Advances in Difference Equations最新文献

Nearly 80% of women are estimated to have at least one HPV infection from high-risk types. Although the majority can clear the infection through their immune system, some are at risk for cervical cancer. Persistent high-risk HPV infections are the leading cause of cervical cancer worldwide. This paper proposes a mathematical model that examines the effects of HPV transmission on cervical cancer patients under vaccine intervention. The model’s fundamental properties are investigated, including the stability of equilibrium points and the existence of forward bifurcations. Subsequently, based on cervical cancer patient data collected from Hungary between 2000 and 2020, the model’s optimal parameter values are identified using a nonlinear least squares method. Further, we perform a sensitivity analysis of the key cervical cancer progression parameters. Our results indicate that both direct HPV vaccination in susceptible populations and additional vaccination in individuals who have recovered can improve immune responses and reduce the risk of cervical cancer. In addition, the study of the effects of intervention measures on cervical cancer patients in Hungary from 2000 to 2030 reveals that reducing the contact rate is conducive in the short term to curbing the development of cervical cancer; however, in the long term, relying solely on this measure is not sufficient to lead to a significant decrease in the number of cervical cancer cases.

In this paper, biodiversity and a saturation treatment rate are introduced into a type of mosquito-borne infectious disease model with an incubation time delay. Through the dynamical analysis of the model, conditions for the existence and stability of disease-free and endemic equilibria are determined. The basic reproduction number of the model is calculated, and the condition for the existence of backward bifurcation is outlined. The study finds that under the dual influence of biodiversity and saturation treatment, the threshold characteristic of the basic reproduction number becomes invalidated. When (R_{0}) is less than 1, the model may exhibit four equilibrium states, with both the disease-free equilibrium and the endemic equilibrium being locally stable. In this scenario, whether the virus will become extinct depends on the initial conditions. The study also finds that when the basic reproduction number (R_{0}) is greater than 1, the stability of the model is influenced by the time delay, with Hopf bifurcation occurring at a specific time delay. In addition, another novel contribution of this paper is the formulation of an optimal control problem that takes into account the minimization of damage caused by humans to biodiversity. Based on the Pontryagin’s maximum principle, the specific characteristics of the optimal control measures are given, and the optimal strategy is derived by comparing five groups of control strategies. The optimal control results highlight the synergistic effect of multiple control measures with biodiversity. Under optimal control, a significant complementary effect between medical inputs and the dilution effect of biodiversity is evident. The findings imply that maintaining high biodiversity levels can decrease the demand for medical resources in mosquito-borne disease control efforts.

I present a review of the recent advancements in scattering theory, which provides a unified approach to studying dispersive and hyperbolic equations with general interaction terms and data. These equations encompass time-dependent potentials, as well as NLS, NLKG, and NLW equations. Additionally, I discuss a series of open problems along with their significance and potential future applications in scattering and inverse scattering.

This paper investigates the variational approach using nabla (denoted as ∇) within the framework of time scales. By employing two different methods, we derive the Euler-Lagrange equations for first-order variational approach to optimization problems involving exponential functions, as well as for those with both exponential functions and their ∇-derivatives. To establish the high-order variational approach to optimization problem, we present the Leibniz Formula for ∇-derivatives along with its proof. Additionally, we determine the high-order variational approach to optimization problem incorporating ∇-derivatives of exponential functions. Through these analyses, we aim to contribute to the understanding and application of the variational calculus on time scales, offering insights into the behavior of dynamic systems governed by exponential functions and their derivatives.

Background

After abandoning the zero-case strategy for COVID-19 in December 2022 in mainland China, the Hong Kong Special Administrative Region of China (HKSAR) has undergone an anticipated surge of the prevalence of COVID-19, as well as other influenzas, such as influenza A/H1N1, influenza A/H3N2, and influenza B as well. Noteworthy, people are usually concerned about the mutual influences between two families of respiratory viruses, like co-circulation or co-infection.

Methods

We fitted a unified model to weekly reported severe COVID-19 cases and the confirmed influenza A laboratory cases in HKSAR, respectively, using the R package POMP to obtain the best fitting and parameter estimates. The reconstructed transmission rates of the COVID-19 (/influenza A) versus the weekly reported influenza A (/COVID-19) confirmations between April 2022 and April 2024 were also compared.

Results

Our numerical results suggest that influenza confirmations remained either at a very low level or were absent before 2023, while starting from 2023, the influenza epidemic re-emerged as expected because of the resumption of international travels and other social communications. Besides, the peak of influenza cases in April 2023 favored the form of the peak of COVID-19 between May–June, 2023.

Additionally, during the sudden abolishment of the zero-case policy in mainland China (December 2022 to January 2023), we estimated that there were approximately 381 cases imported from mainland China into HKSAR.

Conclusions

We estimated the potential number of imported COVID-19 severe cases from mainland China to Hong Kong and revealed some potential population-level interference between the two families of respiratory viruses.

Emerging infectious diseases, such as COVID-19, manifest in outbreaks of varying magnitudes. For large-scale epidemics, continuous models are often employed for forecasting, while discrete models are preferred for smaller outbreaks. We propose a discrete susceptible-infected-susceptible model that integrates interaction between parasitism and hosts, as well as saturation recovery mechanisms, and undertake a thorough theoretical and numerical exploration of this model. Theoretically, the model incorporating nonlinear recovery demonstrates complex behavior, including backward bifurcations and the coexistence of dual equilibria. And the sufficient conditions that guarantee the global asymptotic stability of a disease-free equilibrium have been obtained. Considering the challenges posed by saturation recovery in theoretical analysis, we then consider the case of linear recovery. Bifurcation analysis for of the linear recovery model displays a variety of bifurcations at the endemic equilibrium, such as transcritical, flip, and Neimark–Sacker bifurcations. Numerical simulations reveal complex dynamic behavior, including backward and fold bifurcations, periodic windows, period-doubling cascades, and multistability. Moreover, the proposed model could be used to fit the daily COVID-19 reported cases for various regions, not only revealing the significant advantages of discrete models in fitting, evaluating, and predicting small-scale epidemics, but also playing an important role in evaluating the effectiveness of prevention and control strategies. Furthermore, sensitivity analyses for the key parameters underscore their significant impact on the effective reproduction number during the initial months of an outbreak, advocating for better medical resource allocation and the enforcement of social distancing measures to curb disease transmission.

In this study, the semi-discretization technique is employed to establish a discrete representation of a modified Leslie-Gower prey-predator system that includes a Holling II type functional response. The dynamics of this model are then analyzed through the application of center manifold theory and bifurcation theory. We present comprehensive results for the local stability of the fixed points across the entire parameter space. Additionally, we provide sufficient conditions for the occurrence of flip bifurcation and Neimark-Sacker bifurcation. Besides, the system has experienced a flip bifurcation to chaos controlled using the method of chaos control, viz., state feedback method, pole placement technique, and hybrid control strategy. Furthermore, we provide specific conditions to ensure that bifurcation and chaos can be stabilized. Finally, numerical simulations are conducted to validate theoretical analysis and illustrate several new complex dynamical behaviors between two species.

The global stability of a nonautonomous 3-species ratio-dependent diffusive predator-prey model is studied in this paper. Firstly, some easily verifiable sufficient conditions which guarantee the existence of the strictly positive space homogenous periodic solution (SHPS) of the ratio- dependent predator-prey model (RDPPM) with diffusive and variable coefficient are achieved by using a comparison theorem of differential equation and fixed point theorem. At the same time, some new analysis techniques are developed as a byproduct. Secondly, some sufficient conditions ensuring the globally asymptotically stability of the strictly positive SHPS of the diffusive nonautonomous predator-prey model are given by using the method of upper and lower solutions (UALS) for the parabolic partial differential equations and Lyapunov stability theory. In addition, two numerical examples are given to validate the theoretical results obtained in this paper.

Several factors significantly contribute to the onset of infectious diseases, including direct and indirect transmissions and their respective impacts on incubation periods. The intricate interplay of these factors within social networks remains a puzzle yet to be unraveled. In this study, we conduct a stability analysis within a network-organized SIR model incorporating dual delays to explore the influence of direct and indirect incubation periods on disease spread. Additionally, we investigate how compound networks affect the critical incubation period. Our findings reveal several vital insights. First, by examining crossing curves and the dispersion equation, we establish the conditions for Turing instability and delineate the stable regions associated with dual delays. Second, we ascertain that the critical incubation value exhibits an inverse relationship with a network’s eigenvalues, indicating that the Laplacian matrix does not solely dictate periodic behavior in the context of delays. Furthermore, our study elucidates the impact of delays and networks on pattern formation, revealing distinct pattern types across different regions. Specifically, our observations suggest that effectively curtailing the spread of infectious diseases during an outbreak is more achievable when the incubation period for indirect contact is shorter and for direct contact is longer. Namely, our network framework enables regulation of the optimal combination of ((tau _{1},tau _{2})) to mitigate the risk of infectious diseases. In summary, our results offer valuable theoretical insights that can inform strategies for preventing and managing infectious diseases.

Syphilis is a major sexually transmitted disease, causing a significant public health burden for countries all over the world. Since 2000, there has been a new outbreak of the syphilis epidemic in the United States. Therefore, the prevention and control of syphilis have important research significance. We have established a sex structure and ordinary differential equation model that includes men who have sex with men (MSM). Its epidemiological and biological parameters were obtained by fitting with regional monitoring data from the Centers for Disease Control and Prevention from 1984 to 2014, and the basic reproduction number (({mathcal{R}_{0}})) of syphilis is 1.3876. Through cost-effectiveness analysis, we have found that the most cost-effective strategies in the cases of sufficient and insufficient funds are conducting syphilis screening for 50% of sexually active susceptible individuals and conducting syphilis screening for 30% of sexually active susceptible individuals while increasing the treatment rate, respectively. Therefore, in the prevention and control strategies of syphilis, measures such as increasing the coverage rate of syphilis screening for susceptible individuals and simultaneously increasing both the screening coverage rate and the treatment rate are valuable control strategy measures for reference.