Modelling and estimation of infectious diseases in a population with heterogeneous dynamic immunity

Abstract

The paper presents a model for the evolution of an infectious disease in a population with individual-specific immunity. The immune state of an individual varies with time according to its own dynamics, depending on whether the individual is infected or not. The model involves a system of size-structured (first-order) PDEs that capture both the dynamics of the immune states and the transition between compartments consisting of infected, susceptible, etc. individuals. Due to the unavailability of precise data about the immune states of the individuals, the main focus in the paper is on developing a technique for set-membership estimations of aggregated quantities of interest. The technique involves solving specific optimization problems for the underlying PDE system and is developed up to a numerical method. Results of numerical simulations are presented for a benchmark model of SIS-type, potentially applicable to diseases like influenza and to various sexually transmitted diseases. ARTICLE HISTORY

Infection severity across scales in multi-strain immuno-epidemiological Dengue model structured by host antibody level

“…5, we display calculations of equilibrium recovered and secondary infected distributions for two different cases of waning rates (ξ), µ > ξ and µ < ξ (µ is host death rate), displaying different limiting behavior as antibody level y approaches lower bound y c . Note that we analytically derived this limit dichotomy in (37), and larger waning (µ < ξ) corresponds to larger accumulation of individuals in DHF risk window before r1 (y) → ∞ as y y c in this case. Next we perform simulations utilizing the finite difference and multi-scale method outlined in Section 4.…”

“…Recently, more complex scenarios have also been considered, such as a distribution of immunity among susceptible hosts [30] and a "pathogen size-structured" epidemic model with fully coupled feedback through variable initial pathogen load [17]. In addition, without explicitly modeling the within-host scale, several works have explored dynamic levels of host immunity in delay differential equation (DDE), PDE, and stochastic epidemic models with re-infection, immune boosting and waning [25,6,37,13]. Dengue provides a particular example where host immunity has complex and significant effects on infection dynamics across both within-host and between-host scales.…”

On the usefulness of set-membership estimation in the epidemiology of infectious diseases

“…Also, parameters may depend on the population structure and therefore lie in some infinite dimensional function space. Some results have been presented to deal with unknown initial conditions ( [19,20]), and further research may provide results regarding unknown parameter functions.…”

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

“… 2022 ; Domenech de Celles et al. 2022 ; Veliov and Widder 2016 ). To a lesser extent, the models investigated the optimal timing of vaccine administration, accounting for the waning immunity between seasons for infectious diseases such as influenza (Costantino et al.…”

“…( 2022 ) showed in a simulation study how immunological heterogeneity plays a role in determining the durability of vaccine protection. A model with heterogeneous dynamic immunity where sub-populations were structured with respect to the host immunity was developed and analysed by Veliov and Widder ( 2016 ). In all these cases investigation of control aspects was either not present or played a rather limited role.…”