Identification of dynamical changes of rabies transmission under quarantine: Community-based measures towards rabies elimination

Quarantine has been long used as a public health response to emerging infectious diseases, particularly at the onset of an epidemic when the infected proportion of a population remains identifiable and logistically tractable. In theory, the same logic should apply to low-incidence infections; however, the application and impact of quarantine in low prevalence settings appears less common and lacks a formal analysis. Here, we present a quantitative framework using a series of progressively more biologically realistic models of canine rabies in domestic dogs and from dogs to humans, a suitable example system to characterize dynamical changes under varying levels of dog quarantine. We explicitly incorporate health-seeking behaviour data to inform the modelling of contact-tracing and exclusion of rabies suspect and probable dogs that can be identified through bite-histories of patients presenting at anti-rabies clinics. We find that a temporary quarantine of rabies suspect and probable dogs provides a powerful tool to curtail rabies transmission, especially in settings where optimal vaccination coverage is yet to be achieved, providing a critical stopgap to reduce the number of human and animal deaths due to rabid bites. We conclude that whilst comprehensive measures including sensitive surveillance and large-scale vaccination of dogs will be required to achieve disease elimination and sustained freedom given the persistent risk of rabies re-introductions, quarantine offers a low-cost community driven solution to intersectoral health burden.

Predicting the combined effects of case isolation, safe funeral practices, and contact tracing during Ebola virus disease outbreaks

BACKGROUND

The recent outbreaks of Ebola virus disease (EVD) in Uganda and the Marburg virus disease (MVD) in Ghana reflect a persisting threat of Filoviridae to the global health community. Characteristic of Filoviridae are not just their high case fatality rates, but also that corpses are highly contagious and prone to cause infections in the absence of appropriate precautions. Vaccines against the most virulent Ebolavirus species, the Zaire ebolavirus (ZEBOV) are approved. However, there exists no approved vaccine or treatment against the Sudan ebolavirus (SUDV) which causes the current outbreak of EVD. Hence, the control of the outbreak relies on case isolation, safe funeral practices, and contact tracing. So far, the effectiveness of these control measures was studied only separately by epidemiological models, while the impact of their interaction is unclear.

METHODS AND FINDINGS

To sustain decision making in public health-emergency management, we introduce a predictive model to study the interaction of case isolation, safe funeral practices, and contact tracing. The model is a complex extension of an SEIR-type model, and serves as an epidemic preparedness tool. The model considers different phases of the EVD infections, the possibility of infections being treated in isolation (if appropriately diagnosed), in hospital (if not properly diagnosed), or at home (if the infected do not present to hospital for whatever reason). It is assumed that the corpses of those who died in isolation are buried with proper safety measures, while those who die outside isolation might be buried unsafely, such that transmission can occur during the funeral. Furthermore, the contacts of individuals in isolation will be traced. Based on parameter estimates from the scientific literature, the model suggests that proper diagnosis and hence isolation of cases has the highest impact in reducing the size of the outbreak. However, the combination of case isolation and safe funeral practices alone are insufficient to fully contain the epidemic under plausible parameters. This changes if these measures are combined with contact tracing. In addition, shortening the time to successfully trace back contacts contribute substantially to contain the outbreak.

CONCLUSIONS

In the absence of an approved vaccine and treatment, EVD management by proper and fast diagnostics in combination with epidemic awareness are fundamental. Awareness will particularly facilitate contact tracing and safe funeral practices. Moreover, proper and fast diagnostics are a major determinant of case isolation. The model introduced here is not just applicable to EVD, but also to other viral hemorrhagic fevers such as the MVD or the Lassa fever.

Mathematical analysis of a model of Ebola disease with control measures

The re-emergence of the Ebola virus disease has pushed researchers to investigate more on this highly deadly disease in order to better understand and control the outbreak and recurrence of epidemics. It is in this perspective that we formulate a realistic mathematical model for the dynamic transmission of Ebola virus disease, incorporating relevant control measures and factors such as ban on eating bush-meat, social distancing, observance of hygiene rules and containment, waning of the vaccine-induced, imperfect contact tracing and vaccine efficacy, quarantine, hospitalization and screening to fight against the spread of the disease. First, by considering the constant control parameters case, we thoroughly compute the control reproduction number [Formula: see text] from which the dynamics of the model is analyzed. The existence and stability of steady states are established under appropriate assumptions on [Formula: see text]. Also, the effect of all the control measures is investigated and the global sensitivity analysis of the control reproduction number is performed in order to determine the impact of parameters and their relative importance to disease transmission and prevalence. Second, in the time-dependent control parameters case, an optimal control problem is formulated to design optimal control strategies for eradicating the disease transmission. Using Pontryagin’s Maximum Principle, we derive necessary conditions for optimal control of the disease. The cost-effectiveness analysis of all combinations of the control measures is made by calculating the infection averted ratio and the incremental cost-effectiveness ratio. This reveals that combining the four restrictive measures conveyed through educational campaigns, screening, safe burial and the care of patients in health centers for better isolation is the most cost-effective among the strategies considered. Numerical simulations are performed to illustrate the theoretical results obtained.

EBOLA VIRUS DISEASE DYNAMICS WITH SOME PREVENTIVE MEASURES: A CASE STUDY OF THE 2018–2020 KIVU OUTBREAK

To fight against Ebola virus disease, several measures have been adopted. Among them, isolation, safe burial and vaccination occupy a prominent place. In this paper, we present a model which takes into account these three control strategies as well as the indirect transmission through a polluted environment. The asymptotic behavior of our model is achieved. Namely, we determine a threshold value [Formula: see text] of the control reproduction number [Formula: see text], below which the disease is eliminated in the long run. Whenever the value of [Formula: see text] ranges from [Formula: see text] and 1, we prove the existence of a backward bifurcation phenomenon, which corresponds to the case, where a locally asymptotically stable positive equilibrium co-exists with the disease-free equilibrium, which is also locally asymptotically stable. The existence of this bifurcation complicates the control of Ebola, since the requirement of [Formula: see text] below one, although necessary, is no longer sufficient for the elimination of Ebola, more efforts need to be deployed. When the value of [Formula: see text] is greater than one, we prove the existence of a unique endemic equilibrium, locally asymptotically stable. That is the disease may persist and become endemic. Numerically, we fit our model to the reported data for the 2018–2020 Kivu Ebola outbreak which occurred in Democratic Republic of Congo. Through the sensitivity analysis of the control reproduction number, we prove that the transmission rates of infected alive who are outside hospital are the most influential parameters. Numerically, we explore the usefulness of isolation, safe burial combined with vaccination and investigate the importance to combine the latter control strategies to the educational campaigns or/and case finding.

A hybrid simulation model to study the impact of combined interventions on Ebola epidemic

Pandemics have been recognized as a serious global threat to humanity. To effectively prevent the spread and outbreak of the epidemic disease, theoretical models intended to depict the disease dynamics have served as the main tools to understand its underlying mechanisms and thus interrupt its transmission. Two commonly-used models are mean-field compartmental models and agent-based models (ABM). The former ones are analytically tractable for describing the dynamics of subpopulations by cannot explicitly consider the details of individual movements. The latter one is mainly used to the spread of epidemics at a microscopic level but have limited simulation scale for the randomness of the results. To overcome current limitations, a hierarchical hybrid modeling and simulation method, combining mean-field compartmental model and ABM, is proposed in this paper. Based on this method, we build a hybrid model, which takes both individual heterogeneity and the dynamics of sub-populations into account. The proposed model also investigates the impact of combined interventions (i. e. vaccination and pre-deployment training) for healthcare workers (HCWs) on the spread of disease. Taking the case of 2014-2015 Ebola Virus Disease (EVD) in Sierra Leone as an example, we examine its spreading mechanism and evaluate the effect of prevention by our parameterized and validated hybrid model. According to our simulation results, an optimal combination of pre-job training and vaccination deployment strategy has been identified. To conclude, our hybrid model helps informing the synergistic disease control strategies and the corresponding hierarchical hybrid modeling and simulation method can further be used to understand the individual dynamics during epidemic spreading in large scale population and help inform disease control strategies for different infectious disease.

Automated contact tracing: a game of big numbers in the time of COVID-19

One of the more widely advocated solutions for slowing down the spread of COVID-19 has been automated contact tracing. Since proximity data can be collected by personal mobile devices, the natural proposal has been to use this for automated contact tracing providing a major gain over a manual implementation. In this work, we study the characteristics of voluntary and automated contact tracing and its effectiveness for mapping the spread of a pandemic due to the spread of SARS-CoV-2. We highlight the infrastructure and social structures required for automated contact tracing to work. We display the vulnerabilities of the strategy to inadequate sampling of the population, which results in the inability to sufficiently determine significant contact with infected individuals. Of crucial importance will be the participation of a significant fraction of the population for which we derive a minimum threshold. We conclude that relying largely on automated contact tracing without population-wide participation to contain the spread of the SARS-CoV-2 pandemic can be counterproductive and allow the pandemic to spread unchecked. The simultaneous implementation of various mitigation methods along with automated contact tracing is necessary for reaching an optimal solution to contain the pandemic.

Contact tracing - Old models and new challenges

Contact tracing is an effective method to control emerging infectious diseases. Since the 1980's, modellers are developing a consistent theory for contact tracing, with the aim to find effective and efficient implementations, and to assess the effects of contact tracing on the spread of an infectious disease. Despite the progress made in the area, there remain important open questions. In addition, technological developments, especially in the field of molecular biology (genetic sequencing of pathogens) and modern communication (digital contact tracing), have posed new challenges for the modelling community. In the present paper, we discuss modelling approaches for contact tracing and identify some of the current challenges for the field.

A novel control set-valued approach with application to epidemic models

This work is considered in the framework of studies dedicated to the control problems, especially in epidemiology where the scientist are concerned to develop effective control strategies to minimize the number of infected individuals. In this paper, we set this problem as an asymptotic target control problem under mixed state-control constraints, for a general class of ordinary differential equations that model the temporal evolution of disease spread. The set of initial data, from which the number of infected people decrease to zero, is generated by a new type of Lyapunov functions defined in the sense of viability theory. The associated controls are provided via selections of adequately designed feedback map. The existence of such selections is improved by using Micheal selection theorem. Finally, an application to the SIRS epidemic model, with numerical simulations, is given to show the efficiency of our approach. To the best of our knowledge, our work is the first one that used a set-valued approach based on the viability theory to deal with an epidemic control problem.