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In this paper, a mathematical model of Ebola virus with contact tracing as a control strategy was developed and analyzed. We considered the model without contact tracing and with perfect contact tracing. The two sub-models have been explicitly analyzed. In the first sub-model, it has been found that the disease-free equilibrium (DFE) is both locally and globally asymptotically stable whenever the associated control reproduction number is less than one. The endemic equilibrium point (EEP) is globally asymptotically stable whenever the associated control reproduction number is greater than one. In the second sub-model, it has been found that the DFE is both locally and globally asymptotically stable whenever the control reproduction number is less than one. The EEP is globally asymptotically stable whenever the control reproduction number is greater than one. The full model has also been analyzed, which shows that the DFE is both locally and globally asymptotically stable whenever the associated control reproduction number is less than one. The EEP is globally asymptotically stable whenever the control reproduction number is greater than one. In sensitivity analysis part, effective contact rate for humans was very sensitive in increasing the basic reproduction number and personal hygiene was very sensitive in decreasing the basic reproduction number also, numerical simulation shows that the Ebola virus can be wiped out in society if contact tracing and personal hygiene can be implemented perfectly in the human population.

This study evaluates the impact of COVID-19 on the operations and management of Community Centres (CCs) in Auckland. This Coronavirus posed unprecedented challenges to the communities and public facilities here and in many other countries. To mitigate the pandemic outbreak, the New Zealand government adopted the so-called “go hard, go early” strategy, which put all of the country to strict self-isolation for 52 days [Baker et al. (2020). The Medical Journal of Australia, 213(5), 198–200.e1]. This research aims to explore what challenges some of Auckland’s CCs faced during COVID-19 lockdown and what management decisions were taken to operate the CCs during these periods effectively. The study was based principally on primary data collected from the managers and visitors of eight CCs across Auckland via semi-structured interviews and anonymous online surveys. With all the information gathered and generated through thematic, correlation and deductive analysis, the study produced a “road map” for management actions. This framework should enable CCs to better articulate decisions for more effective and safer operating during future pandemic outbreaks.

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.

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 class of four linear and nonlinear differential equations models is given to describe the detection of HIV-positive individuals in Cuba through random screening and contact tracing. The basic reproduction number is obtained for each of the four models. Cuban HIV data from 1986 to 2002 are used to fit the models for the purpose of comparison. We also use the models to gauge the difference in detection time through random screening and contact tracing. Remarks on the implications for intervention measures and treatment of people living with HIV in Cuba are also given.