The Multi-Compartment SI(RD) Model with Regime Switching: An Application to COVID-19 Pandemic

Abstract

We study—with existence and unicity results—a variant of the SIR model for an infectious disease incorporating both the possibility of a death outcome—in a short period of time—and a regime switch that can account for the mitigation measures used to control the spreading of the infections, such as a total lockdown. This model is parametrised by three parameters: the basic reproduction number, the mortality rate of the infected, and the duration of the disease. We discuss a particular example of application to Portuguese COVID-19 data in two short periods just after the start of the epidemic in 4 March 2020, with the first two cases dated that day. We propose a simple and effective method for the estimation of the main parameters of the disease, namely, the basic reproduction number and the mortality rate of the infected. We correct these estimated values to take into account the asymptomatic non-diagnosed members of the population. We compare the outcome of the model in the cases of the existence, or not, of a regime switch, and under three different scenarios, with a remarkable agreement between model and data deaths in the case of our basis scenario. In a final short remark, we deal with the existence of symmetries for the proposed model.

Estimation–Calibration of Continuous-Time Non-Homogeneous Markov Chains with Finite State Space

“…The general motivation for the study of regime switching in ODE can be seen in [23,24]. Let us elaborate on the motivation to study regime-switching Markov chains.…”

“…in different subintervals of the whole time period. Our study of ordinary differential Equations (ODE) with regimes that began with the work [23] and was exploited in [24] is based on general results of existence and uniqueness of solutions of ODE-due to Caratheodory and Wintner for existence and Osgood for uniqueness, among others-with a non-regular second member. In the case of a second member of the non-regular ODE, the regimes appear clearly in the solutions of the Kolmogorov equations due, for example, to possible discontinuities in the entries of the intensity matrix.…”

An optimal control model for Covid-19 spread with impacts of vaccination and facemask

“…Using a combination of Divide-And-Conquer and Re-Aggregation strategies, the authors demonstrated the viability of this approach against a simulated version of the vaccination program in Greece during the 2020-21 pandemic peaks in Europe. [9] presented a study incorporating a dual-mode variation of a SIR model covering both fatality probability within a set period of time as well as the ability to model the impact of mitigation (lockdown) procedures against the spread of infections. The variation model includes novel estimation methods for the parameters corresponding to mortality rates, reproduction rates, and the time-span of the pandemic.…”

“… Approach Similarity with our work/limitation(weaknesses) [8] Mixed Integer Linear Programming Model for cost optimizing Both studies cost /Not taking the effects of wearing a face mask into consideration. [9] variation of a SIR model Mitigation measures used to control the spread of infections / Not taking the effects of wearing a face mask or of vaccines into consideration. [10] fractional ODEs with variables modeling the five SEIQR Similar compartments from Susceptible to Recovered / Not taking the effects of wearing a face mask, the cost and losses associated with the spread of COVID-19 into consideration.…”

On a Novel Dynamics of SEIR Epidemic Models with a Potential Application to COVID-19

“…Epidemic models are widely applied and helpful to different purposes. Diverse types of epidemic models are available in the literature [1][2][3][4], such as susceptible, infected, recovered (SIR) and its variants: exposed (SEIR), SEIR-asymptomatic (SEIAR), vaccinated (SVIR), SEIAR-vaccinated (SEVIAR), SVIR-asymptomatic (SAVIR), with deceased (SIRD), cross-immunity component (SIRC), and with quarantine (SIRQ).…”