The impact of past epidemics on future disease dynamics

Bansal, Shweta; Meyers, Lauren Ancel

doi:10.1016/j.jtbi.2012.06.012

Cited by 37 publications

(53 citation statements)

References 52 publications

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“…In the case of partial immunity afforded by exposure to the pathogen during the first epidemic, individuals with a higher susceptibility will have been infected at a higher rate so that a larger proportion of them will have some protection. Let us mention the paper of Bansal and Meyers (2008) which studies closely related questions under different heterogeneity assumptions. Let μ be the susceptibility distribution of the population before the first epidemic, and R 0 the reproductive number, so that Z μ (R 0 ) is the attack rate of the first epidemic.…”

Section: Recurring Epidemicsmentioning

confidence: 99%

The size of epidemics in populations with heterogeneous susceptibility

Katriel

2011

J. Math. Biol.

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We formulate and study a general epidemic model allowing for an arbitrary distribution of susceptibility in the population. We derive the final-size equation which determines the attack rate of the epidemic, somewhat generalizing previous work. Our main aim is to use this equation to investigate how properties of the susceptibility distribution affect the attack rate. Defining an ordering among susceptibility distributions in terms of their Laplace transforms, we show that a susceptibility distribution dominates another in this ordering if and only if the corresponding attack rates are ordered for every value of the reproductive number R0. This result is used to prove a sharp universal upper bound for the attack rate valid for any susceptibility distribution, in terms of R0 alone, and a sharp lower bound in terms of R0 and the coefficient of variation of the susceptibility distribution. We apply some of these results to study two issues of epidemiological interest in a population with heterogeneous susceptibility: (1) the effect of vaccination of a fraction of the population with a partially effective vaccine, (2) the effect of an epidemic of a pathogen inducing partial immunity on the possibility and size of a future epidemic. In the latter case, we prove a surprising '50% law': if infection by a pathogen induces a partial immunity reducing susceptibility by less than 50%, then, whatever the value of R0>1 before the first epidemic, a second epidemic will occur, while if susceptibility is reduced by more than 50%, then a second epidemic will only occur if R0 is larger than a certain critical value greater than 1.

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Section: Recurring Epidemicsmentioning

confidence: 99%

The size of epidemics in populations with heterogeneous susceptibility

Katriel

2011

J. Math. Biol.

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“…We assume that T i decreases to T i = T f v (0 ≤ f v < 1) for a vaccinated node i ( figure 1(b)). In epidemiology, the vaccine with f v = 0 and that with f v = 0 are called perfect and leaky vaccination, respectively [22,36].…”

Section: Modelmentioning

confidence: 99%

“…Another (second) critical infection rate, above which the network remaining after all the infected nodes are deleted (we call it residual network) is disintegrated, also exists and is larger than the first critical infection rate. The residual network is important because a second epidemic spread may occur on it [21,22,23,24]. By using the generating functions, Newman derived the second critical infection rate for uncorrelated networks to show that the second critical infection rate is positive even for γ ≤ 3 [21].…”

Section: Introductionmentioning

confidence: 99%

Robustness of networks against propagating attacks under vaccination strategies

Hasegawa¹,

Masuda²

2011

J. Stat. Mech.

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Abstract. We study the effect of vaccination on robustness of networks against propagating attacks that obey the susceptible-infected-removed model. By extending the generating function formalism developed by Newman (2005), we analytically determine the robustness of networks that depends on the vaccination parameters. We consider the random defense where nodes are vaccinated randomly and the degreebased defense where hubs are preferentially vaccinated. We show that when vaccines are inefficient, the random graph is more robust against propagating attacks than the scale-free network. When vaccines are relatively efficient, the scale-free network with the degree-based defense is more robust than the random graph with the random defense and the scale-free network with the random defense.

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“…Vertebrate hosts exist in a somewhat more complex environment than the standard SIR framework assumes, and factors such as competing species, age‐structure and spatial‐structure may well have considerable impacts on our results. For example, Bansal and Meyers () considered the impact immunity has in an SIR model on a network, suggesting that higher pathogen virulence may evolve in the spatial model when hosts acquire immunity as they must be more infectious to infect populations multiple times. There are also an array of genetic and molecular components to the development of an adaptive immune system, all of which we have combined together in to one term for immunity.…”

Section: Discussionmentioning

confidence: 99%

The evolution of costly acquired immune memory

Best

Hoyle

2013

Ecology and Evolution

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A key feature of the vertebrate adaptive immune system is acquired immune memory, whereby hosts launch a faster and heightened response when challenged by previously encountered pathogens, preventing full infection. Here, we use a mathematical model to explore the role of ecological and epidemiological processes in shaping selection for costly acquired immune memory. Applying the framework of adaptive dynamics to the classic SIR (Susceptible-Infected-Recovered) epidemiological model, we focus on the conditions that may lead hosts to evolve high levels of immunity. Linking our work to previous theory, we show how investment in immune memory may be greatest at long or intermediate host lifespans depending on whether immunity is long lasting. High initial costs to gain immunity are also found to be essential for a highly effective immune memory. We also find that high disease infectivity and sterility, but intermediate virulence and immune period, increase selection for immunity. Diversity in host populations through evolutionary branching is found to be possible but only for a limited range of parameter space. Our model suggests that specific ecological and epidemiological conditions have to be met for acquired immune memory to evolve.

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The impact of past epidemics on future disease dynamics

Cited by 37 publications

References 52 publications

The size of epidemics in populations with heterogeneous susceptibility

The size of epidemics in populations with heterogeneous susceptibility

Robustness of networks against propagating attacks under vaccination strategies

The evolution of costly acquired immune memory

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