Chaotic desynchronization of multistrain diseases

Abstract

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 hemorrhagic fever that outbreaks of the four serotypes occur asynchronously. Both autonomous and seasonally driven outbreaks were studied in a model containing ADE. For sufficiently small ADE, the number of infectives of each serotype synchronizes, with outbreaks occurring in phase. When the ADE increases past a threshold, the system becomes chaotic, and infectives of each serotype desynchronize. However, certain groupings of the primary and secondary infectives remain synchronized even in the chaotic regime.

Instabilities in multiserotype disease models with antibody-dependent enhancement

“…Similarly, we can follow approaches used in previous dengue models without ADE, as in Vargas (2000, 2003). Here, we examine a dynamical system with a general number of cocirculating serotypes and an ADE factor that modifies the transmissibility of secondary infections, providing derivations of and extending previous work in Cummings et al (2005) and Schwartz et al (2005). As we begin to understand the complexity of the dengue model, we gain a better perspective in formulating optimal vaccination strategies.…”

“…Understanding the dynamics of a mathematical model of a multiserotype disease with ADE could help in this effort. Foundational work on ADE factors can be found in Ferguson et al (1999a,b), Cummings et al (2005), and Schwartz et al (2005). Similarly, we can follow approaches used in previous dengue models without ADE, as in Vargas (2000, 2003).…”

Dynamic effects of antibody-dependent enhancement on the fitness of viruses

“…Also, these Hopf branches are stable for only a small range of all to the right of the bifurcation point. Another bifurcation leads to chaos-like oscillations as indicated by the Lyapunov exponents (41).…”

Epidemiology of Dengue Fever: A Model with Temporary Cross-Immunity and Possible Secondary Infection Shows Bifurcations and Chaotic Behaviour in Wide Parameter Regions

“…Stochastic versions of such models with only fixed points possible as attractors but oscillating transients are reported to also show stabilization of the oscillations due to population noise [5,25]. To capture differences in primary infection by one strain and secondary infection by another strain we consider a basic two-strain SIR-type model for the host population, which is only slightly refined as opposed to previously suggested models for dengue fever [13,30]. It is capturing the effective dynamics of the human host population for the dengue virus, taking effects of the vector dynamics or seasonality only into account by the effective parameters in the SIR-type model, but not modelling these mechanisms explicitly.…”

“…More recently, modelling attention has focussed on higher viral load of hosts on secondary infection than on the first due to ADE, hence a higher contribution to the force of infection of each strain, reporting deterministically chaotic attractors [13] and chaos desynchronization [30,6] to explain the co-existence of the known four dengue viral strains. Temporary cross-immunity against all strains after a first infection has been included in mathematical models as well, but again limiting the effect of ADE to increase the contribution of secondary cases to the force of infection [33].…”