Search Results (206)

In this paper, we present a mathematical model, $M_{siqr}$, to analyze the dynamics of mobile malware propagation in smartphone networks. The model segments the mobile device population into susceptible, exposed, infected, quarantined, and recovered compartments, integrating critical control parameters such as infection and quarantine rates. The analytical results include the derivation of the basic reproduction number, $R_0$, along with equilibrium and stability analyses that provide insights into long-term system behavior. A focused scenario analysis compares the baseline dynamics with a more aggressive malware variant and a more effective quarantine response. The results show that increased infectivity sharply escalates the peak of infection, while enhanced quarantine measures effectively suppress it. This highlights the importance of prompt containment strategies even under more virulent conditions. The sensitivity analysis identifies the infection rate as the most influential parameter driving peak infection, while the quarantine rate exerts the most significant dampening effect. Monte Carlo simulations of parameter uncertainty reveal a consistently high epidemic potential across varied conditions. A parameter sweep across the infection–quarantine space further maps out the conditions under which malware outbreaks can be mitigated or prevented. Overall, the model demonstrates that mobile malware poses sustained epidemic risk under uncertainty, but effective control parameters—particularly quarantine—can drastically alter outbreak trajectories. Full article

In this paper, we develop an HIV/AIDS epidemic model that incorporates a saturated incidence rate to reflect the limited transmission capacity and the impact of behavioral saturation in contact patterns. The model is formulated as a system of seven non-linear ordinary differential equations representing key population compartments. In addition to model formulation, we introduce an optimal control problem involving three control measures: educational campaigns, screening of unaware infected individuals, and antiretroviral treatment for aware infected individuals. We begin by establishing the positivity and boundedness of the model solutions under constant control inputs. The existence and local and global stability of both the disease-free and endemic equilibrium points are analyzed, depending on the effective reproduction number (${\mathcal{R}}_e$). Bifurcation analysis reveals that the model undergoes a forward bifurcation at ${\mathcal{R}}_e=1$. A local sensitivity analysis of ${\mathcal{R}}_e$ identifies the disease transmission rate as the most sensitive parameter. The optimal control problem is then formulated by incorporating the dynamics of infected subpopulations, control costs, and time-dependent controls. The existence of optimal control solutions is proven, and the necessary conditions for optimality are derived using Pontryagin’s Maximum Principle. Numerical simulations support the theoretical analysis and confirm the stability of the equilibrium points. The optimal control strategies, evaluated using the Incremental Cost-Effectiveness Ratio (ICER), indicate that implementing both screening and treatment (Strategy D) is the most cost-effective intervention. These results provide important insights for designing effective and economically sustainable HIV/AIDS intervention policies. Full article

Despite initial changes in respiratory illness epidemiology due to SARS-CoV-2, influenza activity has returned to pre-pandemic levels, highlighting its ongoing challenges. This paper investigates an influenza epidemic model using a Susceptible-Exposed-Infected-Recovered (SEIR) framework, extended with fuzzy Atangana–Baleanu–Caputo (ABC) fractional derivatives to incorporate uncertainty (via fuzzy numbers for state variables) and memory effects (via the ABC fractional derivative for non-local dynamics). We establish the theoretical foundation by defining the fuzzy ABC derivatives and integrals based on the generalized Hukuhara difference. The existence and uniqueness of the solutions for the fuzzy fractional SEIR model are rigorously proven using fixed-point theorems. Furthermore, we analyze the system’s disease-free and endemic equilibrium points under the fractional framework. A numerical scheme based on the fractional Adams–Bashforth method is used to approximate the fuzzy solutions, providing interval-valued results for different uncertainty levels. The study demonstrates the utility of fuzzy fractional calculus in providing a more flexible and potentially realistic approach to modeling epidemic dynamics under uncertainty. Full article

Objectives: Innate lymphoid cells (ILCs) and natural killer (NK) cells represent a diverse group of innate immune populations that modulate immune responses and tissue equilibrium across various diseases, including cancer. In the present study, we analyzed single-cell RNA sequencing (scRNA-seq) data to explore the landscape and functional status of ILC subsets in patients with head and neck squamous cell carcinoma (HNSCC). Methods: The GSE164690 dataset, which includes preprocessed scRNA-seq and clinical data, was acquired from the Gene Expression Omnibus database. The Cancer Genome Atlas database was used to develop the survival prediction model. Results: A total of 95,809 immune cells were clustered into 16 immune cell clusters, among which 7278 NK cells were further subdivided into 11 clusters. Among the 11 clusters, eight NK cell clusters, two intraepithelial ILC1 (ieILC1) clusters, and one ieILC1–NK-intermediate (ieILC1-NK-int) cluster were identified. Among the ieILC1/NK clusters, ieILC1-1 exhibited the highest immunological activity and was mainly derived from human papillomavirus-positive samples. Further, ieILC1s showed higher enrichment of pathways related to inflammation and effector functions—such as inflammatory response, interferon-gamma response, and interferon-alpha response—compared to the other clusters. Moreover, we developed prognostic prediction models based on differentially expressed genes in the ieILC1/NK clusters. Risk scores of the ieILC1-1, ieILC1-NK-int, and NK clusters were identified as independent prognostic factors for shorter overall survival (OS) and progression-free survival (PFS). Recursive partitioning revealed that combining ieILC1-1 and the NK clusters strongly predicted shorter OS and PFS. Conclusions: Our findings highlight the diverse landscape and prognostic significance of ieILC1/NK cells in patients with HNSCC. Full article

Campylobacteriosis has been described as an ever-changing disease and health issue that is rather dangerous for different population groups all over the globe. The World Health Organization (WHO) reports that 33 million years of healthy living are lost annually, and nearly one in ten persons have foodborne illnesses, including Campylobacteriosis. This explains why there is a need to develop new policies and strategies in the management of diseases at the intergovernmental level. Within this framework, an advanced stochastic fractional delayed model for Campylobacteriosis includes new stochastic, memory, and time delay factors. This model adopts a numerical computational technique called the Grunwald–Letnikov-based Nonstandard Finite Difference (GL-NSFD) scheme, which yields an exponential fitted solution that is non-negative and uniformly bounded, which are essential characteristics when working with compartmental models in epidemic research. Two equilibrium states are identified: the first is an infectious Campylobacteriosis-free state, and the second is a Campylobacteriosis-present state. When stability analysis with the help of the basic reproduction number $R_0$ is performed, the stability of both equilibrium points depends on the $R_0$ value. This is in concordance with the actual epidemiological data and the research conducted by the WHO in recent years, with a focus on the tendency to increase the rate of infections and the necessity to intervene in time. The model goes further to analyze how a delay in response affects the band of Campylobacteriosis spread, and also agrees that a delay in response is a significant factor. The first simulations of the current state of the system suggest that certain conditions can be achieved, and the eradication of the disease is possible if specific precautions are taken. The outcomes also indicate that enhancing the levels of compliance with the WHO-endorsed SOPs by a significant margin can lower infection rates significantly, which can serve as a roadmap to respond to this public health threat. Unlike most analytical papers, this research contributes actual findings and provides useful recommendations for disease management approaches and policies. Full article

In this paper, we establish an age-structured SEIAR epidemic model that incorporates media effects and employ the exponential function approach to demonstrate the crucial role of media influence in disease prevention and control. Notably, our model accounts for the possibility of recessive infected individuals becoming dominant through contact with infectious individuals. Theoretical analysis yields the explicit expression for the basic reproduction number $R_0$, which serves as a critical threshold for disease dynamics. Through comprehensive threshold analysis, we investigate the existence and stability of both disease-free and endemic equilibrium states. By applying characteristic equation analysis and the method of characteristics, we establish the following: (1) when $R_0<1$, the disease-free equilibrium is globally asymptotically stable; (2) when $R_0>1$, a unique endemic equilibrium exists and maintains local asymptotic stability under specific conditions. This study shows that strengthening media promotion, raising awareness, and reducing the density of recessive infected individuals can effectively control the further spread of a disease. To validate our theoretical results, we present numerical simulations that quantitatively assess the impact of varying media reporting intensities on epidemic containment measures. These simulations provide practical insights for public health intervention strategies. Full article

Ubiquitin-specific protease 7 (USP7), a deubiquitinase enzyme responsible for removing ubiquitin (Ub) from target proteins, plays a crucial role in oncogenic pathways and has been implicated in various human diseases. X-ray crystallography has revealed distinct conformations of USP7, including apo (ligand-free), allosteric inhibitor-, and Ub-bound states. However, the dynamic mechanisms underlying the allosteric inhibition of USP7 remain unclear. This study investigates the effect of allosteric inhibitor binding on the dynamics of USP7 through multiple replica molecular dynamics simulations. Our results demonstrate that Ub binding stabilizes the USP7 conformation, while allosteric inhibitor binding increases flexibility and variability in the fingers and palm domains of USP7. Furthermore, our analysis of USP7 local regions reveals that allosteric inhibitor binding not only restrains the dynamics of the C-terminal Ub binding site, thereby impeding the accessibility of Ub to USP7, but also disrupts the proper alignment of the catalytic triad (Cys223-His464-Asp481) in USP7. Additionally, community network analysis indicates that intra-domain communications within the fingers domain in USP7 are significantly enhanced upon allosteric inhibitor binding. This study reveals that the binding of an allosteric inhibitor induces a dynamic shift in enzyme’s conformational equilibrium, effectively disrupting its catalytic activity through allosteric modulation. Full article

Bayoud disease, caused by Fusarium oxysporum f. sp. albedinis, is a major threat to date palm trees. It leads to lower crop yields, financial losses, and decreased biodiversity. The complexity of the disease presents challenges to effective disease management. This study introduces a mathematical model comprising six compartments for palm trees: susceptible trees, resistant varieties, exposed trees, infected trees, isolated trees under treatment, and recovered trees, along with a contaminant water compartment. The model emphasizes the role of resistant varieties, contamination of irrigation water, and the treatment of infected trees in disease control. Theoretical analyses guarantee positivity, boundedness, and the existence of a unique solution. The existence of equilibrium points (disease-free and endemic) and the reproduction number (${\mathcal{R}}_0$) of the model are calculated analytically and validated through numerical simulations. Stability analysis at disease-free and endemic equilibrium points is conducted in terms of ${\mathcal{R}}_0$. Sensitivity analysis identifies key parameters influencing disease dynamics and is helpful to identify the potential control parameters. An optimal control problem is formulated to minimize infection spread and associated costs via preventive isolation and treatments, irrigation water treatment, and the promotion of resistant varieties. Numerical simulations demonstrate the efficacy of these strategies, highlighting the potential of resistant varieties and treatment measures in reducing infection rates and enhancing tree health. This research offers valuable insights into sustainable Bayoud disease management, underscoring the importance of mathematical modeling in addressing agricultural challenges. Full article

Artificial intelligence (AI) plays a crucial role in modern healthcare by enhancing disease modeling and outbreak prediction. In this study, we develop an epidemiological model for the Marburg virus, integrating vaccination and treatment strategies while considering vaccine efficacy and treatment failure. The model exhibits mathematical symmetry in its equilibrium analysis, ensuring a balanced assessment of disease dynamics across human and bat reservoir populations. We compute the Marburg-free and endemic equilibrium points, derive the secondary infection threshold, and conduct sensitivity analysis using the PRCC method to identify key disease transmission parameters that are important for disease control. To validate the theory, we optimized a deep neural network (DNN) via grid search and employed it for dynamic analysis, which also validates the cutting-edge application of AI in healthcare. We also compare AI-based predictions with traditional numerical solutions for reproduction number for humans $R_{0h}>1$ and $R_{0h}<1$ for validation and efficacy of the AI approach. The results demonstrate the model’s stability, efficacy, and predictive power, emphasizing the synergy between AI and mathematical epidemiology. This study provides valuable insights for public health interventions and effective disease control strategies by leveraging AI-driven simulations, highlighting AI’s potential to revolutionize and enhance early detection and tailor treatment strategies. Full article

Diphtheria is a severely infectious and deadly bacterial disease with Corynebacterium diphtheriae as the causative agent. Since the COVID-19 pandemic, contagious diseases such as diphtheria have re-emerged due to disruptions in routine childhood immunization programs worldwide. Nigeria is witnessing a significant increase in diphtheria outbreaks likely due to an inadequate health care system and insufficient public enlightenment campaign. This paper presents a mathematical epidemic diphtheria model in Nigeria, which includes a public enlightenment campaign to assess its positive impact on the prevalence of the disease. The mathematical analysis of the model reveals two equilibrium points: the diphtheria infection-free equilibrium and the endemic equilibrium. These equilibrium points are shown to be stable globally asymptotically if ${\mathcal{R}}_c<1$ and ${\mathcal{R}}_c>1$, respectively. The model was fit using the confirmed diphtheria cases data of Kano State from January to December 2023. Sensitivity analysis indicates that the transmission rate and recovery rate of asymptomatic peopleare crucial parameters to be considered in developing effective strategies for diphtheria control and prevention. This analysis also reveals that the implementation of a high-level public enlightenment campaign and its high efficacy effectively reduce the prevalence of diphtheria. Finally, numerical simulations show that combining the public enlightenment campaign and isolating infected individuals is the best strategy to contain the spread of diphtheria. Full article

This study presents a novel fractional-order mathematical model to investigate zoonotic disease transmission between humans and baboons, incorporating the Generalized Euler Method and highlighting key control strategies such as sterilization, restricted food access, and reduced human–baboon interaction. The model’s structure exhibits an inherent symmetry in the transmission dynamics between baboon and human populations, reflecting balanced interaction patterns. This symmetry is further analyzed through the stability of infection-free and endemic equilibrium points, guided by the basic reproduction number ${\mathcal{R}}_0$. Theoretical analyses confirmed the existence, uniqueness, and boundedness of solutions, while sensitivity analysis identified critical parameters influencing disease spread. Numerical simulations validated the effectiveness of intervention strategies, demonstrating the impact of symmetrical measures on minimizing zoonotic disease risks and promoting balanced population health outcomes. This work contributes to epidemiological modeling by illustrating how symmetry in control interventions can optimize zoonotic disease management. Full article

Redox (reduction–oxidation) imbalance is a physiological feature regulated by a well-maintained equilibrium between reactive oxygen species (ROS) and oxidative stress (OS), the defense system of the body (antioxidant enzymes). The redox system comprises regulated levels of ROS in the cells, tissues and the overall organ system. The levels of ROS are synchronized by gradients of electrons that are generated due to sequential reduction and oxidation of various biomolecules by various enzymes. Such redox reactions are present in each cell, irrespective of any tissue or organ. Failure in such coordinated regulation of redox reactions leads to the production of excessive ROS and free radicals. Excessively produced free radicals and oxidative stress affect various cellular and molecular processes required for cell survival and growth, leading to pathophysiological conditions and, ultimately, organ failure. Overproduction of free radicals and oxidative stress are the key factors involved in the onset and progression of pathophysiological conditions associated with various cardiovascular and renal diseases. Sodium–glucose cotransporter 2 inhibitors (SGLT2is) are glucose-lowering drugs prescribed to diabetic patients. Interestingly, apart from their glucose-lowering effect, these drugs exhibit beneficial effects in non-diabetic patients suffering from various cardiovascular and chronic kidney diseases, perhaps due to their antioxidant properties. Recently, it has been demonstrated that SGLT2is exhibit strong antioxidant properties by reducing ROS and OS. Hence, in this review, we aim to present the novel antioxidant role of SGLT2is and their consequent beneficial effects in various cardiovascular and renal disease states. Full article

Acute diarrhea poses a significant global health challenge, especially in settings with poor sanitation. This study develops a mathematical model of diarrhea, employing a piecewise modified ABC (pmABC) fractional derivative to capture the disease’s transmission dynamics, including crossover effects between classical and fractional behaviors. We analyze the local and global stability of the disease-free equilibrium and calculate the basic reproduction number $R_0$ using the next-generation matrix method. Furthermore, we formulate an optimal control model that incorporates both strategies to reduce contact between susceptible and infected individuals, and to treat infected patients. Numerical simulations demonstrate the model’s behavior, illustrating that enhanced hygiene compliance reduces $R_0$ by decreasing contact rates, while increased effective contact rates elevate $R_0$. Additionally, the simulations reveal a positive correlation between higher concentrations of acute diarrhea bacteria and increased rates of subsequent infections. Full article

This paper presents a new SIRS model for recurrent childhood diseases under the Caputo fractional difference operator. The existence theory is established using Brouwer’s fixed-point theorem and the Banach contraction principle, providing a comprehensive mathematical foundation for the model. Ulam stability is demonstrated using nonlinear functional analysis. Sensitivity analysis is conducted based on the variation of each parameter, and the basic reproduction number $\left({\mathcal{R}}_0\right)$ is introduced to assess local stability at two equilibrium points. The stability analysis indicates that the disease-free equilibrium point is stable when ${\mathcal{R}}_0<1$, while the endemic equilibrium point is stable when ${\mathcal{R}}_0>1$ and otherwise unstable. Numerical simulations demonstrate the model’s effectiveness in capturing realistic scenarios, particularly the recurrent patterns observed in some childhood diseases. Full article

Salmonellosis continues to be a global public health priority in which humans, livestock, and the contaminated environment interact with food to create complex interactions. Here, a new non-autonomous model is proposed to capture seasonal dynamics of Salmonella typhimurium transmission with key compartments that include humans, cattle, and bacteria in environmental and food sources. The model explores how bacterial growth, shedding, and ingestion rates, along with contamination pathways, determine disease dynamics. Some analytical derivations of the basic reproduction number (${\mathcal{R}}_0$) and threshold conditions for disease persistence or extinction are derived by using the spectral radius of a linear operator associated with the monodromy matrix. Parameter estimation for the model was accomplished with the aid of Latin hypercube sampling and least squares methods on Salmonella outbreak data from Saudi Arabia ranging from 2018 to 2021. The model was able to conduct an analysis based on the estimated 0.606 value of ${\mathcal{R}}_0$, and this meant that the model was able to fit reasonably well for both the cumulative and the new individual case data, which in turn, suggests the disease is curable. Predictions indicate a gradual decline in the number of new cases, with stabilization anticipated at approximately 40,000 cumulative cases. Further simulations examined the dynamics of disease extinction and persistence based on ${\mathcal{R}}_0$. When ${\mathcal{R}}_0$ is less than 1, the disease-free equilibrium is stable, resulting in the extinction of the disease. Conversely, when ${\mathcal{R}}_0$ exceeds 1, the disease persists, exhibiting endemic characteristics with recurrent outbreaks. Sensitivity analysis identified several parameters as having a significant impact on the model’s outcomes, specifically mortality and infection rates, along with decay rates. These findings highlight the critical importance of precise parameter estimation in understanding and controlling the transmission dynamics of Salmonella. Sensitivity indices and contour plots were employed to assess the impact of various parameters on the basic reproduction number and provide insights into the factors most influencing disease transmission. Full article