Modeling the COVID-19 pandemic: a primer and overview of mathematical epidemiology

Abstract

Since the start of the still ongoing COVID-19 pandemic, there have been many modeling efforts to assess several issues of importance to public health. In this work, we review the theory behind some important mathematical models that have been used to answer questions raised by the development of the pandemic. We start revisiting the basic properties of simple Kermack-McKendrick type models. Then, we discuss extensions of such models and important epidemiological quantities applied to investigate the role of heterogeneity in disease transmission e.g. mixing functions and superspreading events, the impact of non-pharmaceutical interventions in the control of the pandemic, vaccine deployment, herd-immunity, viral evolution and the possibility of vaccine escape. From the perspective of mathematical epidemiology, we highlight the important properties, findings, and, of course, deficiencies, that all these models have.

Analysis of multi-strain infection of vaccinated and recovered population through epidemic model: Application to COVID-19

“…this reason, we chose q 1 and q 2 to be in the interval [0, 0.63]. In their paper, Saldana [59] shows that about 80% of infection was asymptomatic with average incubation and recovery time of 5 and 10 days, respectively. Also, Hay et al [37] shows that the mean duration of Delta and Omicron's infections is 10.9 days and 9.87 days, with 95% confidence intervals (8.83, 10.9) and (9.41, 12.4), respectively.…”

Mathematical appraisal of SARS-CoV-2 Omicron epidemic outbreak in unprecedented Shanghai lockdown

“…the possibilities of transition of individuals from one disease stage to another (compartments) in the stochastic framework (11). While, deterministically, ordinary differential equations (ODEs) can be applied to approximate the possibilities, which are sufficient to describe the spreading (12). There have been several fundamental/basic mathematical models that can be applied to epidemics (i.e., mathematical epidemiology), for instance, the simplistic SIR model, the SIS model, the SEIR model, and the SEAIR model (11,13).…”

“…SIS premise is that there is no immunity forever for individuals and the infected would return to the susceptible stage again, while SEIR introduces the exposed stage into the whole system, where individuals ingest the pathogen but show no capacity to infect others (13). These models can provide essential information about the epidemic spreading, such as (1) R 0 (basic reproduction number) without the estimation of the initial susceptible population; (2) The epidemic threshold, separating two phases of the epidemic; (3) The final epidemic size (FES); and (4) The endemic equilibrium (10)(11)(12)(13). In addition, it can inform us how to reduce the contagion, for example, adequate pre-emptive vaccination coverage to the formation of herd immunity, reduction of µ, and minimization of φ.…”

The race to understand immunopathology in COVID-19: Perspectives on the impact of quantitative approaches to understand within-host interactions

“…Note that this review does not cover epidemiological models. For further reading on contributions in this field, please see, for example, Iranzo and Pérez-González [1] or Saldaño and Velasco-Hernández [2] . Our review is divided into six sections.…”