Search Results (32)

This paper is concerned with the asymptotical behavior of the impulsive linearly implicit Euler method for the SIR epidemic model with nonlinear incidence rates and proportional impulsive vaccination. We point out the solution of the impulsive linearly implicit Euler method for the impulsive SIR system is positive for arbitrary step size when the initial values are positive. By applying discrete Floquet’s theorem and small-amplitude perturbation skills, we proved that the disease-free periodic solution of the impulsive system is locally stable. Additionally, in conjunction with the discrete impulsive comparison theorem, we show that the impulsive linearly implicit Euler method maintains the global asymptotical stability of the exact solution of the impulsive system. Two numerical examples are provided to illustrate the correctness of the results. Full article

This study develops a high-dimensional impulsive differential equation model to analyze Huanglongbing (HLB) transmission dynamics, incorporating seasonal fluctuations in vector psyllid populations and multi-pronged control measures: (1) periodic removal of infected/dead citrus trees to eliminate pathogen reservoirs and (2) non-uniform pesticide applications timed to disrupt psyllid life cycles. The model analytically derives the basic reproduction number ($R_0$) and proves the existence of a unique disease-free periodic solution. Theoretical analysis reveals a threshold-dependent stability: when $R_0<1$, the disease-free solution is globally asymptotically stable, ensuring pathogen extinction; when $R_0>1$, the system becomes uniformly persistent, indicating endemic HLB. Numerical simulations validate these findings and demonstrate that integrated interventions, combining psyllid population control and removal of infected plants, can significantly suppress HLB spread. The results provide a mathematical framework for optimizing intervention timing and intensity, offering actionable strategies for citrus growers. Full article

Tissue substitution and graft transplantation are currently the best treatment options for patients suffering from severe heart diseases. However, the limited availability of donors and the restricted durability of tissues applied in cardiovascular treatments result in a constraint on applicability and a suboptimal therapeutic approach that is still not fully resolved. There are multiple ways to preserve heart tissue grafts, and the choice of method is solely dependent upon the nature and complexity of the tissue and the length of storage. The conventional cold storage method provides the base to nearly all of the preservation protocols for short- and long-term storage. Short-term storage methods frequently rely on designing preserving solutions to protect the graft against warm and cold ischemia at the temperature above freezing point. As ice-nucleation is the major notorious phenomenon during graft preservation, the modern era of research is focusing on developing ice-free preservation techniques, termed vitrification. However, despite the promising outcomes of vitrification, there are several recognized hurdles required to be overcome to build a biobank of heart grafts for an extended period of time. Besides tissue deterioration due to extreme cold temperature, there is another extreme phenomenon of tissue rejection mainly caused by the presence of cellular antigens. The modern approach of decellularization has the potential to minimize the chances of tissue rejection by removing the cells and providing a structural support and sustained biochemical signal via keeping the extracellular matrix of the graft intact. In conclusion, both nano-warming and decellularization are the leading approaches that have great potential to store the graft tissue in its optimal form via keeping its viability safe for a longer time and extending its applicability. This review article outlines a variety of approaches for the preservation and bioengineering of tissue to fulfill the need for the availability of on-shelf long-lasting grafts both in clinical and laboratory setups. Full article

Frequent outbreaks of respiratory infectious diseases, driven by diverse pathogens, have long posed significant threats to public health, economic productivity, and societal stability. Respiratory infectious diseases are highly contagious, characterized by short incubation periods, diverse symptoms, multiple transmission routes, susceptibility to mutations, and distinct seasonality, contributing to their propensity for outbreaks. The absence of effective antiviral treatments and the heightened vulnerability of individuals with weakened immune systems make them more susceptible to infection, with severe cases potentially leading to complications or death. This situation becomes particularly concerning during peak seasons, such as influenza outbreaks. Therefore, early detection, diagnosis, and treatment are critical, alongside the prevention of cross-infection, ensuring patient safety, and controlling healthcare costs. To address these challenges, this review aims to identify a comprehensive, rapid, safe, and cost-effective diagnostic approach for respiratory infectious diseases. This approach is framed within the existing hierarchical healthcare system, focusing on establishing diagnostic capabilities at hospitals, community, and home levels to effectively tackle the above issues. In addition to PCR and isothermal amplification, the review also explores emerging molecular diagnostic strategies that may better address the evolving needs of respiratory disease diagnostics. A key focus is the transition from amplification technologies to amplification-free biosensing approaches, with particular attention given to their potential for home-based testing. This shift seeks to overcome the limitations of conventional amplification methods, particularly in decentralized and home diagnostics, offering a promising solution to enhance diagnostic speed and safety during outbreaks. In the future, with the integration of AI technologies into molecular amplification technologies, biosensors, and various application levels, the inclusively economic, rapid, and safe respiratory disease diagnosis solutions will be further optimized, and their accessibility will become more widespread. Full article

In the face of global climate change, crop pests and diseases have emerged on a large scale, with diverse species lasting for long periods and exerting wide-ranging impacts. Identifying crop pests and diseases efficiently and accurately is crucial in enhancing crop yields. Nonetheless, the complexity and variety of scenarios render this a challenging task. In this paper, we propose a fine-grained crop disease classification network integrating the efficient triple attention (ETA) module and the AttentionMix data enhancement strategy. The ETA module is capable of capturing channel attention and spatial attention information more effectively, which contributes to enhancing the representational capacity of deep CNNs. Additionally, AttentionMix can effectively address the label misassignment issue in CutMix, a commonly used method for obtaining high-quality data samples. The ETA module and AttentionMix can work together on deep CNNs for greater performance gains. We conducted experiments on our self-constructed crop disease dataset and on the widely used IP102 plant pest and disease classification dataset. The results showed that the network, which combined the ETA module and AttentionMix, could reach an accuracy as high as 98.2% on our crop disease dataset. When it came to the IP102 dataset, this network achieved an accuracy of 78.7% and a recall of 70.2%. In comparison with advanced attention models such as ECANet and Triplet Attention, our proposed model exhibited an average performance improvement of 5.3% and 4.4%, respectively. All of this implies that the proposed method is both practical and applicable for classifying diseases in the majority of crop types. Based on classification results from the proposed network, an install-free WeChat mini program that enables real-time automated crop disease recognition by taking photos with a smartphone camera was developed. This study can provide an accurate and timely diagnosis of crop pests and diseases, thereby providing a solution reference for smart agriculture. Full article

In this paper, a new numerical scheme, which we call the impulsive linearly implicit Euler method, for the SIR epidemic model with pulse vaccination strategy is constructed based on the linearly implicit Euler method. The sufficient conditions for global attractivity of an infection-free periodic solution of the impulsive linearly implicit Euler method are obtained. We further show that the limit of the disease-free periodic solution of the impulsive linearly implicit Euler method is the disease-free periodic solution of the exact solution when the step size tends to 0. Finally, two numerical experiments are given to confirm the conclusions. Full article

The mathematical modeling of infectious diseases plays a vital role in understanding and predicting disease transmission, as underscored by recent global outbreaks; to delve deep into the dynamic of infectious disease considering latent period presciently is inevitable as it bridges the gap between realistic nature and mathematical modeling. This study extended the classical Susceptible–Infected–Recovered (SIR) model by incorporating vaccination strategies during incubation. We introduced multiple time delays to an account incubation period to capture realistic disease dynamics better. The model is formulated as a system of delay differential equations that describe the transmission dynamics of diseases such as polio or COVID-19, or diseases for which vaccination exists. Critical aspects of the study include proving the positivity of the model’s solutions, calculating the basic reproduction number (${\mathcal{R}}_0$) using next-generation matrix theory, and identifying disease-free and endemic equilibrium points. The local stability of these equilibria is then analyzed using the Routh–Hurwitz criterion. Due to the complexity introduced by the delay components, we examine the stability by studying the roots of a fourth-degree exponential polynomial. The effects of educational campaigns and vaccination efficacy are also investigated as control measures. Furthermore, an optimization problem is formulated, based on Pontryagin’s maximum principle, to minimize the number of infections and associated intervention costs. Numerical simulations of the delay differential equations are conducted, and a modified Runge–Kutta method with delays is used to solve the optimal control problem. Finally, we present a few simulation results to illustrate the analytical findings. Full article

This paper introduces stochastic disturbances into a semi-parametric SEIR model with infectivity in an incubation period. The model combines the randomness of disease transmission and the nonlinearity of transmission rate, providing a flexible framework for more accurate description of the process of infectious disease transmission. On the basis of the discussion of the deterministic model, the stochastic semi-parametric SEIR model is studied. Firstly, we use Lyapunov analysis to prove the existence and uniqueness of global positive solutions for the model. Secondly, the conditions for disease extinction are established, and appropriate stochastic Lyapunov functions are constructed to discuss the asymptotic behavior of the model’s solution at the disease-free equilibrium point of the deterministic model. Finally, the specific transmission functions are enumerated, and the accuracy of the results are demonstrated through numerical simulations. Full article

Taking into account the effects of the immune response and delay, and complexity on HIV-1 transmission, a multiscale AIDS/HIV-1 model is formulated in this paper. The multiscale model is described by a within-host fast time model with intracellular delay and immune delay, and a between-host slow time model with latency delay. The dynamics of the fast time model is analyzed, and includes the stability of equilibria and properties of Hopf bifurcation. Further, for the coupled slow time model without an immune response, the basic reproduction number ${\mathcal{R}}_0^h$ is defined, which determines whether the model may have zero, one, or two positive equilibria under different conditions. This implies that the slow time model demonstrates more complex dynamic behaviors, including saddle-node bifurcation, backward bifurcation, and Hopf bifurcation. For the other case, that is, the coupled slow time model with an immune response, the threshold dynamics, based on the basic reproduction number ${\tilde{\mathcal{R}}}_0^h$, is rigorously investigated. More specifically, if ${\tilde{\mathcal{R}}}_0^h<1$, the disease-free equilibrium is globally asymptotically stable; if ${\tilde{\mathcal{R}}}_0^h>1$, the model exhibits a unique endemic equilibrium that is globally asymptotically stable. With regard to the coupled slow time model with an immune response and stable periodic solution, the basic reproduction number ${\mathcal{R}}_0$ is derived, which serves as a threshold value determining whether the disease will die out or lead to periodic oscillations in its prevalence. The research results suggest that the disease is more easily controlled when hosts have an extensive immune response and the time required for new immune particles to emerge in response to antigenic stimulation is within a certain range. Finally, numerical simulations are presented to validate the main results and provide some recommendations for controlling the spread of HIV-1. Full article

Background: garlic reproduces mainly through clove planting, as sexual reproduction via seeds is uncommon. Growers encounter challenges with pathogens due to the larger size and vegetative nature of seed cloves, as well as the storage conditions conducive to fungal growth. Some Phyto-pathogenic fungi, previously unrecognized as garlic infections, can remain latent within bulb tissues long after harvest. Although outwardly healthy, these infected bulbs may develop rot under specific conditions. Aim of review: planting diseased seed cloves can contaminate field soil, with some fungal and bacterial infections persisting for extended periods. The substantial size of seed cloves makes complete eradication of deeply ingrained infections difficult, despite the use of systemic fungicides during the preplanting and postharvest phases. Additionally, viruses, resistant to fungicides, persist in vegetative material. They are prevalent in much of the garlic used for planting, and their host vectors are difficult to eliminate. To address these challenges, tissue-culture techniques are increasingly employed to produce disease-free planting stock. Key scientific concepts of the review: garlic faces a concealed spectrum of diseases that pose a global challenge, encompassing fungal threats like Fusarium’s vascular wilt and Alternaria’s moldy rot, bacterial blights, and the elusive garlic yellow stripe virus. The struggle to eliminate deeply ingrained infections is exacerbated by the substantial size of seed cloves. Moreover, viruses persist in garlic seeds, spreading through carrier vectors, and remain unaffected by fungicides. This review emphasizes eco-friendly strategies to address these challenges, focusing on preventive measures, biocontrol agents, and plant extracts. Tissue-culture techniques emerge as a promising solution for generating disease-free garlic planting material. The review advocates for ongoing research to ensure sustainable garlic cultivation, recognizing the imperative of safeguarding this culinary staple from an array of fungal and viral threats. Full article

Vector-borne diseases, being one of the most difficult infectious diseases to understand, model, and control, account for a large proportion of human infectious diseases. In the current transmission process of infectious diseases, the latent period of pathogens in vivo, the influence of media coverage, and the presence of awareness on the spread and control of diseases are important factors that cannot be ignored. Based on this, a novel vector-borne disease model with latent delay and media coverage delay is proposed to discuss the impact of these factors. First, the global existence and ultimate boundedness of solutions for this model are obtained. Further, the exact expressions for the basic reproduction number are given, from which the existence and local stability of the disease-free and endemic equilibria are analyzed. Moreover, using the delay as a bifurcation parameter, we also discuss the existence, direction, and stability of the Hopf bifurcation. Finally, some numerical examples are carried out to explain the main theoretical results and discuss the impacts of the main parameters of this model on the transmission of vector-borne disease. Full article

Mathematical models play a crucial role in predicting disease dynamics and estimating key quantities. Non-autonomous models offer the advantage of capturing temporal variations and changes in the system. In this study, we analyzed the transmission of typhoid fever in a population using a compartmental model that accounted for dynamic changes occurring periodically in the environment. First, we determined the basic reproduction number, ${\mathcal{R}}_0$, for the periodic model and derived the time-average reproduction rate, $\left[{\mathcal{R}}_0\right]$, for the non-autonomous model as well as the basic reproduction number, ${\mathcal{R}}_0^A$, for the autonomous model. We conducted an analysis to examine the global stability of the disease-free solution and endemic periodic solutions. Our findings demonstrated that when ${\mathcal{R}}_0<1$, the disease-free solution was globally asymptotically stable, indicating the extinction of typhoid fever. Conversely, when ${\mathcal{R}}_0>1$, the disease became endemic in the population, confirming the existence of positive periodic solutions. We also presented numerical simulations that supported these theoretical results. Furthermore, we conducted a sensitivity analysis of ${\mathcal{R}}_0^A$, $\left[{\mathcal{R}}_0\right]$ and the infected compartments, aiming to assess the impact of model parameters on these quantities. Our results showed that the human-to-human infection rate has a significant impact on the reproduction number, while the environment-to-human infection rate and the bacteria excretion rate affect long-cycle infections. Moreover, we examined the effects of parameter modifications and how they impact the implementing of efficient control strategies to combat TyF. Although our model is limited by the lack of precise parameter values, the qualitative results remain consistent even with alternative parameter settings. Full article

We present a nonautonomous compartmental model that incorporates vaccination and accounts for the seasonal transmission of typhoid fever. The dynamics of the system are governed by the basic reproductive number ${\mathcal{R}}_0$. This demonstrates the global stability of the disease-free solution if ${\mathcal{R}}_0<1$. On the contrary, if ${\mathcal{R}}_0>1$, the disease persists and positive periodic solutions exist. Numerical simulations validate our theoretical findings. To accurately fit typhoid fever data in Taiwan from 2008 to 2023, we use the model and estimate its parameters using Latin hypercube sampling and least squares techniques. A sensitivity analysis reveals the significant influence of parameters such as infection rates on the reproduction number. Increasing vaccination coverage, despite challenges in developing countries, reduces typhoid cases. Accessible and highly effective vaccines play a critical role in suppressing the epidemic, outweighing concerns about the efficacy of the vaccine. Investigating possible parameter changes in Taiwan highlights the importance of monitoring and managing transmission rates to prevent recurring annual epidemics. Full article

Infectious diseases include all diseases caused by the transmission of a pathogenic agent such as bacteria, viruses, parasites, prions, and fungi. They, therefore, cover a wide spectrum of benign pathologies such as colds or angina but also very serious ones such as AIDS, hepatitis, malaria, or tuberculosis. Many epidemic diseases exhibit seasonal peak periods. Studying the population behaviours due to seasonal environment becomes a necessity for predicting the risk of disease transmission and trying to control it. In this work, we considered a five-dimensional system for a fatal disease in a seasonal environment. We studied, in the first step, the autonomous system by investigating the global stability of the steady states. In a second step, we established the existence, uniqueness, positivity, and boundedness of a periodic orbit. We showed that the global dynamics are determined using the basic reproduction number denoted by ${\mathcal{R}}_0$ and calculated using the spectral radius of an integral operator. The global stability of the disease-free periodic solution was satisfied if ${\mathcal{R}}_0<1$, and we show also the persistence of the disease once ${\mathcal{R}}_0>1$. Finally, we displayed some numerical investigations supporting the theoretical findings, where the trajectories converge to a limit cycle if ${\mathcal{R}}_0>1$. Full article

In the present study, we formulate a mathematical model to understand breast cancer in the population of Saudi Arabia. We consider a mathematical model and study its mathematical results. We show that the breast cancer model possesses a unique system of solutions. The stability results are shown for the model. We consider the reported cases in Saudi Arabia for the period 2004–2016. The data are given for the female population in Saudi Arabia that is suffering from breast cancer. The data are used to obtain the values of the parameters, and then we predict the long-term behavior with the obtained numerical results. The numerical results are obtained using the proposed parameterized approach. We present graphical results for the breast cancer model under effective parameters such as ${\tau }_1$, ${\tau }_2$, and ${\tau }_3$ that cause decreasing future cases in the population of stages 3 and 4, and the disease-free condition. Chemotherapy generally increases the risk of cardiotoxicity, and, hence, our model result shows this fact. The combination of chemotherapy stages 3 and 4 and the parameters ${\tau }_1$ and ${\tau }_2$ together at a low-level rate and also treating the patients before the chemotherapy will decrease the population of cardiotoxicity. The findings of this study are intended to reduce the number of cardiotoxic patients and raise the number of patients who recover following chemotherapy, which will aid in public health decision making. Full article