Search Results (520)

Foot-and-mouth disease (FMD) is a highly transmissible viral infection of livestock that threatens food security and causes substantial economic losses in endemic regions. Despite its economic impact, the role of environmental viral load and wildlife reservoirs in sustaining FMD transmission remains poorly quantified. The aim of this study is to assess the extent to which community viral load sustains FMD persistence and to identify key transmission drivers in a coupled livestock–wildlife–environment system. A Susceptible–Exposed–Infected (SEI) model with a free-living virus compartment was analyzed via the basic reproduction number ($R_0$) and solved numerically using a Nonstandard Finite Difference Method. Sensitivity analysis identified wild host population size, transmission rates, host recruitment, environmental viral decay, and viral load thresholds as major determinants of $R_0$. Results indicate that higher transmission rates accelerate susceptible depletion and increase exposed and infected classes, with wildlife dominating environmental viral contributions. Community viral load is central to sustaining outbreaks and informs targeted control strategies. Full article

Genetic resources of small ruminants are essential for food security in arid regions; however, basic data for each breed in Saudi Arabia remain incomplete. This study establishes a comprehensive national database through a systematic survey of 104 farms, covering 21,214 heads of livestock (sheep and goats) across the kingdom’s primary agro-ecological zones between January and October 2025. Although national census data indicate that major breeds of sheep such as Naeemi, Najdi, Arabi, and Harri or goats such as Ardi exceed the FAO’s numerical thresholds for “not at risk,” our analysis reveals a fundamental paradox of “genetic vulnerability,” defined as a high risk of inbreeding depression and genetic stagnation despite high census numbers. The results show significant regional variations in prolificacy (p < 0.05), with the southern region displaying a substantial productivity gap compared to the central and eastern regions, mainly due to reliance on traditional grazing (46.7%) and limited infrastructure. This vulnerability is driven by a high risk of systematic inbreeding, with 65.7% of breeders acquiring sires from their own herds, a situation worsened by a severe 80% shortage of high-quality breeding males in the central region. Furthermore, selection criteria heavily emphasize esthetic phenotypic traits (over 80%) rather than production indicators (less than 8%), hindering genetic progress. Correlation analysis showed that higher farmer education levels were negatively associated with reproductive challenges (r = −0.216), while high feed prices remained a near-universal obstacle (97.1%). To mitigate these risks, we recommend implementing region-specific sire exchange programs to break closed breeding loops and establishing a national performance recording system to shift selection focus from phenotypic traits to measurable productivity. This study provides a vital, evidence-based framework for transitioning toward data-driven, resilient conservation and breeding strategies. Full article

Avian influenza (AI) remains a serious threat to poultry and public health worldwide due to its zoonotic nature and pandemic potential. This paper develops and analyzes a coupled system of nonlinear ordinary differential equations and an SEIR-SEIR model that describes the transmission dynamics of avian influenza in both human and bird populations. The model incorporates multiple transmission routes (bird-to-bird, bird-to-human, human-to-human), exposed/latent compartments in both hosts, disease-induced mortality, and demographic processes. From a mathematical perspective, we present a rigorous analysis of this eight-dimensional dynamical system. We prove positivity and boundedness of solutions in ${\mathbb{R}}_{+}^8$, characterize the equilibrium points, and derive the basic reproduction numbers $R_0^b$ and $R_0^h$ using the next-generation matrix method. Local asymptotic stability of the disease-free equilibrium is established via the Routh–Hurwitz criterion. A composite Lyapunov function is constructed to prove global asymptotic stability when both reproduction numbers are less than unity—a result that exploits the cascade structure of the system and provides a template for analyzing similar multi-host models. Sensitivity analysis using normalized forward sensitivity indices identifies critical parameters. In addition, we use neural network models to validate both models and provide error analysis. These results emphasize the crucial role of controlling cross-species transmission and improving recovery efforts, which have significant implications for the design of effective intervention and surveillance programs in the context of the One Health framework. Full article

A within-host HIV dynamics model incorporating latent reservoirs, distributed time delays, and a B-cell-mediated humoral immune response is developed and analyzed mathematically. The model includes five compartments: uninfected CD4⁺ T cells, latently infected cells, actively infected cells, free virions, and B cells. Four distinct distributed delays are introduced to account for the periods between viral entry and the emergence of latently or actively infected cells, reactivation of latently infected cells, and intracellular virion production. For the non-delayed system, the basic reproduction number ${\mathcal{R}}_0$ is derived using the next-generation matrix method. Using Lyapunov functions and LaSalle’s Invariance Principle, a sharp threshold dynamic is proven: the infection-free equilibrium is globally asymptotically stable (GAS) when ${\mathcal{R}}_0\le 1$, whereas a unique endemic equilibrium is GAS when ${\mathcal{R}}_0>1$. For the full distributed-delay system, a delay-dependent reproduction number ${\mathcal{R}}_0^d$ is defined. The global asymptotic stability of the infection-free equilibrium is established for ${\mathcal{R}}_0^d\le 1$, and the global asymptotic stability of the endemic equilibrium is established for ${\mathcal{R}}_0^d>1$, using suitably constructed Lyapunov functionals that account for the delay history. Numerical simulations validate the analytical threshold behavior. A sensitivity analysis of ${\mathcal{R}}_0^d$ identifies the most influential parameters for potential intervention. A treatment-dependent reproduction number is derived, and the critical drug efficacy required for viral eradication is determined. The intracellular production delay is shown to act as a critical threshold for infection clearance. Full article

Human papillomavirus (HPV) is one of the most widespread sexually transmitted infections globally, whose persistent infection plays a major role in causing cervical cancer. Vaccination is therefore a key prevention strategy. Using a gender-stratified dynamic transmission model tailored to a Tunisian case, we investigate the impact of bivalent HPV vaccination. The proposed model accounts for partial cross-immunity and captures both direct and indirect effects of female-only vaccination. We derive the basic reproduction number and the corresponding herd immunity threshold, and a global sensitivity analysis shows that vaccine coverage, efficacy, and cross-protection are strong drivers of transmission reduction. Their combined effects on disease spread are quantified by varying these parameters across biologically relevant ranges. An optimal control problem was formulated and analyzed using Pontryagin’s Maximum Principle to minimize persistent infections and cancer cases while limiting vaccination effort. Three vaccination scenarios are compared: an ideal case with full vaccine availability and two resource-constrained cases with respective maximum coverage rates of $100\%$ and $80\%$. The numerical simulations revealed that the optimal strategy under unconstrained conditions can achieve significant suppression of infection, persistence, and cancer. Under constrained effort, the optimal control still achieves substantial reductions in disease burden, with minor differences in dynamics and speed of immunity buildup. Our results highlight the effectiveness of female-only HPV vaccination in providing both direct and indirect protection. They also emphasize the importance of sustained coverage in constrained settings. Full article

Entomopathogenic fungi are vital components of integrated pest management; however, environmental temperature is one of the key factors that limits their individual-level virulence, population-level transmission dynamics, and field efficacy. In this study, we isolated an indigenous fungal strain from a naturally infected Zeugodacus cucurbitae cadaver, and evaluated its biological characteristics, virulence, and horizontal transmission efficiency against Z. cucurbitae across 20–35 °C. A temperature-driven Susceptible–Infected–Removed (SIR) epidemiological model was developed to simulate infection dynamics and predict its epizootic potential. Morphological and molecular (ITS) analyses identified the isolate as Beauveria bassiana, designated as strain WZS5. WZS5 exhibited notable thermotolerance. At 30 °C, the strain displayed a short median germination time (7.7 h), high sporulation yield (1.1 × 10⁸ conidia mL⁻¹), and fast radial growth (4.8 mm d⁻¹). Additionally, it showed substantial virulence with a median lethal concentration (LC₅₀) of 1.32 × 10⁷ conidia mL⁻¹ and a median lethal time (LT₅₀) of 5.28 days at a concentration of 1.0 × 10⁸ conidia mL⁻¹. Baseline biological activity was maintained even at 35 °C. At 30 °C, horizontal transmission was effective, yielding a cadaver sporulation rate of approximately 70.0%, a 4.0-day sporulation lag, and viable F₁ conidia (88.6% germination). The SIR model adequately captured these dynamics (r = 0.919), predicting potential epizootic spread at 30 °C with a basic reproduction number (R₀) of 1.90. This predictive framework quantifies temperature thresholds for fungal epizootics, providing valuable ecological insights for managing Z. cucurbitae in tropical and subtropical regions. Full article

The Soybean aphid (Aphis glycines) is a destructive pest that threatens soybeans. In order to develop green and effective control strategies, we propose an EQPAL epidemic model that integrates four developmental stages (1st–2nd stage nymphs, 3rd stage nymphs, 4th stage nymphs, and adults) and a ladybug (Harmonia axyridis) compartment. This model achieves green pest control by artificially releasing a natural enemy of soybean aphids to prey on adult soybean aphids. We analyzed the dynamic behavior of the model and derived the basic reproduction number ${\mathcal{R}}_0$. Using field monitoring data from Changchun City, Jilin Province, China in 2025, the segmented nonlinear least squares method was used for parameter estimation and fitting, resulting in an overall determination coefficient of $R^2=0.8204$. The numerical simulation results showed that the release of ladybugs significantly reduced the density and peak value of soybean aphid adults, and the predation rate $\beta$, predation conversion rate c, and ladybug migration rate $\omega$ were identified as key regulatory parameters. In addition, a cost–benefit analysis was conducted to determine the most cost-effective control measures. Full article

This study models trachoma transmission in Cameroon using a deterministic approach with integer and fractional-order derivatives, incorporating direct, fly-mediated, and environmental transmission routes. Fitting disease data from 1990–2019, the model forecasts trachoma prevalence until 2035. The research confirms the solution existence and uniqueness, calculates the basic reproduction number ${\mathcal{R}}_0^{\lambda }$ where $\lambda \in (0,1]$ represents the fractional-order parameter, and analyzes equilibrium stability. A stable trachoma-free equilibrium exists when ${\mathcal{R}}_0^{\lambda }<1$, while an endemic equilibrium is proven stable for ${\mathcal{R}}_0^{\lambda }>1$ under specific conditions. Calibration of a fractional model with Cameroon data yielded an ${\mathcal{R}}_0$ of 1.169 (indicating endemicity) and identified an optimal fractional order of $\lambda =0.98$. By calculating the strength number, we found that another epidemic wave could occur in 50 years. Global sensitivity analysis highlighted key parameters affecting trachoma dynamics. A numerical scheme of the model based on the Adams–Bashforth–Moulton method is constructed and its stability demonstrated. It is then used to perform several numerical simulations, first to validate the theoretical results obtained, and then to compare the different models (statistical and deterministic). The conclusion is reached that the disease will persist in the population (${\mathcal{R}}_0>1$), although the statistical model shows that it could disappear by 2030. This proves that, for trachoma dynamics in Cameroon, it is advisable to use a deterministic model. Full article

Background: The complex interplay between treatment interventions and asymptomatic carriers and its effect on the epidemic duration of an infectious disease is not fully understood. Methods: Here, we used Galton-Watson branching process and generating function technique to estimate the density functions of minor outbreak duration. Simulations were used to calculate the central tendency of outbreak duration and address how changing levels of treatment failure affect this estimated duration. Results:Streptococcus pyogenes infection was used as a case study. Given the existence of the threshold, the change in mean duration as the probability of treatment failure increases is shown to be similar to the pattern driven by the basic reproduction number. In a supercritical regime, the mean duration tends to decrease as the probability of treatment failure increases. The distribution changes in tail behavior, from heavy- to light-tailed, if a large fraction of long extinction times develops to a major outbreak. Conclusions: Treatment failure elevates the probability of secondary transmissions by prolonging the overall infectious period, resulting in an extended the outbreak duration. The threshold of treatment failure identifies the maximum tolerable error for medical intervention. An unusually long period implies a critical early warning signal of a potential major outbreak that was successfully contained. Full article

This paper presents a unified analytical and computational framework for the study of typhoid fever transmission dynamics governed by a Caputo fractional-order compartmental model of order $\kappa \in (0,1]$. The population is stratified into five epidemiological classes, namely susceptible $\left(\mathcal{S}\right)$, asymptomatic $\left(\mathcal{A}\right)$, symptomatic $\left(\mathcal{I}\right)$, hospitalised $\left(\mathcal{H}\right)$, and recovered $\left(\mathcal{R}\right)$, and the governing system explicitly incorporates asymptomatic transmission, treatment dynamics, and temporary immunity with waning. The use of the Caputo fractional derivative is motivated by the well-documented existence of chronic asymptomatic Salmonella Typhi carriers, whose heavy-tailed sojourn times in the carrier state are naturally encoded by the Mittag–Leffler waiting-time distribution arising from the fractional operator. A complete qualitative analysis of the fractional system is carried out: the basic reproduction number ${\mathcal{R}}_0$ is derived via the next-generation matrix method; local and global asymptotic stability of both the disease-free equilibrium ${\mathcal{E}}_0$ (when ${\mathcal{R}}_0\le 1$) and the endemic equilibrium ${\mathcal{E}}^{*}$ (when ${\mathcal{R}}_0>1$) are established using fractional Lyapunov theory and the LaSalle invariance principle; and the normalised sensitivity indices of ${\mathcal{R}}_0$ are computed to identify transmission-amplifying and transmission-suppressing parameters. Existence, uniqueness, and Ulam–Hyers stability of solutions are established via Banach and Leray–Schauder fixed-point arguments. To complement the analytical results, a fractional physics-informed neural network ($\mathcal{PINN}$) framework is developed to simultaneously reconstruct compartmental trajectories and identify unknown biological parameters from sparse synthetic observations. $\mathcal{PINN}$ embeds the L1-Caputo discretisation directly into the training residuals and employs a four-stage Adam–L-BFGS optimisation strategy to recover five trainable parameters $\mathbf{\Theta }$ = $\{\varphi ,\mu ,\sigma ,\psi ,\beta \}$ across three fractional orders $\kappa \in \{1.0,0.95,0.9\}$. The estimated parameters show strong agreement with the true values at the classical limit $\kappa =1.0$ ($\mathrm{MAPE}=2.27\%$), with the natural mortality rate $\mu$ recovered with $\mathrm{APE}\le 0.51\%$ and the transmission rate $\beta$ with $\mathrm{APE}\le 3.63\%$ across all fractional orders, confirming the structural identifiability of the model. Pairwise correlation analysis of the learned parameters establishes the absence of equifinality, validating that $\beta$ can be reliably included in the trainable set. Noise robustness experiments under Gaussian perturbations of $1\%$, $3\%$, and $5\%$ demonstrate graceful degradation ($\mathrm{MAPE}$: $0.82\%\to 3.10\%\to 7.31\%$), confirming the reliability of the proposed framework under realistic observational conditions. Full article

In this paper, we present a mathematical analysis of within-host CHIKV dynamics by developing and studying a novel delay differential equation model that incorporates persistent infected monocytes, discrete time delays, and an antibody-mediated humoral immune response. The model includes five compartments: susceptible monocytes, persistent infected monocytes, actively infected monocytes, CHIKV pathogens, and neutralizing antibodies. To reflect key biological latencies, we introduce four distinct discrete delays accounting for the periods between viral entry and the emergence of infected cell populations, intracellular virion production, and antibody activation. We analyze the model, establishing the positivity, boundedness, and invariance of solutions, and derive the basic reproduction number ${\mathcal{R}}_0$ via the next-generation matrix method. Using Lyapunov functions and LaSalle’s Invariance Principle, we prove a threshold dynamic: the infection-free equilibrium is globally asymptotically stable (GAS) when ${\mathcal{R}}_0\le 1$, while a unique endemic equilibrium is GAS when ${\mathcal{R}}_0>1$. Numerical simulations validate the analytical results and illustrate threshold behavior. A detailed local sensitivity analysis of ${\mathcal{R}}_0$ identifies the most influential parameters, offering theoretical insights into potential intervention strategies. We further investigate the effects of antiviral therapy as a theoretical intervention, deriving a treatment-dependent reproduction number and the critical drug efficacy required for eradication, and explore how the intracellular production delay can itself serve as a critical threshold for infection clearance. The study provides a rigorous theoretical framework that highlights the roles of latency, immune response, and biological delays in CHIKV pathogenesis and offers qualitative insights that may inform future experimental and treatment design studies. Full article

This work develops a fuzzy piecewise fractional derivative (FPFD) model for cancer-immune-angiogenesis dynamics under uncertainty. Five fuzzy state variables track tumor cells, immune effectors, vessel density, oxygen, and drug concentration. We employ fuzzy triangular numbers with $\alpha$-cut interval arithmetic using constrained fuzzy arithmetic model parametric uncertainty, with numerical values. Oxygen-dependent carrying capacity follows a Hill-type function; hypoxia-induced angiogenesis follows a decreasing Michaelis–Menten function. The model transitions at $t_1=50$ days from memoryless fuzzy classical derivative to fuzzy ABC fractional derivative of order $\psi$. The transition time $t_1=50$ days is biologically justified based on experimental observations of the angiogenic switch in solid tumors, which typically occurs within 4–8 weeks post-inoculation. Positivity, boundedness, Lipschitz continuity, existence, and uniqueness of fuzzy solutions are proved via Banach fixed-point theorem in a weighted norm. A basic reproduction number interval ${\mathcal{R}}_0=[{\underline{\mathcal{R}}}_0,{\overline{\mathcal{R}}}_0]$ is derived; local and global stability conditions are established for disease-free and endemic equilibria using fuzzy differential inclusions. Global sensitivity analysis using latin hypercube sampling with $N=500$ samples explores the range of possible outcomes across the fuzzy parameter support. In the numerical implementation, we use a fourth-order fuzzy Runge–Kutta method (Phase I), and a fractional Adams–Bashforth–Moulton predictor-corrector method (Phase II), ensuring preservation of fuzzy number characteristics. Full article

Monkeypox (Mpox), caused by the monkeypox virus (MPXV), has re-emerged as a significant global public health concern, particularly following the 2022 outbreaks. Understanding its transmission dynamics is essential for designing effective control strategies. In this study, we develop and analyze a deterministic compartmental model that captures both human-to-human and rodent-to-human transmission pathways in order to better reflect the zoonotic nature of the disease. The model is investigated using qualitative and quantitative analytical techniques, including stability analysis, bifurcation theory, and sensitivity analysis. The basic reproduction number, $R_0$, is derived and used to determine threshold conditions for disease persistence or eradication. We show that the disease-free equilibrium is globally asymptotically stable when $R_0<1$, while an endemic equilibrium exists and is stable when $R_0>1$. Furthermore, the model exhibits backward bifurcation, indicating that reducing $R_0$ below unity may not be sufficient for disease elimination. Sensitivity analysis identifies key parameters driving transmission, particularly the rodent-to-human and human-to-human contact rates. Numerical simulations further demonstrate that reducing cross-species transmission and improving isolation of infected individuals significantly decrease disease burden. These findings highlight the complexity of Mpox transmission and emphasize that effective control requires not only lowering $R_0$, but also targeting critical transmission pathways. This study provides useful insights for public health planning by identifying priority intervention strategies such as minimizing rodent–human interactions and strengthening isolation measures. Full article

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

Substance abuse addictions and hepatitis B infections are two major public health problems facing humanity globally, especially in areas where the two problems co-exist. A mathematical model was used in this work to study the co-dynamics of substance abuse addictions and hepatitis B infections and investigate their possible control strategies. The mathematical features of the model, such as the disease-free equilibrium, endemic equilibrium, and basic reproduction number, were computed. The stability analysis of the disease-free equilibrium and endemic equilibrium was conducted analytically. The impact of multiple control measures, including public enlightenment, rehabilitation of individuals with substance abuse disorders, treatment of persons infected with hepatitis B, and vaccination of susceptible individuals, was examined numerically. The study reveals how co-existence fundamentally alters system behavior and control effectiveness and offers new insights for designing effective control management strategies. Full article