A self-regulating and patch subdivided population

Belhadji, Lamia; Bertacchi, Daniela; Zucca, Fabio

doi:10.1017/s0001867800050497

Cited by 5 publications

(4 citation statements)

References 9 publications

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“…In order to obtain a more realistic behaviour, where only a certain maximal viral load can be achieved (or at least, growth slows down when the viral population is too large), we can put interaction into play (logistic competition is perhaps the simplest interaction). Spatially displaced interacting particle systems have been studied for instance in [2,3,4].…”

Section: Stochastic Model and Deterministic Approximationmentioning

confidence: 99%

Combination versus sequential monotherapy in chronic HBV infection: a mathematical approach

et al. 2014

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Sequential monotherapy is the most widely used therapeutic approach in the treatment of hepatitis B virus (HBV) chronic infection. Unfortunately, under therapy, in some patients the hepatitis virus mutates and gives rise to variants which are drug resistant. We wonder whether those patients would have benefited from the choice of combination therapy instead of sequential monotherapy. To study the action of these two therapeutic approaches and to explain the emergence of drug resistance, we propose a stochastic model for the infection within a patient who is treated with two drugs, either sequentially or contemporaneously, and who, under the first kind of therapy develops a strain of the virus which is resistant to both drugs. Our stochastic model has a deterministic approximation which is a slight modification of a classic three-strain model. We discuss why stochastic simulations are more suitable than the study of the deterministic approximation, when modelling the rise of mutations (this is mainly due to the amplitude of the stochastic fluctuations). We run stochastic simulations with suitable parameters and compare the time when, under the two therapeutic approaches, the resistant strain first reaches detectability in the serum viral load. Our results show that the best choice is to start an early combination therapy, which allows one to stay drug resistance free for a longer time and in many cases leads to viral eradication.

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Section: Stochastic Model and Deterministic Approximationmentioning

confidence: 99%

Combination versus sequential monotherapy in chronic HBV infection: a mathematical approach

et al. 2014

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“…For the simplest among this models, the branching random walk, much has been done: for instance in [4,5,7,32,45,47] one finds characterization of the persistence/disappearance of genotypes (seen as locations for the model), on general space structures; the same can be found, for some random graphs, in [8,35]. Stochastic modelling and interacting particle systems have been successfully applied to biology and ecology (see [1,2,3,12,13,24,25,26,28,19,48] just to mention a few). Although stochastic modelling is very interesting and complex, here we will assume that over many generations, our populations have been sufficiently large to justify the use of a model where stochasticity appears only in the random time at which the disturbance strikes.…”

Section: Introductionmentioning

confidence: 99%

The timing of life history events in the presence of soft disturbances

Bertacchi

Zucca

Ambrosini

2016

Journal of Theoretical Biology

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We study a model for the evolutionarily stable strategy (ESS) used by biological populations for choosing the time of life-history events, such as migration and breeding. In our model we accounted for both intra-species competition (early individuals have a competitive advantage) and a disturbance which strikes at a random time, killing a fraction 1 − p of the population. Disturbances include spells of bad weather, such as freezing or heavily raining days. It has been shown in [23], that when p = 0, then the ESS is a mixed strategy, where individuals wait for a certain time and afterwards start arriving (or breeding) every day. We remove the constraint p = 0 and show that if 0 < p < 1 then the ESS still implies a mixed choice of times, but strong competition may lead to a massive arrival at the earliest time possible of a fraction of the population, while the rest will arrive throughout the whole period during which the disturbance may occur. More precisely, given p, there is a threshold for the competition parameter a, above which massive arrivals occur and below which there is a behaviour as in [23]. We study the behaviour of the ESS and of the average fitness of the population, depending on the parameters involved. We also discuss how the population may be affected by climate change, in two respects: first, how the ESS should change under the new climate and whether this change implies an increase of the average fitness; second, which is the impact of the new climate on a population that still follows the old strategy. We show that, at least under some conditions, extreme weather events imply a temporary decrease of the average fitness (thus an increasing mortality). If the population adapts to the new climate, the survivors may have a larger fitness. * The first two authors contributed equally to this work.

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“…In the literature one can find BRWs both in continuous and discrete time. The continuous-time setting has been studied by many authors (see [17,18,19,20,22] just to name a few) along with some variants of the process (see [2,3,4,5,8]). The discrete-time case has been initially considered as a natural generalization of branching processes (see [1,10,11,12,13,16]).…”

Section: Introductionmentioning

confidence: 99%

Strong Local Survival of Branching Random Walks is Not Monotone

Bertacchi

Zucca

2014

Adv. Appl. Probab.

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Abstract. The aim of this paper is the study of the strong local survival property for discretetime and continuous-time branching random walks. We study this property by means of an infinite dimensional generating function G and a maximum principle which, we prove, is satisfied by every fixed point of G. We give results about the existence of a strong local survival regime and we prove that, unlike local and global survival, in continuous time, strong local survival is not a monotone property in the general case (though it is monotone if the branching random walk is quasi transitive). We provide an example of an irreducible branching random walk where the strong local property depends on the starting site of the process. By means of other counterexamples we show that the existence of a pure global phase is not equivalent to nonamenability of the process, and that even an irreducible branching random walk with the same branching law at each site may exhibit non-strong local survival. Finally we show that the generating function of a irreducible BRW can have more than two fixed points; this disproves a previously known result.

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A self-regulating and patch subdivided population

Cited by 5 publications

References 9 publications

Combination versus sequential monotherapy in chronic HBV infection: a mathematical approach

Combination versus sequential monotherapy in chronic HBV infection: a mathematical approach

The timing of life history events in the presence of soft disturbances

Strong Local Survival of Branching Random Walks is Not Monotone

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