Mathematical modeling of contact tracing as a control strategy of Ebola virus disease

Abstract

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 [Formula: see text] of each sub-model and for the full model are computed. Theoretically, we prove that when [Formula: see text] is less than one, the corresponding model has a unique globally asymptotically stable disease-free equilibrium. Conversely, when [Formula: see text] 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.

Automated Contact Tracing: a game of big numbers in the time of COVID-19

“…Hence, the number of individuals that have tested positive, are using contact tracing and will confirm that they are sick is f c f e r c f i N. • We define a c as the average number of contacts per person in the period of time t 0 who are at risk of being infected due to proximity with a sick individual and is assumed to be greater than 0. 3 Since only f e fraction of contacts are using the service, we can estimate the number of individuals that can be traced as f c f e r c f i N × a c × f e . To compute the number of individuals that need to be quarantined or isolated since they are now at risk of being infected from coming in contact with a sick person, we define the following.…”

“…This preemptive method allows for the containment of the pathogen by isolating potentially infected individuals that have been traced. Extensive studies of manual contact tracing were done during the previous outbreak of the Ebola virus [3][4][5], SARS-CoV and MERS-CoV [6]. More recently, mathematical models have been formulated to study contact tracing assuming the disease spread to be quantifiable by the SIR model [7].…”

Dynamical analysis and control strategies in modelling Ebola virus disease

“…subject to the constraints given by (31) with the efforts in educational campaigns for patch 1 and 2, respectively. We seek the pair…”

“…Work done by Berge et al [29] was an extension of their previous work done in 2015 [26], in which a simple mathematical model was developed, which incorporated both the direct and the indirect Ebola virus transmission in such a way that there is a provision of Ebola viruses. Models have also been developed to try and understand various intervention strategies in trying to curtail the spread of EVD [31][32][33][34][35][36][37][38][39][40]. The impact of vaccination and vaccines was investigated in [35,36,39,40] and the issue of quarantining analysed in [35,37] through mathematical models.…”

“…The impact of vaccination and vaccines was investigated in [35,36,39,40] and the issue of quarantining analysed in [35,37] through mathematical models. Further, Berge et al [31] developed a mathematical model to understand the impact of contact tracing as a control strategy of EVD. In recent times, optimal control problems have generated a lot of interest from researchers.…”