Quarantine Model Research Articles

On a quarantine model of coronavirus infection and data analysis

Attempts to curb the spread of coronavirus by introducing strict quarantine measures apparently have different effect in different countries: while the number of new cases has reportedly decreased in China and South Korea, it still exhibit significant growth in Italy and other countries across Europe. In this brief note, we endeavour to assess the efficiency of quarantine measures by means of mathematical modelling. Instead of the classical SIR model, we introduce a new model of infection progression under the assumption that all infected individual are isolated after the incubation period in such a way that they cannot infect other people. Disease progression in this model is determined by the basic reproduction numberR0(the number of newly infected individuals during the incubation period), which is different compared to that for the standard SIR model. IfR0> 1, then the number of latently infected individuals exponentially grows. However, ifR0< 1 (e.g.due to quarantine measures and contact restrictions imposed by public authorities), then the number of infected decays exponentially. We then consider the available data on the disease development in different countries to show that there are three possible patterns: growth dynamics, growth-decays dynamics, and patchy dynamics (growth-decay-growth). Analysis of the data in China and Korea shows that the peak of infection (maximum of daily cases) is reached about 10 days after the restricting measures are introduced. During this period of time, the growth rate of the total number of infected was gradually decreasing. However, the growth rate remains exponential in Italy. Arguably, it suggests that the introduced quarantine is not sufficient and stricter measures are needed.

The Public Health-Quarantine Model

One of the most frequently voiced criticisms of free will skepticism is that it is unable to adequately deal with criminal behavior and that the responses it would permit as justified are insufficient for acceptable social policy. This concern is fueled by two factors. The first is that one of the most prominent justifications for punishing criminals, retributivism, is incompatible with free will skepticism. The second concern is that alternative justifications that are not ruled out by the skeptical view per se face significant independent moral objections (Pereboom 2014:153). Despite these concerns, I maintain that free will skepticism leaves intact other ways to respond to criminal behavior—in particular incapacitation, rehabilitation, and alteration of relevant social conditions—and that these methods are both morally justifiable and sufficient for good social policy. The position I defend is similar to Derk Pereboom’s (2001, 2013, 2014), taking as its starting point his quarantine analogy, but it sets out to develop the quarantine model within a broader justificatory framework drawn from public health ethics. The resulting model—which I call the public health-quarantine model (Caruso 2016, 2017a)—provides a framework for justifying quarantine and criminal sanctions that is more humane than retributivism and preferable to other non-retributive alternatives. It also provides a broader approach to criminal behavior than Pereboom’s quarantine analogy does on its own since it prioritizes prevention and social justice. In Section 1, I begin by (very) briefly summarizing my arguments against free will and basic desert moral responsibility. In Section 2, I then introduce and defend my public health-quarantine model, which is a non-retributive alternative to criminal punishment that prioritizes prevention and social justice. In Sections 3 and 4, I take up and respond to two general objections to the public health-quarantine model. Since objections by Michael Corrado (2016), John Lemos (2016), Saul Smilanksy (2011, 2017), and Victor Tadros (2017) have been addressed in detail elsewhere (see Pereboom 2017a; Pereboom and Caruso 2018), I will here focus on objections that have not yet been addressed. In particular, I will respond to concerns about proportionality, human dignity, and victims’ rights. I will argue that each of these concerns can be met and that in the end the public health-quarantine model offers a superior alternative to retributive punishment and other non-retributive accounts.

Two Time Delay Quarantine Model for the Transmission of Worms in Wireless Network

Two Time Delay Quarantine Model for the Transmission of Worms in Wireless Network

Asymptotic Behavior of A Stochastic Quarantine Model

Asymptotic Behavior of A Stochastic Quarantine Model

Chapter Four: Quarantine and the Problem of the Third Man

Non-retributive attempts to justify punishment are open to some of the same objections that retributive attempts are subject to. Should we return to the preventive Quarantine Model? The attempt to justify that approach by analogy to medical quarantine fails. But Pereboom, Slobogin, and Robinson have raised a problem that I would call the Problem of the Third Man: the problem of the sane and rational but undeterrable offender. Pereboom raises it in support of Quarantine, and the inability to deal with it must be added to the objections to retributive and non-retributive theories of punishment; the problem is to deal with it without adopting the Quarantine Model of criminal justice. The “double track” solution, I suggest, amounts to the tacking together of two unacceptable models and in any event is unstable.

Moral Concerns About Responsibility Denial and the Quarantine of Violent Criminals

Some contemporary philosophers maintain we lack the kind of free will that makes us morally responsible for our actions. Some of these philosophers, such as Derk Pereboom, Gregg Caruso, and Bruce Waller, also argue that such a view supports the case for significant reform of the penal system. Pereboom and Caruso explicitly endorse a quarantine model for dealing with dangerous criminals, arguing that while not responsible for their crimes such criminals should be detained in non-harsh conditions and offered the opportunity for rehabilitation. Waller does not explicitly endorse the quarantine model, but his view is similar in significant respects. I argue that such views can too easily lead to the endorsement of legal policies which would result in more frequent punishment of innocent persons for crimes they have not committed. Thus, we should have deep moral reservations about such views.

Chapter One. Two Models of Criminal Justice

Skepticism about moral responsibility has moved to the center of the debate about free will and responsibility, aided perhaps by recent work in neuroscience, and the number of important philosophers who consider themselves skeptics appears to be growing. The problem is that skepticism about responsibility, a skepticism that calls retribution and desert – the Retributive Model of criminal justice – into question as well, seems to leave us only utilitarian alternatives in criminal justice. But the utilitarian answers here are unsatisfactory. Deterrence without (non-utilitarian) side constraints is an easy target for counter-examples, and that has led many skeptics to the conclusion that the only justifiable approach to criminal justice is the therapeutic approach – the Quarantine Model. But a world without something very much like punishment, a world in which the approach to crime is to cure or to incapacitate, seems unacceptable, treating human beings (in the words of David Hodgson) “as vehicles for treatment to be manipulated for the general good.” The problem for the skeptic is to find a way out of this dilemma. My object is to isolate the desirable elements of punishment and incorporate them into an alternative institution focused in part on benefit to the offender. I call that institution “Correction.”

Free Will Skepticism and Criminal Behavior

One of the most frequently voiced criticisms of free will skepticism is that it is unable to adequately deal with criminal behavior and that the responses it would permit as justifi ed are insuffi cient for acceptable social policy. This concern is fueled by two factors. The fi rst is that one of the most prominent justifi cations for punishing criminals, retributivism, is incompatible with free will skepticism. The second concern is that alternative justifi cations that are not ruled out by the skeptical view per se face signifi cant independent moral objections (Pereboom, 2014, p. 153). Yet despite these concerns, I maintain that free will skepticism leaves intact other ways to respond to criminal behavior—in particular incapacitation, rehabilitation, and alteration of relevant social conditions—and that these methods are both morally justifi able and suffi cient for good social policy. The position I defend is similar to Derk Pereboom’s (2001, 2013, 2014), taking as its starting point his quarantine analogy, but it sets out to develop the quarantine model within a broader justifi catory framework drawn from public health ethics. The resulting model—which I call the public healthquarantine model—provides a framework for justifying quarantine and criminal sanctions that is more humane than retributivism and preferable to other non-retributive alternatives. It also provides a broader approach to criminal behavior than Pereboom’s quarantine analogy does on its own.

Mathematical Modelling of the Transmission Dynamics of Ebola Virus

The study simulated the transmission dynamics of Ebola Zaire virus using two models: a modified SIR model with the understanding that the recovered can become infected again and the infected die at a certain rate and a quarantine model, which ascertained the effects of quarantining the infected. Furthermore, an appropriate system of Ordinary Differential Equations (ODE) was formulated for the transmission and the method of linearized stability approach was used to solve the equations. Stability analysis of both models indicated that, the Disease Free Equilibrium (DFE) states of the models were unstable if they exist. These equilibria states showed that the disease can easily be triggered off, so there is need to be constantly alert and effective preventive measures put in place against its spread. In addition, numerical experiments were carried out with the models' parameters assigned specific hypothetical values and graphs were plotted to investigate the effect of these parameters on the transmission of the disease. The results showed that, with the nature of Ebola Zaire virus, uncontrolled transmittable contacts between the infected and the susceptible can lead to a very serious outbreak with high mortality rate, since no immunity and drugs at moment. However, with effective quarantining structures put in place such situation can be better managed and outbreak controlled.

Dynamics analysis of a quarantine model in two patches

A new deterministic model for assessing the impact of quarantine on the transmission dynamics of a communicable disease in a two‐patch community is designed. Rigorous analysis of the model shows that the imperfect nature of quarantine (in the two patches) could induce the phenomenon of backward bifurcation when the associated reproduction number of the model is less than unity. For the case when quarantined susceptible individuals do not acquire infection during quarantine, the disease‐free equilibrium of the model is shown to be globally asymptotically stable when the associated reproduction number is less than unity. Furthermore, the model has a unique Patch i‐only boundary equilibrium (i = 1,2) whenever the associated reproduction number for Patch i is greater than unity. The unique Patch i‐only boundary equilibrium is locally asymptotically stable whenever the invasion reproduction number of Patch 3 − i is less than unity (and the associated reproduction number for Patch i exceeds unity). The model has at least one endemic equilibrium when its reproduction number exceeds unity (and the disease persists in both patches in this case). It is shown that adding multi‐patch dynamics to a single‐patch quarantine model (which allow the quarantine of susceptible individuals) in a single patch does not alter its quantitative dynamics (with respect to the existence and asymptotic stability of its associated equilibria as well as its backward bifurcation property). Copyright © 2014 John Wiley & Sons, Ltd.

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

A new deterministic model for the spread of a communicable disease that is controllable using mass quarantine is designed. Unlike in the case of the vast majority of prior quarantine models in the literature, the new model includes a quarantine-adjusted incidence function for the infection rate and the quarantine of susceptible individuals suspected of being exposed to the disease (thereby making it more realistic epidemiologically). The earlier quarantine models tend to only explicitly consider individuals who are already infected, but show no clinical symptoms of the disease (i.e., those latently-infected), in the quarantine class (while ignoring the quarantine of susceptible individuals). In reality, however, the vast majority of people in quarantine (during a disease outbreak) are susceptible. Rigorous analysis of the model shows that the assumed imperfect nature of quarantine (in preventing the infection of quarantined susceptible individuals) induces the phenomenon of backward bifurcation when the associated reproduction threshold is less than unity (thereby making effective disease control difficult). For the case when the efficacy of quarantine to prevent infection during quarantine is perfect, the disease-free equilibrium is globally-asymptotically stable when the reproduction threshold is less than unity. Furthermore, the model has a unique endemic equilibrium when the reproduction threshold exceeds unity (and the disease persists in the population in this case).

Passive Benign Worm Propagation Modeling with Dynamic Quarantine Defense

Worm attacks can greatly distort network performance, and countering infections can exact a heavy toll on economic and technical resources. Worm modeling helps us to better understand the spread and propagation of worms through a network, and combining effective types of mitigation techniques helps prevent and mitigate the effects of worm attacks. In this paper, we propose a mathematical model which combines both dynamic quarantine and passive benign worms. This Passive Worm Dynamic Quarantine (PWDQ) model departs from previous models in that infected hosts will be recovered either by passive benign worms or quarantine measure. Computer simulation shows that the performance of our proposed model is significantly better than existing models, in terms of decreasing the number of infectious hosts and reducing the worm propagation speed.