Mathematical Model of the Role of Asymptomatic Infection in Outbreaks of Some Emerging Pathogens

Preparation for outbreaks of emerging infectious diseases is often predicated on beliefs that we will be able to understand the epidemiological nature of an outbreak early into its inception. However, since many rare emerging diseases exhibit different epidemiological behaviors from outbreak to outbreak, early and accurate estimation of the epidemiological situation may not be straightforward in all cases. Previous studies have proposed considering the role of active asymptomatic infections co-emerging and co-circulating as part of the process of emergence of a novel pathogen. Thus far, consideration of the role of asymptomatic infections in emerging disease dynamics have usually avoided considering some important sets of influences. In this paper, we present and analyze a mathematical model to explore the hypothetical scenario that some (re)emerging diseases may actually be able to maintain stable, endemic circulation successfully in an entirely asymptomatic state. We argue that an understanding of this potential mechanism for diversity in observed epidemiological dynamics may be of considerable importance in understanding and preparing for outbreaks of novel and/or emerging diseases.

A Tour of the Basic Reproductive Number and the Next Generation of Researchers

The Mathematical and Theoretical Biology Institute (MTBI) is a national award winning Research Experience for Undergraduates (REU) that has been running every summer since 1996. Since 1997, students have developed and proposed their own research questions and derived their research projects from them as the keystone of the program. Because MTBI’s mentors have no control over what students are interested in, we need to introduce a suite of flexible techniques that can be applied to a broad variety of interests. In this paper, we walk through examples of some of the most popular techniques at MTBI: epidemiological or contagion modeling and reproductive number analysis. We include an overview of the next generation matrix method of finding the basic reproductive number, sensitivity analysis as a technique for investigating the effect of parameters on the reproductive number, and recommendations for interpreting the results. Lastly, we provide some advice to mentors who are looking to advise student-led research projects. All examples are taken from actual student projects that are generally available through the MTBI website.

Challenges, Opportunities and Theoretical Epidemiology

Lessons learned from the HIV pandemic, SARS in 2003, the 2009 H1N1 influenza pandemic, the 2014 Ebola outbreak in West Africa, and the ongoing Zika outbreaks in the Americas can be framed under a public health policy model that responds after the fact. Responses often come through reallocation of resources from one disease control effort to a new pressing need. The operating models of preparedness and response are ill-equipped to prevent or ameliorate disease emergence or reemergence at global scales. Epidemiological challenges that are a threat to the economic stability of many regions of the world, particularly those depending on travel and trade, remain at the forefront of the Global Commons. Consequently, efforts to quantify the impact of mobility and trade on disease dynamics have dominated the interests of theoreticians for some time. Our experience includes an H1N1 influenza pandemic crisscrossing the world during 2009 and 2010, the 2014 Ebola outbreaks, limited to regions of West Africa lacking appropriate medical facilities, health infrastructure, and sufficient levels of preparedness and education, and the expanding Zika outbreaks, moving expeditiously across habitats suitable for Aedes aegypti. These provide opportunities to quantify the impact of disease emergence or reemergence on the decisions that individuals take in response to real or perceived disease risks. The case of SARS 2003 in 2003, the efforts to reduce the burden of H1N1 influenza cases in 2009, and the challenges faced in reducing the number of Ebola cases in 2014 are the three recent scenarios that required a timely global response. Studies addressing the impact of centralized sources of information, the impact of information along social connections, or the role of past disease outbreak experiences on the risk-aversion decisions that individuals undertake may help identify and quantify the role of human responses to disease dynamics while recognizing the importance of assessing the timing of disease emergence and reemergence. The co-evolving human responses to disease dynamics are prototypical of the feedbacks that define complex adaptive systems. In short, we live in a socioepisphere being reshaped by ecoepidemiology in the “Era of Information.”

Modeling ebola virus disease transmissions with reservoir in a complex virus life ecology

We propose a new deterministic mathematical model for the transmission dynamics of Ebola Virus Disease (EVD) in a complex Ebola virus life ecology. Our model captures as much as possible the features and patterns of the disease evolution as a three cycle transmission process in the two ways below. Firstly it involves the synergy between the epizootic phase (during which the disease circulates periodically amongst non-human primates populations and decimates them), the enzootic phase (during which the disease always remains in fruit bats population) and the epidemic phase (during which the EVD threatens and decimates human populations). Secondly it takes into account the well-known, the probable/suspected and the hypothetical transmission mechanisms (including direct and indirect routes of contamination) between and within the three different types of populations consisting of humans, animals and fruit bats. The reproduction number R0 for the full model with the environmental contamination is derived and the global asymptotic stability of the disease free equilibrium is established when R0andlt;1. It is conjectured that there exists a unique globally asymptotically stable endemic equilibrium for the full model when R0andgt;1. The role of a contaminated environment is assessed by comparing the human infected component for the sub-model without the environment with that of the full model. Similarly, the sub-model without animals on the one hand and the sub-model without bats on the other hand are studied. It is shown that bats influence more the dynamics of EVD than the animals. Global sensitivity analysis shows that the effective contact rate between humans and fruit bats and the mortality rate for bats are the most influential parameters on the latent and infected human individuals. Numerical simulations, apart from supporting the theoretical results and the existence of a unique globally asymptotically stable endemic equilibrium for the full model, suggest further that: (1) fruit bats are more important in the transmission processes and the endemicity level of EVD than animals. This is in line with biological findings which identified bats as reservoir of Ebola viruses; (2) the indirect environmental contamination is detrimental to human beings, while it is almost insignificant for the transmission in bats.

Perspectives on the role of mobility, behavior, and time scales in the spread of diseases

The dynamics, control, and evolution of communicable and vector-borne diseases are intimately connected to the joint dynamics of epidemiological, behavioral, and mobility processes that operate across multiple spatial, temporal, and organizational scales. The identification of a theoretical explanatory framework that accounts for the pattern regularity exhibited by a large number of host-parasite systems, including those sustained by host-vector epidemiological dynamics, is but one of the challenges facing the coevolving fields of computational, evolutionary, and theoretical epidemiology. Host-parasite epidemiological patterns, including epidemic outbreaks and endemic recurrent dynamics, are characteristic to well-identified regions of the world; the result of processes and constraints such as strain competition, host and vector mobility, and population structure operating over multiple scales in response to recurrent disturbances (like El Niño) and climatological and environmental perturbations over thousands of years. It is therefore important to identify and quantify the processes responsible for observed epidemiological macroscopic patterns: the result of individual interactions in changing social and ecological landscapes. In this perspective, we touch on some of the issues calling for the identification of an encompassing theoretical explanatory framework by identifying some of the limitations of existing theory, in the context of particular epidemiological systems. Fostering the reenergizing of research that aims at disentangling the role of epidemiological and socioeconomic forces on disease dynamics, better understood as complex adaptive systems, is a key aim of this perspective.