Dynamics of a model with quarantine-adjusted incidence and quarantine of susceptible individuals

Investigating the trade-off between self-quarantine and forced quarantine provisions to control an epidemic: An evolutionary approach

During a pandemic event like the present COVID-19, self-quarantine, mask-wearing, hygiene maintenance, isolation, forced quarantine, and social distancing are the most effective nonpharmaceutical measures to control the epidemic when the vaccination and proper treatments are absent. In this study, we proposed an epidemiological model based on the SEIR dynamics along with the two interventions defined as self-quarantine and forced quarantine by human behavior dynamics. We consider a disease spreading through a population where some people can choose the self-quarantine option of paying some costs and be safer than the remaining ones. The remaining ones act normally and send to forced quarantine by the government if they get infected and symptomatic. The government pays the forced quarantine costs for individuals, and the government has a budget limit to treat the infected ones. Each intervention derived from the so-called behavior model has a dynamical equation that accounts for a proper balance between the costs for each case, the total budget, and the risk of infection. We show that the infection peak cannot be reduced if the authority does not enforce a proactive (quantified by a higher sensitivity parameter) intervention. While comparing the impact of both self- and forced quarantine provisions, our results demonstrate that the latter is more influential to reduce the disease prevalence and the social efficiency deficit (a gap between social optimum payoff and equilibrium payoff).

Post pandemic fatigue: what are effective strategies?

Recurrent updates in non-pharmaceutical interventions (NPIs) aim to control successive waves of the coronavirus disease 2019 (COVID-19) but are often met with low adherence by the public. This study evaluated the effectiveness of gathering restrictions and quarantine policies based on a modified Susceptible-Exposed-Infectious-Hospitalized-Recovered (SEIHR) model by incorporating cross-boundary travellers with or without quarantine to study the transmission dynamics of COVID-19 with data spanning a nine-month period during 2020 in Hong Kong. The asymptotic stability of equilibria reveals that the model exhibits the phenomenon of backward bifurcation, which in this study is a co-existence between a stable disease-free equilibrium (DFE) and an endemic equilibrium (EE). Even if the basic reproduction number ([Formula: see text]) is less than unity, this disease cannot be eliminated. The effect of each parameter on the overall dynamics was assessed using Partial Rank Correlation Coefficients (PRCCs). Transmission rates (i.e., [Formula: see text] and [Formula: see text]), effective contact ratio [Formula: see text] between symptomatic individuals and quarantined people, and transfer rate [Formula: see text] related to infection during quarantine were identified to be the most sensitive parameters. The effective contact ratios between the infectors and susceptible individuals in late July were found to be over twice as high as that in March of 2020, reflecting pandemic fatigue and the potential existence of infection during quarantine.

Structure of epidemic models: toward further applications in economics

In this paper, we review the structure of various epidemic models in mathematical epidemiology for the future applications in economics. The heterogeneity of population and the generalization of nonlinear terms play important roles in making more elaborate and realistic models. The basic, effective, control and type reproduction numbers have been used to estimate the intensity of epidemic, to evaluate the effectiveness of interventions and to design appropriate interventions. The advanced epidemic models includes the age structure, seasonality, spatial diffusion, mutation and reinfection, and the theory of reproduction numbers has been generalized to them. In particular, the existence of sustained periodic solutions has attracted much interest because they can explain the recurrent waves of epidemic. Although the theory of epidemic models has been developed in decades and the development has been accelerated through COVID-19, it is still difficult to completely answer the uncertainty problem of epidemic models. We would have to mind that there is no single model that can solve all questions and build a scientific attitude to comprehensively understand the results obtained by various researchers from different backgrounds.

Optimal control of an SIR epidemic through finite-time non-pharmaceutical intervention

We consider the problem of controlling an SIR-model epidemic by temporarily reducing the rate of contact within a population. The control takes the form of a multiplicative reduction in the contact rate of infectious individuals. The control is allowed to be applied only over a finite time interval, while the objective is to minimize the total number of individuals infected in the long-time limit, subject to some cost function for the control. We first consider the no-cost scenario and analytically determine the optimal control and solution. We then study solutions when a cost of intervention is included, as well as a cost associated with overwhelming the available medical resources. Examples are studied through the numerical solution of the associated Hamilton-Jacobi-Bellman equation. Finally, we provide some examples related directly to the current pandemic.

The threshold of a deterministic and a stochastic SIQS epidemic model with varying total population size

In this paper, a stochastic and a deterministic SIS epidemic model with isolation and varying total population size are proposed. For the deterministic model, we establish the threshold R 0. When R 0 is less than 1, the disease-free equilibrium is globally stable, which means the disease will die out. While R 0 is greater than 1, the endemic equilibrium is globally stable, which implies that the disease will spread. Moreover, there is a critical isolation rate δ*, when the isolation rate is greater than it, the disease will be eliminated. For the stochastic model, we also present its threshold R 0s . When R 0s is less than 1, the disease will disappear with probability one. While R 0s is greater than 1, the disease will persist. We find that stochastic perturbation of the transmission rate (or the valid contact coefficient) can help to reduce the spread of the disease. That is, compared with stochastic model, the deterministic epidemic model overestimates the spread capacity of disease. We further find that there exists a critical the stochastic perturbation intensity of the transmission rate σ*, when the stochastic perturbation intensity of the transmission rate is bigger than it, the disease will disappear. At last, we apply our theories to a realistic disease, pneumococcus amongst homosexuals, carry out numerical simulations and obtain the empirical probability density under different parameter values. The critical isolation rate δ* is presented. When the isolation rate δ is greater than δ*, the pneumococcus amongst will be eliminated.

Modeling the impact of quarantine during an outbreak of Ebola virus disease

The quarantine of people suspected of being exposed to an infectious agent is one of the most basic public health measure that has historically been used to combat the spread of communicable diseases in human communities. This study presents a new deterministic model for assessing the population-level impact of the quarantine of individuals suspected of being exposed to disease on the spread of the 2014-2015 outbreaks of Ebola viral disease. It is assumed that quarantine is imperfect (i.e., individuals can acquire infection during quarantine). In the absence of quarantine, the model is shown to exhibit global dynamics with respect to the disease-free and its unique endemic equilibrium when a certain epidemiological threshold (denoted byR 0 ) is either less than or greater than unity. Thus, unlike the full model with imperfect quarantine (which is known to exhibit the phenomenon of backward bifurcation), the version of the model with no quarantine does not undergo a backward bifurcation. Using data relevant to the 2014-2015 Ebola transmission dynamics in the three West African countries (Guinea, Liberia and Sierra Leone), uncertainty analysis of the model show that, although the current level and effectiveness of quarantine can lead to significant reduction in disease burden, they fail to bring the associated quarantine reproduction number (R 0 Q ) to a value less than unity (which is needed to make effective disease control or elimination feasible). This reduction ofR 0 Q is, however, very possible with a modest increase in quarantine rate and effectiveness. It is further shown, via sensitivity analysis, that the parameters related to the effectiveness of quarantine (namely the parameter associated with the reduction in infectiousness of infected quarantined individuals and the contact rate during quarantine) are the main drivers of the disease transmission dynamics. Overall, this study shows that the singular implementation of a quarantine intervention strategy can lead to the effective control or elimination of Ebola viral disease in a community if its coverage and effectiveness levels are high enough.

Dynamics of an SEQIHRS epidemic model with media coverage, quarantine and isolation in a community with pre-existing immunity

An autonomous deterministic non-linear epidemic model SEQIHRS is proposed for the transmission dynamics of an infectious disease with quarantine and isolation control strategies in a community with pre-existing immunity. The model exhibits two equilibria, namely, the disease-free and a unique endemic equilibrium. The existence and local stability of the disease free and endemic equilibria are explored in terms of the effective reproduction numberR C . It is observed that media coverage does not affect the effective reproduction number, but it helps to mitigate disease burden by lowering the number of infectious individuals at the endemic steady state and also lowering the infection peak. A new approach is proposed to estimate the coefficient of media coverage. Using the results of central manifold theory, it is established that asR C passes through unity, transcritical bifurcation occurs in the system and the unique endemic equilibrium is asymptotically stable. It is observed that the population level impact of quarantine and isolation depend on the level of transmission by the isolated individuals. Moreover, the higher level of pre-existing immunity in the population decreases the infection peak and causes its early arrival. Theoretical findings are supported by numerical simulation. Sensitivity analysis is performed forR C and state variables at endemic steady state with respect to model parameters.