Oscillatory Dynamics of Heterogeneous Stem Cell Regeneration

Stem cell regeneration is an essential biological process in the maintenance of tissue homeostasis;dysregulation of stem cell regeneration may result in dynamic diseases that show oscillations in cell numbers.Cell heterogeneity and plasticity are necessary for the dynamic equilibrium of tissue homeostasis;however,how these features may affect the oscillatory dynamics of the stem cell regeneration process remains poorly understood.Here,based on a mathematical model of heterogeneous stem cell regeneration that includes cell heterogeneity and random transition of epigenetic states,we study the conditions to have oscillation solutions through bifurcation analysis and numerical simulations.Our results show various model system dynamics with changes in different parameters associated with kinetic rates,cellular heterogeneity,and plasticity.We show that introducing heterogeneity and plasticity to cells can result in oscillation dynamics,as we have seen in the homogeneous stem cell regeneration system.However,increasing the cell heterogeneity and plasticity intends to maintain tissue homeostasis under certain conditions.The current study is an initiatory investigation of how cell heterogeneity and plasticity may affect stem cell regeneration dynamics,and many questions remain to be further studied both biologically and mathematically.

害虫治理SI模型的最优脉冲控制策略

考虑到农药的副作用,释放有病害虫作为一种有价值的非化学工具在害虫治理的过程中变得越来越重要.受到Xiang(2009)和Bhattacharyya等人(2006)工作的启发,该文研究了一类害虫管理SI传染病模型.虽然该模型具有多种动力学行为但易感害虫不能灭绝.为此,在该模型中引入多次脉冲干预措施,得到了易感害虫灭绝周期解全局渐近稳定的充分条件.然而,从生态和经济方面来说,让易感害虫灭绝的策略是不可取的,这是因为田间适当数量的害虫对于保护天敌,以及维持农作物的经济补偿是有益的.因此,用最小的成本最小化害虫在终端时刻的数量,基于不同的控制策略,三种最优害虫控制问题被详细研究.通过时间缩放和时间平移变换的方法,计算了目标函数关于脉冲时间间隔,农药致死率和病虫释放量的梯度,这对获得最优害虫控制策略是至关重要的.最后,数值模拟的结果显示,与其他两种策略相比,非固定时刻的交替综合控制策略是最有效的.另外,通过对比发现,该文提出的策略比害虫灭绝策略更可取.

Modelling COVID-19 epidemic with confirmed cases-driven contact tracing quarantine

The pandemic of novel coronavirus disease 2019(COVID-19)has been a severe threat to public health.The policy of close contract tracing quarantine is an effective strategy in controlling the COVID-19 epidemic outbreak.In this paper,we developed a mathematical model of the COVID-19 epidemic with confirmed case-driven contact tracing quarantine,and applied the model to evaluate the effectiveness of the policy of contact tracing and quarantine.The model is established based on the combination of the compartmental model and individual-based model simulations,which results in a closed-form delay differential equation model.The proposed model includes a novel form of quarantine functions to represent the number of quarantine individuals following the confirmed cases every day and provides analytic expressions to study the effects of changing the quarantine rate.The proposed model can be applied to epidemic dynamics during the period of community spread and when the policy of confirmed cases-driven contact tracing quarantine is efficient.We applied the model to study the effectiveness of contact tracing and quarantine.The proposed delay differential equation model can describe the average epidemic dynamics of the stochastic-individual-based model,however,it is not enough to describe the diverse response due to the stochastic effect.Based on model simulations,we found that the policy of contact tracing and quarantine can obviously reduce the epidemic size,however,may not be enough to achieve zero-infectious in a short time,a combination of close contact quarantine and social contact restriction is required to achieve zeroinfectious.Moreover,the effect of reducing epidemic size is insensitive to the period of quarantine,there are no significant changes in the epidemic dynamics when the quarantine days vary from 7 to 21 days.

Optimal control problem in an epidemic disease SIS model with stages and delays

Based on literature [J. Q. Li, Z. E. Ma and F. Q. Zhang, Stability analysis for an epidemic model with stage structure, J. Appl. Math. Comput. 9 （2008） 1672-1679], incorporating the recovery of the infected population with the length of the infectious periods, a modified epidemic disease SIS model with delay and stage was investigated. First, the criteria keeping stability with delay were given. Next, in order to lower the level of the infected individuals and minimize the cost of treatment, mixed, early and late therapeutic strategies were introduced into our model, respectively. Then we investigated the existence and uniqueness of optimal controls. And then, we expressed the unique optimal control in terms of the solution of the optimality systems. Finally, by numerical simulations, several important results were acquired： （1） The terminal time influenced the early optimal control largely. In detail, for a shorter terminal time it was optimal to initiate treatment with maximal effort at the start of the epidemic and continue treatment with maximal effort until the switch time was arrived. But for a longer terminal time, the maximal treatment effort need not be a prerequisite at the start or end of the epidemic but it was obligatory at the metaphase of the epidemic. （2） For our SIS model, minimizing the total infectious burden of the disease can be achieved by only early optimal treatment tactics. （3） For a disease with a shorter infectious period time,more cost would be spent to control the disease in order to achieve the optimal control objective. Otherwise, a relative lower cost would be to control the disease with a longer infectious period.

Analysis and optimization based on a sex pheromone and pesticide pest model with gestation delay

Sex pheromone,aiming at mating disruption (MD),being species specific and leaving no toxic residues in the produce grown,offers an attractive alternative to conventional pesticides.In this paper,by incorporating the gestation delay and sex pheromone,we explore the impact of MD control on the dynamic behaviors of pest system.Firstly,the boundness,stability and bifurcation of system are deliberated.Secondly,an optimal control problem based on sex pheromone and pesticide is transformed into an equivalent optimal parameter selection problem by introducing the constrain violation function.Additionally,the gradients of the cost function with respect to the dose of sex pheromone and the killing rate are given.Furthermore,simulations are executed to validate the validity of our method.Meanwhile,our results indicate that gestation delay increases the extinction risk of the population and liberating sex pheromone destroys the stability of equilibrium states.