Global stability and optimal control of an age-structured SVEIR epidemic model with waning immunity and relapses.

The efficacy of vaccination, incomplete treatment and disease relapse are critical challenges that must be faced to prevent and control the spread of infectious diseases. Age heterogeneity is also a crucial factor for this study. In this paper, we investigate a new age-structured SVEIR epidemic model with the nonlinear incidence rate, waning immunity, incomplete treatment and relapse.

Dynamics and optimal control of tuberculosis model with the combined effects of vaccination, treatment and contaminated environments.

Tuberculosis has affected human beings for thousands of years, and until today, tuberculosis still ranks third among 29 infectious diseases in China. However, most of the existing mathematical models consider a single factor, which is not conducive to the study of tuberculosis transmission dynamics. Therefore, this study considers the combined effects of vaccination, treatment, and contaminated environments on tuberculosis, and builds a new model with seven compartments of $ SVEITRW $ based on China's tuberculosis data.

Modelling mosquito population suppression based on competition system with strong and weak Allee effect.

Mosquito-borne diseases are threatening half of the world's population. To prevent the spread of malaria, dengue fever, or other mosquito-borne diseases, a new disease control strategy is to reduce or eradicate the wild mosquito population by releasing sterile mosquitoes. To study the effects of sterile insect technique on mosquito populations, we developed a mathematical model of constant release of sterile mosquitoes with strong and weak Allee effect and considered interspecific competition with mosquitoes.

Global dynamics of a tuberculosis model with age-dependent latency and time delays in treatment.

Since there exists heterogeneity in incubation periods of tuberculosis and a time lag between treatment and recovery. In this study, we develop a tuberculosis model that takes into account age-dependent latency and time delays in treatment to describe the transmission of tuberculosis. We first show that the solution semi-flow of the model is well-posed and has a global attractor [Formula: see text] within an infinite dimensional space [Formula: see text].

Dynamics and optimal control of a Zika model with sexual and vertical transmissions.

A new transmission model of Zika virus with three transmission routes including human transmission by mosquito bites, sexual transmission between males and females and vertical transmission is established. The basic reproduction number $ R_{0} $ is derived. When $ R_{0} < 1 $, it is proved that the disease-free equilibrium is globally stable.

Spatiotemporal dynamics for impulsive eco-epidemiological model with Crowley-Martin type functional response.

Spatiotemporal dynamics of an impulsive eco-epidemiological model with Crowley-Martin type functional responses in a heterogeneous space is studied. The ultimate boundedness of solutions is obtained. The conditions of persistence and extinction under impulsive controls are derived.

On threshold dynamics for periodic and time-delayed impulsive systems and application to a periodic disease model.

The basic reproduction ratio R of more general periodic and time-delayed impulsive model which the period of model coefficients is different from that of fixed impulsive moments, is developed. That R is the threshold parameter for the stability of the zero solution of the associated linear system is also shown. The developed theory is further applied to a swine parasitic disease model with pulse therapy.

Spatial propagation for a reaction-diffusion SI epidemic model with vertical transmission.

In this paper, we focus on spreading speed of a reaction-diffusion SI epidemic model with vertical transmission, which is a non-monotone system. More specifically, we prove that the solution of the system converges to the disease-free equilibrium as $ t \rightarrow \infty $ if $ R_{0} \leqslant 1 $ and if $ R_0 > 1 $, there exists a critical speed $ c^\diamond > 0 $ such that if $ \|x\| = ct $ with $ c \in (0, c^\diamond) $, the disease is persistent and if $ \|x\| \geqslant ct $ with $ c > c^\diamond $, the infection dies out. Finally, we illustrate the asymptotic behaviour of the solution of the system via numerical simulations.

Analysis of an age-structured tuberculosis model with treatment and relapse.

A new tuberculosis model consisting of ordinary differential equations and partial differential equations is established in this paper. The model includes latent age (i.e.

Modelling the effects of media coverage and quarantine on the COVID-19 infections in the UK.

A new COVID-19 epidemic model with media coverage and quarantine is constructed. The model allows for the susceptibles to the unconscious and conscious susceptible compartment. First, mathematical analyses establish that the global dynamics of the spread of the COVID-19 infectious disease are completely determined by the basic reproduction number .

Modeling the Effects of Meteorological Factors and Unreported Cases on Seasonal Influenza Outbreaks in Gansu Province, China.

Influenza usually breaks out seasonally in temperate regions, especially in winter, infection rates and mortality rates of influenza increase significantly, which means that dry air and cold temperatures accelerate the spread of influenza viruses. However, the meteorological factors that lead to seasonal influenza outbreaks and how these meteorological factors play a decisive role in influenza transmission remain unclear. During the epidemic of infectious diseases, the neglect of unreported cases leads to an underestimation of infection rates and basic reproduction number.

Dynamics of an edge-based SEIR model for sexually transmitted diseases.

A new edge-based sexually transmitted SEIR model on the contact network is introduced in this paper. The contact infection between the opposite sex and no infectivity during the latent period on bipartite networks are included. The basic reproduction number and the equations of the final size of epidemic are derived.

Analysis of the SAITS alcoholism model on scale-free networks with demographic and nonlinear infectivity.

A more realistic alcoholism model on scale-free networks with demographic and nonlinear infectivity is introduced in this paper. The basic reproduction number [Formula: see text] is derived from the next-generation method. Global stability of the alcohol-free equilibrium is obtained.

CRISPR/Cas9-mediated LMP1 knockout inhibits Epstein-Barr virus infection and nasopharyngeal carcinoma cell growth.

Background: A strong association between Epstein-Barr virus (EBV) infection and nasopharyngeal carcinoma (NPC) has been widely recognized in recent decades. The aim of the present study was to investigate latent membrane protein 1 (LMP1) regulation of nasopharyngeal carcinoma (NPC) CNE-2 cell growth and then examine the effects of LMP1-knockout with CRISPR (Clustered Regularly Interspaced Short Palindromic Repeats)/Cas9on Epstein-Barr virus (EBV) infection and CNE-2 cell growth.

Methods: Human NPC CNE-2 cells were infected with the recombinant LMP1- and LMP2A-carrying lentivirus, and then examined for cell growth with the colony forming assay as well as for the activation of transcription of eukaryotic translation initiation factor 4E (eIF4E) with reverse-transcriptase quantitative polymerase chain reaction (RT-qPCR) and western blot.

Modelling and analysis of an alcoholism model with treatment and effect of Twitter.

A new alcoholism model with treatment and effect of Twitter is introduced. The stability of all equilibria which is determined by the basic reproductive number ro is obtained. The occurrence of backward and forward bifurcation for a certain defined range of ro are established by the center manifold theory.

Hopf bifurcation of an age-structured HIV infection model with logistic target-cell growth.

In this paper, we investigate an age-structured HIV infection model with logistic growth for target cell. We rewrite the model as an abstract non-densely defined Cauchy problem and obtain the condition which guarantees the existence of the unique positive steady state. By linearizing the model at steady state and analysing the associated characteristic transcendental equations, we study the local asymptotic stability of the steady state.

Bifurcation analysis of an age-structured alcoholism model.

In this paper, we investigate a new alcoholism model in which alcoholics have age structure. We rewrite the model as an abstract non-densely defined Cauchy problem and obtain the condition which guarantees the existence of the unique positive steady state. By linearizing the model at steady state and analyzing the associated characteristic transcendental equations, we study the local asymptotic stability of the steady state.

RPA1 downregulation enhances nasopharyngeal cancer radiosensitivity via blocking RAD51 to the DNA damage site.

Background/aim: Nasopharyngeal cancer (NPC) has a high local recurrence rate due to its resistance to ionizing radiation (IR). Replication protein A1 (RPA1) is one of the main elements in the homologous repair (HR) pathway, which is closely associated with the repair of DNA double strand breaks (DDBs). Studies on the relationship between RPA1 and the radiosensitivity of NPC are substantially limited.

Dynamics analysis of a predator-prey system with harvesting prey and disease in prey species.

In this paper, a predator-prey system with harvesting prey and disease in prey species is given. In the absence of time delay, the existence and stability of all equilibria are investigated. In the presence of time delay, some sufficient conditions of the local stability of the positive equilibrium and the existence of Hopf bifurcation are obtained by analysing the corresponding characteristic equation, and the properties of Hopf bifurcation are given by using the normal form theory and centre manifold theorem.

Modelling the effect of immigration on drinking behaviour.

A drinking model with immigration is constructed. For the model with problem drinking immigration, the model admits only one problem drinking equilibrium. For the model without problem drinking immigration, the model has two equilibria, one is problem drinking-free equilibrium and the other is problem drinking equilibrium.

Optimal control of a social epidemic model with media coverage.

A new social epidemic model to depict alcoholism with media coverage is proposed in this paper. Some fundamental properties of the model including existence and positivity as well as boundedness of equilibria are investigated. Stability of all equilibria are studied.

Stability of a binge drinking model with delay.

A more realistic binge drinking model with time delay is introduced. Time delay is used to represent the time lag of the immunity against drinking in our model. For the model without the time delay, using Routh-Hurwitz criterion, we obtain that the alcohol-free equilibrium is locally asymptotically stable if [Formula: see text].

Complex dynamics in an alcoholism model with the impact of Twitter.

A novel alcoholism model which involves impact of Twitter is formulated. It is shown that the model has multiple equilibria. Stability of all the equilibria are obtained in terms of the basic reproductive number R.

The analysis of the SIRS alcoholism models with relapse on weighted networks.

Two SIRS alcoholism models with relapse on networks with fixed and adaptive weight are introduced. The spread of alcoholism threshold [Formula: see text] is calculated by the next generation matrix method. For the model with fixed weight, we prove that when [Formula: see text] the alcohol free equilibrium is globally asymptotically stable, then the drinking crowd gradually disappear.

Impact of media coverage on the drinking dynamics in the scale-free network.

A binge drinking model with the impact of media in the scale-free network is proposed. The basic reproduction number [Formula: see text] is derived by the next generation matrix method. Stability of the alcohol free equilibrium is proved by the comparison theorem.