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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

Examples of incidence time series under eight different levels of cross-immunity. Other parameters: κ = 4, λ = 10, σ = 0.005, and μ = 0.0005. Two strains are represented by different lines. In graph (f) ψ = 1, two strains completely synchronize so that their incidences overlap
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Fig4: Examples of incidence time series under eight different levels of cross-immunity. Other parameters: κ = 4, λ = 10, σ = 0.005, and μ = 0.0005. Two strains are represented by different lines. In graph (f) ψ = 1, two strains completely synchronize so that their incidences overlap

Mentions: Without cross-immunity, our model demonstrates that the total incidence oscillates and two strains anti-synchronize as shown in Fig. 4a, which can be understood as a consequence of competition between strains and spatial correlation of nodes within the random network as argued above (cf., [58, 59]). On another extreme situation of full cross-immunity (ψ = 1.0), the total incidence oscillates but two strains synchronizes as shown in Fig. 4f. This is in agreement with the conclusions from [5] who consider complete cross-immune strains within a well-mixing population. However, the underlying mechanisms for oscillatory epidemics are different. In this study it is due to the interplay of competition and spatial correlation in contact structure while in [5], it is due to the enhanced infectivity within concurrent infection. With intermediate levels of cross-immunity, recurrent epidemics oscillate irregularly and dominant strains alternate between epidemics (Figs. 4b–e; cf., [12, 59]).Fig. 4


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

Zhang XS - Theor Biol Med Model (2016)

Examples of incidence time series under eight different levels of cross-immunity. Other parameters: κ = 4, λ = 10, σ = 0.005, and μ = 0.0005. Two strains are represented by different lines. In graph (f) ψ = 1, two strains completely synchronize so that their incidences overlap
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

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

Fig4: Examples of incidence time series under eight different levels of cross-immunity. Other parameters: κ = 4, λ = 10, σ = 0.005, and μ = 0.0005. Two strains are represented by different lines. In graph (f) ψ = 1, two strains completely synchronize so that their incidences overlap
Mentions: Without cross-immunity, our model demonstrates that the total incidence oscillates and two strains anti-synchronize as shown in Fig. 4a, which can be understood as a consequence of competition between strains and spatial correlation of nodes within the random network as argued above (cf., [58, 59]). On another extreme situation of full cross-immunity (ψ = 1.0), the total incidence oscillates but two strains synchronizes as shown in Fig. 4f. This is in agreement with the conclusions from [5] who consider complete cross-immune strains within a well-mixing population. However, the underlying mechanisms for oscillatory epidemics are different. In this study it is due to the interplay of competition and spatial correlation in contact structure while in [5], it is due to the enhanced infectivity within concurrent infection. With intermediate levels of cross-immunity, recurrent epidemics oscillate irregularly and dominant strains alternate between epidemics (Figs. 4b–e; cf., [12, 59]).Fig. 4

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