A Spatiotemporal Dynamics Study Of Two Classes Of HIV Models With Age-spatial Structure

This article takes the spread of HIV infectious diseases as the main research background,and mainly uses the basic theories and methods of the reaction-diffusion equation to study the spatiotemporal dynamics of two types of HIV models with age-space structures:one is the reaction diffusion with non-local time lag HIV model,this model derives and analyzes an HIV infection model including virus-cell infection and cell-cell infection with a fixed incubation period.The model consists of a spa-tial non-local reaction diffusion with zero flux conditions on the boundary System description.Our research results show that the elimination or persistence of HIV virus is determined by?₀.The other is an age-spatial HIV infection model with Neumann boundary conditions,which studies a kind of HIV infection model that involves virus on cells and Cell-to-cell infection pathway reaction diffusion and age structure of HIV infection model.In mathematics,we give a rigorous analysis,study the well-posedness of the model,prove the existence,uniqueness,and boundedness of the solution through the Krein-Rutman theorem and the comparison principle,and analyze the asymptotic dynamics and consistency of the solution.Sustainability is theoretically analyzed.In the case of spatial homogeneity,the basic reproduction number is established,If the basic reproduction number(threshold value)?₀<1,the disease will be extinct,and if the basic reproduction number?₀>1,the disease will continue to be consistent which controls the extinction and persistence of the disease.By studying the characteristic root distribution of the characteristic equation and constructing a suitable Lyapunov function,obtain the global asymptotic stability of the model at the disease-free equilibrium point and the endemic equilibrium point.