Using dimension reduction to improve outbreak predictability of multistrain diseases

A Framework for Inferring Unobserved Multistrain Epidemic Subpopulations Using Synchronization Dynamics

A new method is proposed to infer unobserved epidemic subpopulations by exploiting the synchronization properties of multistrain epidemic models. A model for dengue fever is driven by simulated data from secondary infective populations. Primary infective populations in the driven system synchronize to the correct values from the driver system. Most hospital cases of dengue are secondary infections, so this method provides a way to deduce unobserved primary infection levels. We derive center manifold equations that relate the driven system to the driver system and thus motivate the use of synchronization to predict unobserved primary infectives. Synchronization stability between primary and secondary infections is demonstrated through numerical measurements of conditional Lyapunov exponents and through time series simulations.

Predicting unobserved exposures from seasonal epidemic data

We consider a stochastic Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model with a contact rate that fluctuates seasonally. Through the use of a nonlinear, stochastic projection, we are able to analytically determine the lower dimensional manifold on which the deterministic and stochastic dynamics correctly interact. Our method produces a low dimensional stochastic model that captures the same timing of disease outbreak and the same amplitude and phase of recurrent behavior seen in the high dimensional model. Given seasonal epidemic data consisting of the number of infectious individuals, our method enables a data-based model prediction of the number of unobserved exposed individuals over very long times.

Antagonistic pleiotropy and fitness trade-offs reveal specialist and generalist traits in strains of canine distemper virus

Theoretically, homogeneous environments favor the evolution of specialists whereas heterogeneous environments favor generalists. Canine distemper is a multi-host carnivore disease caused by canine distemper virus (CDV). The described cell receptor of CDV is SLAM (CD150). Attachment of CDV hemagglutinin protein (CDV-H) to this receptor facilitates fusion and virus entry in cooperation with the fusion protein (CDV-F). We investigated whether CDV strains co-evolved in the large, homogeneous domestic dog population exhibited specialist traits, and strains adapted to the heterogeneous environment of smaller populations of different carnivores exhibited generalist traits. Comparison of amino acid sequences of the SLAM binding region revealed higher similarity between sequences from Canidae species than to sequences from other carnivore families. Using an in vitro assay, we quantified syncytia formation mediated by CDV-H proteins from dog and non-dog CDV strains in cells expressing dog, lion or cat SLAM. CDV-H proteins from dog strains produced significantly higher values with cells expressing dog SLAM than with cells expressing lion or cat SLAM. CDV-H proteins from strains of non-dog species produced similar values in all three cell types, but lower values in cells expressing dog SLAM than the values obtained for CDV-H proteins from dog strains. By experimentally changing one amino acid (Y549H) in the CDV-H protein of one dog strain we decreased expression of specialist traits and increased expression of generalist traits, thereby confirming its functional importance. A virus titer assay demonstrated that dog strains produced higher titers in cells expressing dog SLAM than cells expressing SLAM of non-dog hosts, which suggested possible fitness benefits of specialization post-cell entry. We provide in vitro evidence for the expression of specialist and generalist traits by CDV strains, and fitness trade-offs across carnivore host environments caused by antagonistic pleiotropy. These findings extend knowledge on CDV molecular epidemiology of particular relevance to wild carnivores.

The effect of antibody-dependent enhancement, cross immunity, and vector population on the dynamics of dengue fever

Dengue is a major international public health concern and impacts one-third of the world's population. No specific vaccine and treatment are available for this vector-borne disease. There are four similar but distinct serotypes of dengue viruses (DENV). Infection with one serotype affords life-long immunity to that serotype but only temporary partial immunity, or cross immunity (CI), to others. This increases the risk of developing lethal complications upon re-infection, mainly because of the effect of antibody-dependent enhancement (ADE). There have been multiple studies of the dynamic behavior created by the interplay of ADE and CI using mathematical models. However, models in the literature seldom capture the vector population, which we consider important because combating the mosquito vector is the only way to contain dengue transmission in the absence of vaccines. We therefore propose two differential-equation models of dengue fever (DF) with different levels of complexity and details. Our results support the need for ADE to explain the complexity of the epidemiological data.

Maximal sensitive dependence and the optimal path to epidemic extinction

Extinction of an epidemic or a species is a rare event that occurs due to a large, rare stochastic fluctuation. Although the extinction process is dynamically unstable, it follows an optimal path that maximizes the probability of extinction. We show that the optimal path is also directly related to the finite-time Lyapunov exponents of the underlying dynamical system in that the optimal path displays maximum sensitivity to initial conditions. We consider several stochastic epidemic models, and examine the extinction process in a dynamical systems framework. Using the dynamics of the finite-time Lyapunov exponents as a constructive tool, we demonstrate that the dynamical systems viewpoint of extinction evolves naturally toward the optimal path.

Epidemics with multistrain interactions: the interplay between cross immunity and antibody-dependent enhancement

This paper examines the interplay of the effect of cross immunity and antibody-dependent enhancement (ADE) in multistrain diseases. Motivated by dengue fever, we study a model for the spreading of epidemics in a population with multistrain interactions mediated by both partial temporary cross immunity and ADE. Although ADE models have previously been observed to cause chaotic outbreaks, we show analytically that weak cross immunity has a stabilizing effect on the system. That is, the onset of disease fluctuations requires a larger value of ADE with small cross immunity than without. However, strong cross immunity is shown numerically to cause oscillations and chaotic outbreaks even for low values of ADE.

Vaccinations in disease models with antibody-dependent enhancement

This paper examines the effects of single-strain vaccine campaigns on the dynamics of an epidemic multistrain model with antibody-dependent enhancement (ADE). ADE is a disease spreading process causing individuals with their secondary infection to be more infectious than during their first infection by a different strain. We follow the two-strain ADE model described in Cummings et al. [D.A.T. Cummings, Doctoral Thesis, Johns Hopkins University, 2004] and Schwartz et al. [I.B. Schwartz, L.B. Shaw, D.A.T. Cummings, L. Billings, M. McCrary, D. Burke, Chaotic desynchronization of multi-strain diseases, Phys. Rev. E, 72:art. no. 066201, 2005]. After describing the model and its steady state solutions, we modify it to include vaccine campaigns and explore if there exists vaccination rates that can eradicate one or more strains of a virus with ADE.