An age-dependent immuno-epidemiological model with distributed recovery and death rates

Multiple pandemic waves vs multi-period/multi-phasic epidemics: Global shape of the COVID-19 pandemic

The overall course of the COVID-19 pandemic in Western countries has been characterized by complex sequences of phases. In the period before the arrival of vaccines, these phases were mainly due to the alternation between the strengthening/lifting of social distancing measures, with the aim to balance the protection of health and that of the society as a whole. After the arrival of vaccines, this multi-phasic character was further emphasized by the complicated deployment of vaccination campaigns and the onset of virus' variants. To cope with this multi-phasic character, we propose a theoretical approach to the modeling of overall pandemic courses, that we term multi-period/multi-phasic, based on a specific definition of phase. This allows a unified and parsimonious representation of complex epidemic courses even when vaccination and virus' variants are considered, through sequences of weak ergodic renewal equations that become fully ergodic when appropriate conditions are met. Specific hypotheses on epidemiological and intervention parameters allow reduction to simple models. The framework suggest a simple, theory driven, approach to data explanation that allows an accurate reproduction of the overall course of the COVID-19 epidemic in Italy since its beginning (February 2020) up to omicron onset, confirming the validity of the concept.

Effect of vaccine dose intervals: Considering immunity levels, vaccine efficacy, and strain variants for disease control strategy

In this study, we present an immuno-epidemic model to understand mitigation options during an epidemic break. The model incorporates comorbidity and multiple-vaccine doses through a system of coupled integro-differential equations to analyze the epidemic rate and intensity from a knowledge of the basic reproduction number and time-distributed rate functions. Our modeling results show that the interval between vaccine doses is a key control parameter that can be tuned to significantly influence disease spread. We show that multiple doses induce a hysteresis effect in immunity levels that offers a better mitigation alternative compared to frequent vaccination which is less cost-effective while being more intrusive. Optimal dosing intervals, emphasizing the cost-effectiveness of each vaccination effort, and determined by various factors such as the level of immunity and efficacy of vaccines against different strains, appear to be crucial in disease management. The model is sufficiently generic that can be extended to accommodate specific disease forms.

Mathematical model explains differences in Omicron and Delta SARS-CoV-2 dynamics in Caco-2 and Calu-3 cells

Within-host infection dynamics of Omicron dramatically differs from previous variants of SARS-CoV-2. However, little is still known about which parameters of virus-cell interplay contribute to the observed attenuated replication and pathogenicity of Omicron. Mathematical models, often expressed as systems of differential equations, are frequently employed to study the infection dynamics of various viruses. Adopting such models for results of in vitro experiments can be beneficial in a number of aspects, such as model simplification (e.g., the absence of adaptive immune response and innate immunity cells), better measurement accuracy, and the possibility to measure additional data types in comparison with in vivo case. In this study, we consider a refinement of our previously developed and validated model based on a system of integro-differential equations. We fit the model to the experimental data of Omicron and Delta infections in Caco-2 (human intestinal epithelium model) and Calu-3 (lung epithelium model) cell lines. The data include known information on initial conditions, infectious virus titers, and intracellular viral RNA measurements at several time points post-infection. The model accurately explains the experimental data for both variants in both cell lines using only three variant- and cell-line-specific parameters. Namely, the cell entry rate is significantly lower for Omicron, and Omicron triggers a stronger cytokine production rate (i.e., innate immune response) in infected cells, ultimately making uninfected cells resistant to the virus. Notably, differences in only a single parameter (e.g., cell entry rate) are insufficient to obtain a reliable model fit for the experimental data.