Joint impacts of media, vaccination and treatment on an epidemic Filippov model with application to COVID-19

Abstract

A non-smooth SIR Filippov system is proposed to investigate the impacts of three control strategies (media coverage, vaccination and treatment) on the spread of an infectious disease. We synthetically consider both the number of infected population and its changing rate as the switching condition to implement the curing measures. By using the properties of the Lambert W function, we convert the proposed switching condition to a threshold value related to the susceptible population. The classical epidemic model involving media coverage, linear functions describing injecting vaccine and treatment strategies is examined when the susceptible population exceeds the threshold value. In addition, we consider another SIR model accompanied with the vaccination and treatment strategies represented by saturation functions when the susceptible population is smaller than the threshold value. The dynamics of these two subsystems and the sliding domain are discussed in detail. Four types of local sliding bifurcation are investigated, including boundary focus, boundary node, boundary saddle and boundary saddle-node bifurcations. In the meantime, the global bifurcation involving the appearance of limit cycles is examined, including touching bifurcation, homoclinic bifurcation to the pseudo-saddle and crossing bifurcation. Furthermore, the influence of some key parameters related to the three treatment strategies is explored. We also validate our model by the epidemic data sets of A/H1N1 and COVID-19, which can be employed to reveal the effects of media report and existing strategy related to the control of emerging infectious diseases on the variations of confirmed cases.

Long-term predictions of current confirmed and dead cases of COVID-19 in China by the non-autonomous delayed epidemic models

“…Geng et al (2021) used the SIR model exploring the ramifications of targeted intervention on spatial patterns of new infections in the population agglomeration template. Deng et al (2021) proposed a non-smooth SIR Filippov system to investigate the impacts of three control strategies (media coverage, vaccination and treatment) on the spread of an infectious disease. Lazebnik et al (2021) developed an extended mathematical SIR model, allowing a multidimensional analysis of the impact of non-pharmaceutical intervention on the pandemic.…”

A behavioural modelling approach to assess the impact of COVID-19 vaccine hesitancy

“…Many other relevant studies have focused on assessing the effects of containment measures and predicting epidemic peaks and ICU accesses, see e.g., Elie et al, 2020 , Flaxman et al, 2020 , Supino et al, 2020 . As soon as COVID–19 vaccines became available, many compartmental models have began to appear in the literature with the specific aim of investigating vaccination’s effects on the spread of the disease as well as determining the optimal allocation of vaccine supply Buckner et al, 2021 , Choi and Shim, 2020 , Mukandavire et al, 2020 , Deng et al, 2021 . A limitation of classical Mathematical Epidemiology (ME) is that it is built up on Statistical Mechanics; the agents are modelled as if they were molecules, and the contagion is abstracted as a chemical reaction between ‘molecules’ of the healthy species with those of the infectious species.…”

Mathematical Modeling for COVID-19 with Focus on Intervention Strategies and Cost-Effectiveness Analysis

“…Due to the adoption of some interventions for inhibiting the COVID-19, the new mathematical models began to consider the impact of interventions to reestimate the course of COVID-19. Specifically, some models have been devised to explore the practical implications of public health interventions [13][14][15][16][17][18][19]. Zhou et al [20] used a deterministic dynamical model to study the interaction between media publicity and disease progression so as to investigate the effectiveness of media publicity on combating the COVID-19 epidemic.…”