Limits...
Epidemic cycling in a multi-strain SIRS epidemic network model.

Zhang XS - Theor Biol Med Model (2016)

Bottom Line: The standard pair approximation is applied to describe the changing numbers of individuals in different infection states and contact pairs.We show that spatial correlation due to contact network and interactions between strains through both ecological interference and immune response interact to generate epidemic cycling.Our results suggest that co-circulation of multiple strains within a contact network provides an explanation for epidemic cycling.

View Article: PubMed Central - PubMed

Affiliation: Department of Statistics, Modelling and Economics, Centre for Infectious Disease Surveillance and Control, Public Health England, 61 Colindale Avenue, London, NW9 5EQ, UK. xu-sheng.zhang@phe.gov.uk.

ABSTRACT

Background: One common observation in infectious diseases caused by multi-strain pathogens is that both the incidence of all infections and the relative fraction of infection with each strain oscillate with time (i.e., so-called Epidemic cycling). Many different mechanisms have been proposed for the pervasive nature of epidemic cycling. Nevertheless, the two facts that people contact each other through a network rather than following a simple mass-action law and most infectious diseases involve multiple strains have not been considered together for their influence on the epidemic cycling.

Methods: To demonstrate how the structural contacts among people influences the dynamical patterns of multi-strain pathogens, we investigate a two strain epidemic model in a network where every individual randomly contacts with a fixed number of other individuals. The standard pair approximation is applied to describe the changing numbers of individuals in different infection states and contact pairs.

Results: We show that spatial correlation due to contact network and interactions between strains through both ecological interference and immune response interact to generate epidemic cycling. Compared to one strain epidemic model, the two strain model presented here can generate epidemic cycling within a much wider parameter range that covers many infectious diseases.

Conclusion: Our results suggest that co-circulation of multiple strains within a contact network provides an explanation for epidemic cycling.

No MeSH data available.


Related in: MedlinePlus

The effect of cross-immunity on the oscillatory phase. The parameter area for cycling epidemics (II) increases with cross-immunity but reduces rapidly when cross-immunity becomes complete. Other parameters: κ = 8, λ = 10 and two birth rates are assumed: μ = 0.0005 (solid line) and μ = σ (dashed line). In the later situation the threshold waning rate of immunity nearly halves, which indicates that most of individuals stay in the recovery and immune compartments
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

License 1 - License 2
getmorefigures.php?uid=PMC4836137&req=5

Fig3: The effect of cross-immunity on the oscillatory phase. The parameter area for cycling epidemics (II) increases with cross-immunity but reduces rapidly when cross-immunity becomes complete. Other parameters: κ = 8, λ = 10 and two birth rates are assumed: μ = 0.0005 (solid line) and μ = σ (dashed line). In the later situation the threshold waning rate of immunity nearly halves, which indicates that most of individuals stay in the recovery and immune compartments

Mentions: Introduction of cross-immunity between strains further enlarges the oscillatory phase in the two strain model (Figs. 2 and 3). In contrast to the one strain model where oscillatory phase disappears on networks of degree κ > 6 [16], the oscillatory epidemics in the two strain model persist on contact networks of a very high degree κ (Fig. 2). This implies that the ecological interference and cross-immunity in some ways compensate weakened spatial correlation at highly contact networks. Therefore, the two strain SIRS epidemic model can easily explain the oscillatory behaviours observed in childhood infectious diseases. Under the extreme circumstance of complete cross-immunity, the oscillatory phase decreases considerably (Fig. 3); for the situation shown in Fig. 2 recurrent epidemics emerge only on contact networks of a degree κ < 5.Fig. 2


Epidemic cycling in a multi-strain SIRS epidemic network model.

Zhang XS - Theor Biol Med Model (2016)

The effect of cross-immunity on the oscillatory phase. The parameter area for cycling epidemics (II) increases with cross-immunity but reduces rapidly when cross-immunity becomes complete. Other parameters: κ = 8, λ = 10 and two birth rates are assumed: μ = 0.0005 (solid line) and μ = σ (dashed line). In the later situation the threshold waning rate of immunity nearly halves, which indicates that most of individuals stay in the recovery and immune compartments
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

License 1 - License 2
Show All Figures
getmorefigures.php?uid=PMC4836137&req=5

Fig3: The effect of cross-immunity on the oscillatory phase. The parameter area for cycling epidemics (II) increases with cross-immunity but reduces rapidly when cross-immunity becomes complete. Other parameters: κ = 8, λ = 10 and two birth rates are assumed: μ = 0.0005 (solid line) and μ = σ (dashed line). In the later situation the threshold waning rate of immunity nearly halves, which indicates that most of individuals stay in the recovery and immune compartments
Mentions: Introduction of cross-immunity between strains further enlarges the oscillatory phase in the two strain model (Figs. 2 and 3). In contrast to the one strain model where oscillatory phase disappears on networks of degree κ > 6 [16], the oscillatory epidemics in the two strain model persist on contact networks of a very high degree κ (Fig. 2). This implies that the ecological interference and cross-immunity in some ways compensate weakened spatial correlation at highly contact networks. Therefore, the two strain SIRS epidemic model can easily explain the oscillatory behaviours observed in childhood infectious diseases. Under the extreme circumstance of complete cross-immunity, the oscillatory phase decreases considerably (Fig. 3); for the situation shown in Fig. 2 recurrent epidemics emerge only on contact networks of a degree κ < 5.Fig. 2

Bottom Line: The standard pair approximation is applied to describe the changing numbers of individuals in different infection states and contact pairs.We show that spatial correlation due to contact network and interactions between strains through both ecological interference and immune response interact to generate epidemic cycling.Our results suggest that co-circulation of multiple strains within a contact network provides an explanation for epidemic cycling.

View Article: PubMed Central - PubMed

Affiliation: Department of Statistics, Modelling and Economics, Centre for Infectious Disease Surveillance and Control, Public Health England, 61 Colindale Avenue, London, NW9 5EQ, UK. xu-sheng.zhang@phe.gov.uk.

ABSTRACT

Background: One common observation in infectious diseases caused by multi-strain pathogens is that both the incidence of all infections and the relative fraction of infection with each strain oscillate with time (i.e., so-called Epidemic cycling). Many different mechanisms have been proposed for the pervasive nature of epidemic cycling. Nevertheless, the two facts that people contact each other through a network rather than following a simple mass-action law and most infectious diseases involve multiple strains have not been considered together for their influence on the epidemic cycling.

Methods: To demonstrate how the structural contacts among people influences the dynamical patterns of multi-strain pathogens, we investigate a two strain epidemic model in a network where every individual randomly contacts with a fixed number of other individuals. The standard pair approximation is applied to describe the changing numbers of individuals in different infection states and contact pairs.

Results: We show that spatial correlation due to contact network and interactions between strains through both ecological interference and immune response interact to generate epidemic cycling. Compared to one strain epidemic model, the two strain model presented here can generate epidemic cycling within a much wider parameter range that covers many infectious diseases.

Conclusion: Our results suggest that co-circulation of multiple strains within a contact network provides an explanation for epidemic cycling.

No MeSH data available.


Related in: MedlinePlus