New simulation model for bone formation markers in osteoporosis patients treated with once-weekly teriparatide

Daily 20-mg and once-weekly 56.5-mg teriparatide（parathyroid hormone 1–34） treatment regimens increase bone mineral density（BMD） and prevent fractures, but changes in bone turnover markers differ between the two regimens. The aim of the present study was to explain changes in bone turnover markers using once-weekly teriparatide with a simulation model. Temporary increases in bone formation markers and subsequent decreases were observed during once-weekly teriparatide treatment for 72 weeks. These observations support the hypothesis that repeated weekly teriparatide administration stimulates bone remodeling, replacing old bone with new bone and leading to a reduction in the active remodeling surface. A simulation model was developed based on the iterative remodeling cycle that occurs on residual old bone. An increase in bone formation and a subsequent decrease were observed in the preliminary simulation. For each fitted time point, the predicted value was compared to the absolute values of the bone formation and resorption markers and lumbar BMD. The simulation model strongly matched actual changes in bone turnover markers and BMD. This simulation model indicates increased bone formation marker levels in the early stage and a subsequent decrease. It is therefore concluded that remodeling-based bone formation persisted during the entire treatment period with once-weekly teriparatide.

Modelling the preventive treatment under media impact on tuberculosis:A comparison in four regions of China

Preventive treatment for people with latent Tuberculosis infection(LTBI)has aroused our great interest.In this paper,we propose and analyze a novel mathematical model of TB considering preventive treatment with media impact.The basic reproduction number R_(0)is defined by the next generation matrix method.In the case without media impact,we prove that the disease-free equilibrium is globally asymptotically stable(unstable)if R_(0)<1(R_(0)>1).Furthermore,we obtain that a unique endemic equilibrium exists when R_(0)>1,which is globally asymptotically stable in the case of permanent immunity and no media impact.We fit the model to the newly reported TB cases data from 2009 to 2019 of four regions in China and estimate the parameters.And we estimatedR_(0)=0.5013<1 in Hubei indicating that TB in Hubei will be eliminated in the future.However,the estimatedR_(0)=1.015>1 in Henan,R_(0)=1.282>1 in Jiangxi and R_(0)=1.930>1 in Xinjiang imply that TB will continue to persist in these three regions without further prevention and control measures.Besides,sensitivity analysis is carried out to illustrate the role of model parameters for TB control.Our finding reveals that appropriately improving the rate of timely treatment for actively infected people and increasing the rate of individuals with LTBI seeking preventive treatment could achieve the goal of TB elimination.In addition,another interesting finding shows that media impact can only reduce the number of active infections to a limited extent,but cannot change the prevalence of TB.

A Delayed HIV Infection Model with the Homeostatic Proliferation of CD4^(+)T Cells

In this paper,we investigate a delayed HIV infection model that considers the homeostatic prolif-eration of CD4^(+)T cells.The existence and stability of uninfected equilibrium and infected equilibria(smaller and larger ones)are studied by analyzing the characteristic equation of the system.The intracellular delay does not affect the stability of uninfected equilibrium,but it can change the stability of larger positive equilibrium and Hopf bifurcation appears inducing stable limit cycles.Furthermore,direction and stability of Hopf bifur-cation are well investigated by using the central manifold theorem and the normal form theory.The numerical simulation results show that the stability region of larger positive equilibrium becomes smaller as the increase of time delay.Moreover,when the maximum homeostatic growth rate is very small,the larger positive equilibrium is always stable.On the contrary,when the rate of supply of T cells is very small,the larger positive equilibrium is always unstable.

Modeling the effect of time delay in budget allocation to control an epidemic through awareness

The emergence of any new infectious disease poses much stress on the government to control the spread of such disease. The easy, fast and less expensive way to slow down the spread of disease is to make the population be aware of its spread and possible control mechanisms. For this purpose, government allocates some funds to make public aware through mass media, print media, pamphlets, etc. Keeping this in view, in this paper, a nonlinear mathematical model is proposed and analyzed to assess the effect of time delay in providing funds by the government to warn people. It is assumed that suscep- tible individuals contract infection through the direct contact with infected individuals; however the rate of contracting infection is a decreasing function of funds availability. The proposed model is analyzed using stability theory of delay differential equations and numerical simulations. The model analysis shows that the increase in funds to warn people reduces the number of infected individuals but delay in providing the funds desta- bilizes the interior equilibrium and may cause stability switches.

A MULTI-GROUP SVEIR EPIDEMIC MODEL WITH DISTRIBUTED DELAY AND VACCINATION

In this paper, based on a class of multi-group epidemic models of SEIR type with bilinear incidences, we introduce a vaccination compartment, leading to multi-group SVEIR model. We establish that the global dynamics are completely determined by the basic reproduction number R0V which is defined by the spectral radius of the next generation matrix. Our proofs of global stability of the equilibria utilize a graph-theoretical approach to the method of Lyapunov functionals. Mathematical results suggest that vaccination is helpful for disease control by decreasing the basic reproduction number. However, there is a necessary condition for successful elimination of disease. If the time for the vaccines to obtain immunity or the possibility for them to be infected before acquiring immunity is neglected in each group, this condition will be satisfied and the disease can always be eradicated by suitable vaccination strategies. This may lead to over evaluation for the effect of vaccination.

COEVOLUTIONARY DYNAMICS OF PREDATOR-PREY INTERACTIONS

In this paper, with the method of adaptive dynamics, we investigate the coevolution of phenotypic traits of predator and prey species. The evolutionary model is constructed from a deterministic approximation of the underlying stochastic ecological processes. Firstly, we investigate the ecological and evolutionary conditions that allow for continu- ously stable strategy and evolutionary branching. We find that evolutionary branching in the prey phenotype will occur when the frequency dependence in the prey carrying capacity is not strong. Furthermore, it is found that if the two prey branches move far away enough, the evolutionary branching in the prey phenotype will induce the sec- ondary branching in the predator phenotype. The final evolutionary outcome contains two prey and two predator species. Secondly, we show that under symmetric interactions the evolutionary model admits a supercritical Hopf bifurcation if the frequency depen- dence in the prey carrying capa.city is very weak. Evolutionary cycle is a likely outcome of the nmtation-selection processes. Finally, we find that frequency-dependent selection can drive the predator population to extinction under asymmetric interactions.