A continuous phenotype space model of RNA virus evolution within a host

Korobeinikov, Andrei; Dempsey, Conor

doi:10.3934/mbe.2014.11.919

Cited by 19 publications

(16 citation statements)

References 24 publications

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“…Naturally, the latter condition is automatically satisfied for the endemic equilibrium point P * f associated with the fittest strain f (since R 0f ≡ max i R 0i ). 21 Beyond the non-negativity of the endemic equilibrium solutions we should also investigate the analytic form and relative magnitudes of the various infectious populations at P * i . For this purpose we again turn to the recursive relation (35).…”

Section: ≥0mentioning

confidence: 99%

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Coupled, multi-strain epidemic models of mutating pathogens

Meehan

Cocks

Trauer

et al. 2018

Mathematical Biosciences

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We introduce and analyze coupled, multi-strain epidemic models designed to simulate the emergence and dissemination of mutant (e.g. drug-resistant) pathogen strains. In particular, we investigate the mathematical and biological properties of a general class of multi-strain epidemic models in which the infectious compartments of each strain are coupled together in a general manner. We derive explicit expressions for the basic reproduction number of each strain and highlight their importance in regulating the system dynamics (e.g. the potential for an epidemic outbreak) and the existence of nonnegative endemic solutions. Importantly, we find that the basic reproduction number of each strain is independent of the mutation rates between the strains -even under quite general assumptions for the form of the infectious compartment coupling. Moreover, we verify that the coupling term promotes strain coexistence (as an extension of the competitive exclusion principle) and demonstrate that the strain with the greatest reproductive capacity is not necessarily the most prevalent. Finally, we briefly discuss the implications of our results for public health policy and planning.

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Section: ≥0mentioning

confidence: 99%

“…Here we are focusing specifically on population-level models. For examples of withinhost models see[19,20,21].…”

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confidence: 99%

Coupled, multi-strain epidemic models of mutating pathogens

Meehan

Cocks

Trauer

et al. 2018

Mathematical Biosciences

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“…A reasonably simple mechanistic model of HIV within-host evolution was recently suggested by Korobeinikov & Dempsey [ 7 ]. This model is based upon the Nowak and May model of HIV intra-host dynamics [ 8 ] and is mechanistic (as far as the Nowak–May model is mechanistic).…”

Section: Introductionmentioning

confidence: 99%

A mathematical model of marine bacteriophage evolution

Pagliarini

Korobeinikov

2018

R. Soc. open sci.

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To explore how particularities of a host cell–virus system, and in particular host cell replication, affect viral evolution, in this paper we formulate a mathematical model of marine bacteriophage evolution. The intrinsic simplicity of real-life phage–bacteria systems, and in particular aquatic systems, for which the assumption of homogeneous mixing is well justified, allows for a reasonably simple model. The model constructed in this paper is based upon the Beretta–Kuang model of bacteria–phage interaction in an aquatic environment (Beretta & Kuang 1998 Math. Biosci. 149, 57–76. (doi:10.1016/S0025-5564(97)10015-310.1016/S0025-5564(97)10015-3)). Compared to the original Beretta–Kuang model, the model assumes the existence of a multitude of viral variants which correspond to continuously distributed phenotypes. It is noteworthy that the model is mechanistic (at least as far as the Beretta–Kuang model is mechanistic). Moreover, this model does not include any explicit law or mechanism of evolution; instead it is assumed, in agreement with the principles of Darwinian evolution, that evolution in this system can occur as a result of random mutations and natural selection. Simulations with a simplistic linear fitness landscape (which is chosen for the convenience of demonstration only and is not related to any real-life system) show that a pulse-type travelling wave moving towards increasing Darwinian fitness appears in the phenotype space. This implies that the overall fitness of a viral quasi-species steadily increases with time. That is, the simulations demonstrate that for an uneven fitness landscape random mutations combined with a mechanism of natural selection (for this particular system this is given by the conspecific competition for the resource) lead to the Darwinian evolution. It is noteworthy that in this system the speed of propagation of this wave (and hence the rate of evolution) is not constant but varies, depending on the current viral fitness and the abundance of susceptible bacteria. A specific feature of the original Beretta–Kuang model is that this model exhibits a supercritical Hopf bifurcation, leading to the loss of stability and the rise of self-sustained oscillations in the system. This phenomenon corresponds to the paradox of enrichment in the system. It is remarkable that under the conditions that ensure the bifurcation in the Beretta-Kuang model, the viral evolution model formulated in this paper also exhibits a rise in self-sustained oscillations of the abundance of all interacting populations. The propagation of the travelling wave, however, remains stable under these conditions. The only visible impact of the oscillations on viral evolution is a lower speed of the evolution.

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“…Hence we choose to model the type of strain by a continuous variable, see e.g. [20]. We assume that different strains may have different infective capabilities.…”

Section: Introductionmentioning

confidence: 99%

On a strain-structured epidemic model

Calsina

Farkas

2016

Nonlinear Analysis: Real World Applications

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Abstract. We introduce and investigate an SIS-type model for the spread of an infectious disease, where the infected population is structured with respect to the different strain of the virus/bacteria they are carrying. Our aim is to capture the interesting scenario when individuals infected with different strains cause secondary (new) infections at different rates. Therefore, we consider a nonlinear infection process, which generalises the bilinear process arising from the classic mass-action assumption. Our main motivation is to study competition between different strains of a virus/bacteria. From the mathematical point of view, we are interested whether the nonlinear infection process leads to a well-posed model. We use a semilinear formulation to show global existence and positivity of solutions up to a critical value of the exponent in the nonlinearity. Furthermore, we establish the existence of the endemic steady state for particular classes of nonlinearities.

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A continuous phenotype space model of RNA virus evolution within a host

Cited by 19 publications

References 24 publications

Coupled, multi-strain epidemic models of mutating pathogens

Coupled, multi-strain epidemic models of mutating pathogens

A mathematical model of marine bacteriophage evolution

On a strain-structured epidemic model

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