Narrow Results

More than 20 outbreaks of Ebola virus disease have occurred in Africa since 1976, and yet no adequate treatment is available. Hence, prevention, control measures and supportive treatment remain the only means to avoid the disease. Among these measures, contact tracing occupies a prominent place. In this paper, we propose a simple mathematical model that incorporates imperfect contact tracing, quarantine and hospitalization (or isolation). The control reproduction number ${{ℛ}}_c$ of each sub-model and for the full model are computed. Theoretically, we prove that when ${{ℛ}}_c$ is less than one, the corresponding model has a unique globally asymptotically stable disease-free equilibrium. Conversely, when ${{ℛ}}_c$ is greater than one, the disease-free equilibrium becomes unstable and a unique globally asymptotically stable endemic equilibrium arises. Furthermore, we numerically support the analytical results and assess the efficiency of different control strategies. Our main observation is that, to eradicate EVD, the combination of high contact tracing (up to 90%) and effective isolation is better than all other control measures, namely: (1) perfect contact tracing, (2) effective isolation or full hospitalization, (3) combination of medium contact tracing and medium isolation.

A mathematical model is proposed in this paper to study the transmission and control of COVID-19. The mathematical model is formulated using system of nonlinear ordinary differential equations. The model includes disease-related parameters such as contact rate, disease-induced death rates, immigration rate and transition rates along with parameters for control measures such as implementation of social distancing practices, isolation and quarantine rates. From the stability analysis of the model, it is shown that if the social distancing is practiced by the large number of susceptible population, then the disease will not spread, and it may eventually die out. Further, it is derived from the analysis of the model that if most of the infected populations are isolated or quarantined, then the spread of the disease can be eventually controlled. However, from the analysis of the model, it is observed that if there is constant immigration of asymptomatic infected persons, then the disease will continue to spread and will remain pandemic. For controlling the disease, two more parameters, that is, vaccination and testing rates, are introduced in the original mathematical model and from the numerical analysis of this model, it has been shown that the control strategy involving vaccination and testing in combination can have synergistic effect for minimizing the COVID-19 infected cases.

In this paper, we investigate an epidemic model with quarantine and recovery-age effects. Reformulating the model as an abstract nondensely defined Cauchy problem, we discuss the existence and uniqueness of solutions to the model and study the stability of the steady state based on the basic reproduction number. After analyzing the distribution of roots to a fourth degree exponential polynomial characteristic equation, we also derive the conditions of Hopf bifurcation. Numerical simulations are performed to illustrate the results.

A nonlinear mathematical model is proposed and analyzed to study the dynamics of 2009 H1N1 flu epidemic in a homogeneous population with constant immigration of susceptibles. The effect of contact tracing and quarantine (isolation) strategies in reducing the spread of H1N1 flu is incorporated. The model monitors the dynamics of five sub-populations (classes), namely susceptible with high infection risk, susceptible with reduction of infection risk, infective, quarantined and recovered individuals. The model analysis includes the determination of equilibrium points and carrying out their stability analysis in terms of the threshold parameter R₀. Moreover, the numerical simulation of the proposed model is also performed by using fourth order Runge–Kutta method along with the sensitivity analysis of the endemic equilibrium point. The analysis and numerical simulation results demonstrate that the maximum implementation of contact tracing and quarantine strategies help in reducing endemic infective class size and hence act as effective intervention strategy to control the disease. This gives a theoretical interpretation to the practical experiences that the early contact tracing and quarantine strategies are critically important to control the outbreak of epidemics.

The quarantine of suspected cases and isolation of individuals with symptoms are two of the primary public health control measures for combating the spread of a communicable emerging or re-emerging disease. Implementing these measures, however, can inflict significant socio-economic and psychological costs. This paper presents a deterministic compartmental model for assessing the single and combined impact of quarantine and isolation to contain an epidemic. Comparisons are made with a mass vaccination program. The model is simulated using parameters for influenza-type diseases such as SARS. The study shows that even for an epidemic in which asymptomatic transmission does not occur, the quarantine of asymptomatically-infected individuals can be more effective than only isolating individuals with symptoms, if the associated reproductive number is high enough. For the case where asymptomatic transmission occurs, it is shown that isolation is more effective for a disease with a small basic reproduction number and transmission coefficient of asymptomatically-infected individuals. If asymptomatic individuals transmit at a rate that is at least 20% that of symptomatic individuals, quarantine is always more effective. The study further shows that the reduction in disease burden obtained from a combined quarantine and isolation program can be comparable to that obtained by a vaccination program, if the former is implemented quickly enough after the onset of the outbreak. If the implementation of such a quarantine/isolation program is delayed, however, even for a short while, its effectiveness decreases rapidly.

We develop an influenza pandemic model with quarantine and treatment, and analyze the dynamics of the model. Analytical results of the model show that, if basic reproduction number , the disease-free equilibrium (DFE) is globally asymptotically stable, if , the disease is uniformly persistent. The model is then extended to assess the impact of three anti-influenza control measures, precaution, quarantine and treatment, by re-formulating the model as an optimal control problem. We focus primarily on controlling disease with a possible minimal the systemic cost. Pontryagin's maximum principle is used to characterize the optimal levels of the three controls. Numerical simulations of the optimality system, using a set of reasonable parameter values, indicate that the precaution measure is more effective in reducing disease transmission than the other two control measures. The precaution measure should be emphasized.

As medical countermeasures are usually not immediately available during pandemics, non-pharmaceutical measures are important and often the only options available to governments before the arrival of pharmaceutical interventions. This chapter provides an overview of containment measures historically and typically used in pandemic outbreak of respiratory diseases and in the context of Coronavirus disease 2019 (COVID-19) up until August 2021, summarizes the evidence on their effectiveness and efficiency, and considerations and impact from their deployment.