This talk is concerned with the optimal harvesting of a predator–prey model with a prey refuge and imprecise biological parameters. We consider the model under impreciseness and introduce a parametric functional form of an interval which differs from those of models with precise biological parameters. The existence of all possible equilibria and stability of system are discussed. The bionomic equilibrium of the model is analyzed. Also, the optimal harvesting policy is derived using Pontryagin’s maximal principle. Numerical simulations are presented to verify the feasibilities of our analytical results.

An epidemic model for yellow fever virus is formulated and used to study the 2016 yellow fever (YF) outbreak in Luanda, Angola. We explore the complex vector-host dynamics of this system taking into account mosquito abundance, vaccination and asymptomatic cases in the human population, that are generally not included in other modelling studies of YF. The model successfully fits existing time-series of weekly reported cases and deaths from YF during the epidemic. This allows us to study the impact of the vaccination campaign in Luanda and hypothetical delayed vaccination scenarios.

The Lyapunov functionals are very useful for the analysis of the global asymptotic behavior of the delay differential equations models. In this talk, we present several delay epidemiological models, in which time delays appear in different position of models and describe different biological meanings. Several Lyapunov functionals were applied to delay models above. And we develop further the Lyapunov functional to more delay differential equations in population dynamics.

Diapause (or named as dormancy traditionally) as a process of physiological rest is widespread in insects and other invertebrate organisms, which serves as a key survival mechanism in response to adverse environmental conditions. In this paper, a novel modelling framework is proposed to investigate the effects of diapause on population growth, where diapause period is taken as an independent dynamic process, during which the population dynamics is completely different from that in the normal developmental and post-diapause periods. To explicitly describe population growth with different diapausing stages, either immature or adult ones, two different delay differential equation models are constructed with an emphasis on mosquitoes.

In this talk, we will prove the dual log-Brunn-Minkowski inequality and the dual log-Minkowski inequality. Moreover, the equivalence between the dual log-Brunn-Minkowski inequality and the dual log-Minkowski inequality is demonstrated.

One of the fifty problems of dynamical systems formulated by J. Palis and C. Pugh is the problem of the existence of a simple arc joining two structural stable systems on a smooth closed manifold [1]. Simplicity means that the arc consists of structural stable systems with the exception of a finite set of points where the system has the least deviation from a rough system, that is simple bifurcations: a saddle-node, a doubling period or a bifurcation of a heteroclinic tangency. We show that by means of such arc it is possible to change the dimension of a basic set. Namely we joint arbitrary structural stable 3-diffeomorphism with an expanding two-dimensional attractor with an Anosov diffeomorphism.

We consider astrophysical systems that are modeled by the multidimensional Euler equations with gravity. First for the homogeneous Euler equations we look at flow in the low Mach number regime. Here for conventional finite volume discretization one has excessive dissipation in this regime. We identify inconsistent scaling for low Mach numbers of the numerical flux function as the origin of this problem. Based on the Roe solver a technique that allows to correctly represent low Mach number flows with a discretization of the compressible Euler equations is proposed. We analyze properties of this scheme and demonstrate that its limit yields a discretization of the incompressible limit system.

We consider the dynamic vector-host-pathogen interaction motivated by such tick borne diseases as tick-borne encephalitis and Lyme disease. We stratify the vector population in terms of the stage before and after the contact with the host when co-feeding transmission may take place, and we consider the case where vector development may involve two time lags due to diapause. We derive and calculate the critical rate for the model to exhibit nonlinear oscillations.