Julien Arino

We consider an SLIARS mathematical epidemiology model including intervention in the form of vaccination and treatment. Contrary to classical models, it is assumed that treatment doses can be limited in availability. Mathematically, we show that most scenarios actually reduce to classic well-known scenarios: having an unreplenished number of doses is akin to having none, while being able to restore stocks is (often) equivalent to the classic situation with vaccination and treatment. We also perform a computational analysis, illustrating some of the transient and stochastic dynamics that diverge from deterministic long-term behaviour, as well as the impact of budgetary constraints.

We present a methodology providing a one-directional link from within-host individual heterogeneity to population-level disease transmission dynamics. The methodology works in several steps. A within-host model is investigated numerically to determine pathogen and immunological parameters leading to the largest variation of model responses. These key parameters are used to generate a synthetic population of individuals whose temporal immunological response profiles are recorded. These responses are ranked in terms of the severity of experienced outcomes, from mild infections to death, as a function of time since infection. This is used to parametrise an age-of-infection structured epidemiological model to study the transmission dynamics of the disease at the population level. The approach is illustrated using a within-host model describing SARS-CoV-2 infection and an SIR population-level model.

We consider a model for the spread of bovine tuberculosis in herds comprising three species (bovids, caprids and equids) in Chad. The epidemiological model is built on top of a classic Lotka-Volterra competition model, which is exploited in a regime where stable coexistence of the three species holds. The epidemiological model itself is an SLI model, because of the absence of treatment for herds in the area. After studying some mathematical properties of the model, we perform a short computational analysis, investigating sensitivity of the model and comparing solutions with and without competition. To gain more understanding on the timing of events, we also consider the continuous time Markov chain analogue of the model.