An immuno-epidemiological model with waning immunity after infection or vaccination.

In epidemics, waning immunity is common after infection or vaccination of individuals. Immunity levels are highly heterogeneous and dynamic. This work presents an immuno-epidemiological model that captures the fundamental dynamic features of immunity acquisition and wane after infection or vaccination and analyzes mathematically its dynamical properties.

A mathematical model for the within-host (re)infection dynamics of SARS-CoV-2.

Interactions between SARS-CoV-2 and the immune system during infection are complex. However, understanding the within-host SARS-CoV-2 dynamics is of enormous importance for clinical and public health outcomes. Current mathematical models focus on describing the within-host SARS-CoV-2 dynamics during the acute infection phase.

On the solution stability of parabolic optimal control problems.

The paper investigates stability properties of solutions of optimal control problems constrained by semilinear parabolic partial differential equations. Hölder or Lipschitz dependence of the optimal solution on perturbations are obtained for problems in which the equation and the objective functional are affine with respect to the control. The perturbations may appear in both the equation and in the objective functional and may nonlinearly depend on the state and control variables.

Optimal vaccination strategies using a distributed model applied to COVID-19.

Optimal distribution of vaccines to achieve high population immunity levels is a desirable aim in infectious disease epidemiology. A distributed optimal control epidemiological model that accounts for vaccination was developed and applied to the case of the COVID-19 pandemic. The model proposed here is nonstandard and takes into account the heterogeneity of the infected sub-population with respect to the time since infection, which is essential in the case of COVID-19.

Set-membership estimations for the evolution of infectious diseases in heterogeneous populations.

The paper presents an approach for set-membership estimation of the state of a heterogeneous population in which an infectious disease is spreading. The population state may consist of susceptible, infected, recovered, etc. groups, where the individuals are heterogeneous with respect to traits, relevant to the particular disease.

On the effect of population heterogeneity on dynamics of epidemic diseases.

The paper investigates a class of SIS models of the evolution of an infectious disease in a heterogeneous population. The heterogeneity reflects individual differences in the susceptibility or in the contact rates and leads to a distributed parameter system, requiring therefore, distributed initial data, which are often not available. It is shown that there exists a corresponding homogeneous (ODE) population model that gives the same aggregated results as the distributed one, at least in the expansion phase of the disease.