delays, highlighting how these factors can shift the system from persistence to clearance. This study provides a rigorous mathematical framework for understanding HIV dynamics, with actionable insights for designing targeted treatment protocols aimed at achieving viral suppression. Full article

This paper is dedicated to the analytical investigation of the global dynamics of an SEIR epidemiological model that incorporates latency age (the time spent by an individual in the exposed class before becoming infectious) and a general nonlinear incidence rate. In this model, to reflect the dependence of disease progress on the latency age, the exposed class is structured by the latency age, and the rate at which the latent individual becomes infected, and the removal rate are assumed to depend on the latency age. By analyzing the characteristic equations associated with each equilibrium, we study the local stability of both the disease-free and endemic steady states of the model. Moreover, it is proven that the semiflow generated by this system is asymptotically smooth, and if the basic reproduction number is greater than unity, the system is uniformly persistent. Furthermore, based on Lyapunov functional and LaSalle’s invariance principle, the global dynamics of the model are established. It is obtained that if the basic reproduction number is less than unity, the disease-free steady state is globally asymptotically stable and hence the disease dies out; however, if the basic reproduction number is greater than unity, the endemic steady state is globally asymptotically stable, and the disease persists. Numerical simulations are carried out to illustrate the main analytic results. Full article