Search

Hepatitis B is a disease that damages the liver, and its control has become a public health problem that needs to be solved urgently. In this paper, we investigate analytically and numerically the dynamics of a new stochastic HBV infection model with antiviral therapies and immune response represented by CTL cells. Through using the theory of stochastic differential equations, constructing appropriate Lyapunov functions and applying Itô's formula, we prove that the disease-free equilibrium of the stochastic HBV model is stochastically asymptotically stable in the large, which reveals that the HBV infection will be eradicated with probability one. Moreover, the asymptotic behavior of globally positive solution of the stochastic model near the endemic equilibrium of the corresponding deterministic HBV model is studied. By using the Milstein's method, we provide the numerical simulations to support the analysis results, which shows that sufficiently small noise will not change the dynamic behavior, while large noise can induce the disappearance of the infection. In addition, the effect of inhibiting virus production is more significant than that of blocking new infection to some extent, and the combination of two treatment methods may be the better way to reduce HBV infection and the concentration of free virus.

In this paper, considering the proven role of exosomes and the inevitable randomization within-host, we establish a hepatitis B virus (HBV) model with cell-to-cell transmission and CTL immune response from a deterministic framework to a stochastic differential equation (SDE). By introducing the reproduction number $R_0$, we prove that $R_0$ can be used to govern the stochastic dynamics of the SDE HBV model. Under certain assumptions, if $R_{0}\leq1$, the solution of the SDE model always fluctuates around the infection-free equilibrium of the deterministic model, which indicates that the HBV will eventually disappear almost surely; if $R_{0}>1$, under extra conditions, the solution of the SDE model fluctuates around endemic equilibrium of the corresponding deterministic model, which leads to the stochastic persistence of the HBV with probability one. One of the most interesting findings is that the fluctuation amplitude is positively related to the intensity of the white noise, which can provide us some useful control strategies to regulate HBV infection dynamics.

In theory, pure competition often leads to competitive exclusion of species. However, what we often see in nature is a large number of distinct predator or consumer species coexist in a community consisting a smaller number of prey or plant species. In an effort of dissecting how indirect competition and selective predation may have contributed to the coexistence of species in an insect community, according to the replicated cage experiments (two aphid species and a specialist parasitoid that attacks only one of the aphids) and proposed mathematical models, van Veen et. al. [5] conclude that the coexistence of the three species is due to a combination of density-mediated and trait-mediated indirect interactions. In this paper, we formulate an alternative model that observes the conventional law of mass conservation and provides a better fitting to their experimental data sets. Moreover, we present an initial attempt in studying the stabilities of the nonnegative steady states of this model.

A new mathematical model was proposed to study the effect of self-proliferation and delayed activation of immune cells in the process of virus infection. The global stability of the boundary equilibria was obtained by constructing appropriate Lyapunov functional. For positive equilibrium, the conditions of stability and Hopf bifurcation were obtained by taking the delay as the bifurcation parameter. Furthermore, the direction and stability of the Hopf bifurcation are derived by using the theory of normal form and center manifold. These results indicate that self-proliferation intensity can significantly affect the kinetics of viral infection, and the delayed activation of immune cells can induce periodic oscillation scenario. Along with the increase of delay time, numerical simulations give the corresponding bifurcation diagrams under different self-proliferation rates, and verify that there exists stability switch phenomenon under some conditions.

The outbreak of coronavirus disease 2019 (COVID-19) in Wuhan, which is caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), is still severe. In order to optimize the epidemic response strategy, it is urgent to evaluate the implemented prevention and control interventions (PCIs). Based on the reported data of Chongqing and Guizhou Provinces, the phased dynamic models of COVID-19 were constructed, the average intensity of the existing PCIs (from January 25 to March 2) was estimated in these two provinces. The results indicate that both provinces have carried out better control of the infected, but there are still differences in the intensity of control for people who need close observation. Especially in Chongqing, the estimated strength is significantly smaller than that in Guizhou. Furthermore, qualitative evaluations on the epidemic of COVID-19 under different PCIs scenarios suggest that containment strategy is still necessary to ensure the safety of resumption of work and school, and quarantining the city of Wuhan is an important and effective containment strategy to reduce the epidemic in other provinces.

Background: Several outbreaks of severe hand-foot-mouth disease (HFMD) in East Asia and Southwest Asia in recent years have had a serious impact on the countries. However, the factors that contribute to annual multiple-peak pattern of HFMD outbreaks, and how and when do these factors play the decisive role in the HFMD transmission is still unclear. Methods: Based on the surveillance data of HFMD between 1 January 2010 to 31 December 2015 in Wenzhou, China, the daily modelfree basic reproduction number and its annual average were first estimated by incorporating incubation and infection information, then the annual model-based basic reproduction number was computed by the proposed kinetic model, and finally the potential impact factors of multiple-peak pattern are assessed through the global and time-varying sensitivity analyses. Results: All annual model-based and model-free basic reproduction numbers were significantly higher than one. The school opening both in the spring and fall semester, meteorological e ect in the spring semester, and the interactions among them were strongly correlated with the annual model-based basic reproduction number, which were the main underlying factors on the annual multiple-peak pattern of HFMD outbreaks. Conclusions: School opening was primarily responsible for peaks of HFMD outbreaks and meteorological factors in the spring semester should also be highly concerned. The optimum timing for social distance implementation is at the beginning of every school semester and health education focusing on personal hygiene and good sanitation should be highlighted in the spring semester.