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Evolution of pathogens towards low R0 in heterogeneous populations.

Kao RR - J. Theor. Biol. (2006)

Bottom Line: However, exploitation of heterogeneities results in a more rapid depletion of the potentially susceptible neighbourhood for an infected host.In this model, it is shown that pathogens may evolve towards lower R(0), even if this results in pathogen extinction.For sufficiently high transmissibility, two locally stable strategies exist for an evolving pathogen, one that exploits heterogeneities and results in higher R(0), and one that does not, and results in lower R(0).

View Article: PubMed Central - PubMed

Affiliation: Department of Zoology, University of Oxford, South Parks Rd., OX1 3PS, UK. rowland.kao@zoo.ox.ac.uk

ABSTRACT
Maximization of the basic reproduction ratio or R(0) is widely believed to drive the emergence of novel pathogens. The presence of exploitable heterogeneities in a population, such as high variance in the number of potentially infectious contacts, increases R(0) and thus pathogens that can exploit heterogeneities in the contact structure have an advantage over those that do not. However, exploitation of heterogeneities results in a more rapid depletion of the potentially susceptible neighbourhood for an infected host. Here a simple model of pathogen evolution in a heterogeneous environment is developed and placed in the context of HIV transmission. In this model, it is shown that pathogens may evolve towards lower R(0), even if this results in pathogen extinction. For sufficiently high transmissibility, two locally stable strategies exist for an evolving pathogen, one that exploits heterogeneities and results in higher R(0), and one that does not, and results in lower R(0). While the low R(0) strategy is never evolutionarily stable, invading strains with higher R(0) will also converge to the low R(0) strategy if not sufficiently different from the resident strain. Heterogenous transmission is increasingly recognized as fundamental to epidemiological dynamics and the evolution of pathogens; here, it is shown that the ability to exploit heterogeneity is a strategy that can itself evolve.

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Related in: MedlinePlus

Time evolution of disease following introduction of a single highly connected individual into a population of 10 000, showing evolution to extinction. On the left, the pathogen evolves towards a low-variance strategy (starting value , solid line) and drives itself to extinction, on the right the pathogen evolves towards the high-variance strategy and persists . The remaining curves show the proportion of highly connected (high risk) population infected (short dashes), proportion of poorly connected (low risk) population infected (dot–dash), and proportion of total population infected (long dashes). Parameters are scaling factor , and infection rate  and population shift rate .
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fig5: Time evolution of disease following introduction of a single highly connected individual into a population of 10 000, showing evolution to extinction. On the left, the pathogen evolves towards a low-variance strategy (starting value , solid line) and drives itself to extinction, on the right the pathogen evolves towards the high-variance strategy and persists . The remaining curves show the proportion of highly connected (high risk) population infected (short dashes), proportion of poorly connected (low risk) population infected (dot–dash), and proportion of total population infected (long dashes). Parameters are scaling factor , and infection rate and population shift rate .

Mentions: Fig. 4 shows the resultant phase diagram in z and γ under these parameters (Fig. 4a), and with the same parameters but with the scaling factor reduced to (Fig. 4b). This is equivalent to changing the behaviour of a targeted proportion of the population (e.g. increased use of prophylactics in the high risk population to prevent STD transmission). For , the disease-free equilibrium is the only steady-state. As γ increases, the high variance strategy becomes locally stable, but the low-R0 strategy remains unstable. The locally stable region around appears as soon as the low-R0 strategy becomes viable (i.e. ). Fig. 4 shows the existence of a region where , but the solution can still tend towards the , regime, and thus the pathogen disappears. This is illustrated in Fig. 5. At higher γ the low-R0 strategy becomes more likely, but dependence on γ is not strong (less than a 5% increase in the locally stable region, for a doubling of γ from 0.5 to 1). Changing the scaling factor s (i.e. decreasing the extent of heterogeneity) can have a more dramatic effect on the phase diagram, as reducing σ from 5 to 3 increasing the stable regime by approximately 20% at .


Evolution of pathogens towards low R0 in heterogeneous populations.

Kao RR - J. Theor. Biol. (2006)

Time evolution of disease following introduction of a single highly connected individual into a population of 10 000, showing evolution to extinction. On the left, the pathogen evolves towards a low-variance strategy (starting value , solid line) and drives itself to extinction, on the right the pathogen evolves towards the high-variance strategy and persists . The remaining curves show the proportion of highly connected (high risk) population infected (short dashes), proportion of poorly connected (low risk) population infected (dot–dash), and proportion of total population infected (long dashes). Parameters are scaling factor , and infection rate  and population shift rate .
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC1919410&req=5

fig5: Time evolution of disease following introduction of a single highly connected individual into a population of 10 000, showing evolution to extinction. On the left, the pathogen evolves towards a low-variance strategy (starting value , solid line) and drives itself to extinction, on the right the pathogen evolves towards the high-variance strategy and persists . The remaining curves show the proportion of highly connected (high risk) population infected (short dashes), proportion of poorly connected (low risk) population infected (dot–dash), and proportion of total population infected (long dashes). Parameters are scaling factor , and infection rate and population shift rate .
Mentions: Fig. 4 shows the resultant phase diagram in z and γ under these parameters (Fig. 4a), and with the same parameters but with the scaling factor reduced to (Fig. 4b). This is equivalent to changing the behaviour of a targeted proportion of the population (e.g. increased use of prophylactics in the high risk population to prevent STD transmission). For , the disease-free equilibrium is the only steady-state. As γ increases, the high variance strategy becomes locally stable, but the low-R0 strategy remains unstable. The locally stable region around appears as soon as the low-R0 strategy becomes viable (i.e. ). Fig. 4 shows the existence of a region where , but the solution can still tend towards the , regime, and thus the pathogen disappears. This is illustrated in Fig. 5. At higher γ the low-R0 strategy becomes more likely, but dependence on γ is not strong (less than a 5% increase in the locally stable region, for a doubling of γ from 0.5 to 1). Changing the scaling factor s (i.e. decreasing the extent of heterogeneity) can have a more dramatic effect on the phase diagram, as reducing σ from 5 to 3 increasing the stable regime by approximately 20% at .

Bottom Line: However, exploitation of heterogeneities results in a more rapid depletion of the potentially susceptible neighbourhood for an infected host.In this model, it is shown that pathogens may evolve towards lower R(0), even if this results in pathogen extinction.For sufficiently high transmissibility, two locally stable strategies exist for an evolving pathogen, one that exploits heterogeneities and results in higher R(0), and one that does not, and results in lower R(0).

View Article: PubMed Central - PubMed

Affiliation: Department of Zoology, University of Oxford, South Parks Rd., OX1 3PS, UK. rowland.kao@zoo.ox.ac.uk

ABSTRACT
Maximization of the basic reproduction ratio or R(0) is widely believed to drive the emergence of novel pathogens. The presence of exploitable heterogeneities in a population, such as high variance in the number of potentially infectious contacts, increases R(0) and thus pathogens that can exploit heterogeneities in the contact structure have an advantage over those that do not. However, exploitation of heterogeneities results in a more rapid depletion of the potentially susceptible neighbourhood for an infected host. Here a simple model of pathogen evolution in a heterogeneous environment is developed and placed in the context of HIV transmission. In this model, it is shown that pathogens may evolve towards lower R(0), even if this results in pathogen extinction. For sufficiently high transmissibility, two locally stable strategies exist for an evolving pathogen, one that exploits heterogeneities and results in higher R(0), and one that does not, and results in lower R(0). While the low R(0) strategy is never evolutionarily stable, invading strains with higher R(0) will also converge to the low R(0) strategy if not sufficiently different from the resident strain. Heterogenous transmission is increasingly recognized as fundamental to epidemiological dynamics and the evolution of pathogens; here, it is shown that the ability to exploit heterogeneity is a strategy that can itself evolve.

Show MeSH
Related in: MedlinePlus