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In this paper, we identify a mechanism for chaos in the presence of noise. In a study of the SEIR model, which predicts epidemic outbreaks in childhood diseases, we show how chaotic dynamics can be attained by adding stochastic perturbations at parameters where chaos does not exist apriori. Data recordings of epidemics in childhood diseases are still argued… (More)

Multistrain diseases are diseases that consist of several strains, or serotypes. The serotypes may interact by antibody-dependent enhancement (ADE), in which infection with a single serotype is asymptomatic, but infection with a second serotype leads to serious illness accompanied by greater infectivity. It has been observed from serotype data of dengue… (More)

This paper investigates the complex dynamics induced by antibody-dependent enhancement (ADE) in multiserotype disease models. ADE is the increase in viral growth rate in the presence of immunity due to a previous infection of a different serotype. The increased viral growth rate is thought to increase the infectivity of the secondary infectious class. In… (More)

- Lora Billings, James H Curry
- 1996

This article is concerned with the dynamics of noninvertible transformations of the plane. Three examples are explored and possibly a new bifurcation, or \eruption", is described. A fundamental role is played by the interactions of xed points and singular curves. Other critical elements in the phase space include periodic points and an invariant line. The… (More)

Multistrain diseases have multiple distinct coexisting serotypes (strains). For some diseases, such as dengue fever, the serotypes interact by antibody-dependent enhancement (ADE), in which infection with a single serotype is asymptomatic, but contact with a second serotype leads to higher viral load and greater infectivity. We present and analyze a dynamic… (More)

- L Billings, E M Bollt
- 1999

We consider a family of chaotic skew tent maps. The skew tent map is a two-parameter, piecewise-linear, weakly-unimodal, map of the interval F aYb. We show that F aYb is Markov for a dense set of parameters in the chaotic region, and we exactly ®nd the probability density function (pdf), for any of these maps. It is well known (Boyarsky A, G ora P. Laws of… (More)

- Lora Billings, William M Spears, Ira B Schwartz
- 2002

We derive two models of viral epidemiology on connected networks and compare results to simulations. The differential equation model easily predicts the expected long term behavior by defining a boundary between survival and extinction regions. The discrete Markov model captures the short term behavior dependent on initial conditions, providing extinction… (More)

Antibody-dependent enhancement (ADE), a phenomenon in which viral replication is increased rather than decreased by immune sera, has been observed in vitro for a large number of viruses of public health importance, including flaviviruses, coronaviruses, and retroviruses. The most striking in vivo example of ADE in humans is dengue hemorrhagic fever, a… (More)

- Erik M Bollt, Lora Billings, Ira B Schwartz, E M Bollt
- 2002

We develop a new collection of tools aimed at studying stochastically perturbed dynamical systems. Specifically, in the setting of bi-stability, that is a two-attractor system, it has previously been numerically observed that a small noise volume is sufficient to destroy would be zero-noise case barriers in the phase space (pseudo-barriers), thus creating a… (More)

- Lora Billings, James H Curry, Eric Phipps
- 1997

There are few examples in dynamical systems theory which lend themselves to exact computations of macroscopic variables of interest. One such variable is the transverse Lyapunov exponent which measures the average attraction of an invariant set. This article presents a family of noninvertible transformations of the plane for which such computations are… (More)