报告题目（一）：Stability and bifurcation analysis of an HIV-1 infection model with a general incidence and CTL immune response

报告人：陈玉明教授

报告时间：2021年10月30日(周六)8:30—10:00

报告地点：腾讯会议，ID：613 952 676

报告摘要：In this talk, taking into account of eclipse, wepropose an HIV-1 infection model with a general incidence rate and CTL immune response. We first study the existence and local stability of equilibria, which is characterized by the basic infection reproduction numberR₀and the basic immunity reproduction numberR₁. The local stability analysis indicates the occurrence of transcritical bifurcations of equilibria. We confirm the bifurcations at the disease-free equilibrium and the infected immune-free equilibrium with transmission rate and the decay rate of CTLs as bifurcation parameters, respectively. Then we apply the approach of Lyapunov functions to establish the global stability of the equilibria, which is determined by the two basic reproduction numbers. These theoretical results are supported with numerical simulations. Moreover, we also identify the high sensitivity parameters by carrying out the sensitivity analysis of the two basic reproduction numbers to the model parameters.

报告人简介:陈玉明，加拿大罗瑞尔大学(Wilfrid Laurier University)数学系正教授、博士生导师，主要研究兴趣为动力系统和泛函微分方程理论及其在生物数学和神经网络中的应用。已在包括SIAM Journal on Mathematical Analysis, Transactions on the American Mathematical Society, Nonlinearity, Journal of Differential Equations, Physica D, Proceedings of the American Mathematical Society，Mathematical Biosciences, Neural Networks等国际著名刊物发表论文一百三十余篇，其成果被同行广泛引用，曾获安大略省科技与创新部早期研究者奖。主持5项加拿大国家自然科学与工程理事会(NSERC)科研基金项目，参与3项中国国家自然科学基金面上项目。

报告题目（二）：Optimal control applied tomosquito-borne diseases: Malaria and WNV

报告人：丁婉菂 教授

报告时间：2021年10月30日(周六)10:00—11:30

报告地点：腾讯会议，ID：613 952 676

报告摘要：We present some optimal control work on mosquito-borne diseases: Malaria and West Nile Virus. First, a malaria transmission model with SEIR (susceptible-exposed-infected-recovered) classes for the human population, SEI (susceptible-exposed-infected) classes for the wild mosquitoes and an additional class for sterile mosquitoes is formulated. We derive the basic reproduction number of the infection. We formulate an optimal control problem in which the goal is to minimize both the infected human populations and the cost to implement two control strategies: the release of sterile mosquitoes and the usage of insecticide-treated nets to reduce the malaria transmission. Adjoint equations are derived and the characterization of the optimal controls are established. Finally, we quantify the effectiveness of the two interventions aimed at limiting the spread of Malaria. A combination of both strategies leads to a more rapid elimination of the wild mosquito population that can suppress Malaria transmission. Secondly, we consider a West-Nile Virus transmission model that describes the interaction between bird and mosquito populations (eggs, larvae, adults) and the dynamics for larvicide and adulticide, with impulse controls. We derive the basic reproduction number of the infection.We reformulate the impulse control problems as nonlinear optimization problems to deriveadjoint equations and establish optimality conditions.We formulate three optimal control problems which seek to balance the cost of insecticide applications (both the timing and application level) with (1) the benefit of reducing the number of mosquitoes, (2) the benefit of reducing the disease burden, or (3) the benefit of preserving the healthy bird population. Numerical simulations are provided to illustrate the results of both models.

报告人简介:丁婉菂，美国中田纳西州立大学数学科学系和计算与数据科学中心教授。主要研究领域是生物数学、计算生物学与最优控制。主持2项美国国家自然科学基金项目，发表SCI文章20余篇。担任Society for Mathematical Biology Digest编辑(7年)及Phi Kappa Phi中田纳西州立大学分会会长。

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