Lockdown Measures and their Impact on Single- and Two-age-structured Epidemic Model for the COVID-19 Outbreak in Mexico

Abstract

The role of lockdown measures in mitigating COVID-19 in Mexico is investigated using a comprehensive nonlinear ODE model. The model includes both asymptomatic and presymptomatic populations with the latter leading to sickness (with recovery, hospitalization and death possibilities). We consider the situation involving the imposed application of partial social distancing measures in the time series of interest and find optimal parametric fits to the time series of deaths (only), as well as to that of deaths and cumulative infections. We discuss the merits and disadvantages of each approach, we interpret the parameters of the model and assess the realistic nature of the parameters resulting from the optimization procedure. Importantly, we explore a model involving two sub-populations (younger and older than a specific age), to more accurately reflect the observed impact as concerns symptoms and behavior in different age groups. For definitiveness and to separate people that are (typically) in the active workforce, our partition of population is with respect to members younger vs. older than the age of 65. The basic reproductive number of the model is computed for both the single- and the two-population variant. Finally, we consider what would be the impact on the number of deaths and cumulative infections upon imposition of partial lockdown (involving only the older population) and full lockdown (involving the entire population).

Reaction-diffusion spatial modeling of COVID-19: Greece and Andalusia as case examples

“…This procedure led to the determination of the median values and their interquartiles. In addition, and as argued in [59], one approach to specifying confidence intervals is through the Hessian of the variation of the Euclidean norm (9), the objective function of our optimizations, with respect to model parameters [60]. Specifically, if we denote model parameters by θ the Hessian is H i j = ∂ 2 N /∂θ i ∂θ j , suggesting that if it remains invariant to parameter changes, these parameters would not be identifiable (since their changes would not modify the optimized norm).…”

“…Alternatively, as discussed in [60], the inversion of the Hessian leads to the confidence intervals associated with each parameter. When we carried out this programme for a model similar to the 0D model presented here [59], we found that the Hessian was singular: in fact, it had two zero eigenvalues. Our above line of argumentation (expanded upon in [59]) suggests that these two "zero-cost" eigendirections are closely connected to the identifiability of the model, and specifically that a number of parameters associated with these eigendirections are not independently identifiable.…”

Editorial

“…El número reproductivo básico del modelo se calculó tanto para la variante de una población como para la de dos. Sus resultados comparan el impacto de un confinamiento parcial (que involucra solo a la población mayor) y un confinamiento total (que involucra a toda la población) en el número de muertes e infecciones acumuladas (Cuevas-Maraver et al, 2021).…”