Qualitative study of a quarantine/isolation model with multiple disease stages

Abstract

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / a m c Newcastle disease and rabies [11,14]. It is known, however, that quarantine and isolation measures, especially in the context of a new emerging disease, are initially not administered effectively, but are gradually refined (as more data and knowledge of the disease transmission process becomes available (see, for instance, [8])).Numerous mathematical modeling work have been carried out to assess the impact of quarantine and isolation in combatting the spread of the diseases (such as some of the aforementioned modeling studies for SARS). However, many of the models used for assessing the impact of the quarantine and isolation measures tend to be built based on the assumption that the disease stages are exponentially distributed. However, some recent studies [7,30] show that it is more realistic to use gamma distribution assumption for the waiting time in the disease stages (rather than exponential distribution assumption). Furthermore, Feng et al. [7] showed that quarantine and isolation models that assume exponential distribution (for the disease stages) may not be suitable for diseases with relatively long latent and/or infectious periods for the case when isolation is not completely effective (i.e., isolated individuals can transmit infection).The purpose of the current study is to provide a rigorous qualitative analysis of a new deterministic model for transmission dynamics of a communicable disease, subject to the use of quarantine and isolation, where the waiting time in the associated infected classes are assumed to have gamma distribution. The model to be designed extends the SEIQHR model given in [24] by considering multiple stages of the exposed, infectious, quarantined and hospitalized individuals (unlike in [24], it is assumed here that hospitalized individuals do not transmit the infection). Diseases like HIV [25] and influenza [6] are known to have multiple disease (infection) stages.The paper is organized as follows. The model is formulated in Section 2. The global asymptotic stability of the disease-free equilibrium (DFE) is established in Section 3. The existence of the endemic equilibrium is analyzed in Section 4. Local and global stability proofs for the endemic equilibrium, for special cases, are also provided using a Krasnoselskii sub-linearity trick and a non-linear Lyapunov function of Goh-Voltera type, respectively.

The global dynamics for a stochastic SIS epidemic model with isolation

“…The various types of classical epidemic models with quarantine/isolation have been investigated in many articles. See, for example [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] and the references cited therein.…”

Dynamics analysis of a quarantine model in two patches

“…Using the same approach given in [8,9,13], it can be shown that every solution of the equations of the model (4), with initial conditions in D r , approaches the DFE, E r 0 , as t ! 1 for Q R…”

“…A number of mathematical modeling work have been carried out to assess the impact of quarantine and isolation in combatting the spread of diseases (see, for instance, [1][2][3][4][6][7][8][9] and some of the references therein). In this study, quarantine is defined in terms of the removal (from the general population) of individuals suspected of being exposed to a communicable disease (and that individuals in quarantine can be susceptible or infected).…”

“…In this study, quarantine is defined in terms of the removal (from the general population) of individuals suspected of being exposed to a communicable disease (and that individuals in quarantine can be susceptible or infected). It should be mentioned that the vast majority of quarantine models in the literature do not include the important fact that susceptible people can also be placed in quarantine during times of disease outbreaks (see, for instance [1][2][3][4][6][7][8][9]). The SARS outbreaks of 2002/2003 clearly showed that the vast majority of individuals in quarantine are actually susceptible (i.e., not infected).…”

Disease control through removal of population using Z-control approach

“…Incorporation of different intervention strategies into the model can be executed in different ways. For instance, to model the behavioural change such as awareness [10,11], isolation [12,13] or to study the impact of vaccination [14], an extra compartment is usually introduced in the model. On the other hand, in the context of vector borne disease modelling, incorporation of self protection such as use of bed net, application of vector repellent on skin, etc.…”