arXiv subjects

Sona John

Publications and source records attributed to Sona John.

6 recordsLinked to original sources

arXiv2025

Stochastic Time to Extinction of an SIQS Epidemic Model with Quiescence

Parasite quiescence is the ability for the pathogen to be inactive, with respect to metabolism and infectiousness, for some amount of time and then become active (infectious) again. The population is thus composed of an inactive proportion, and an active part in which evolution and reproduction takes place. In this paper, we investigate the effect of parasite quiescence on the time to extinction of infectious disease epidemics. We build a Susceptible-Infected-Quiescent-Susceptible (SIQS) epidemiological model. Hereby, host individuals infected by a quiescent parasite strain cannot recover, but are not infectious. We particularly focus on stochastic effects. We show that the quiescent state does not affect the reproduction number, but for a wide range of parameters the model behaves as an SIS model at a slower time scale, given by the fraction of time infected individuals are within the I state (and not in the Q state). This finding, proven using a time scale argument and singular perturbation theory for Markov processes, is illustrated and validated by numerical experiments based on the quasi-steady state distribution. We find here that the result even holds without a distinct time scale separation. Our results highlight the influence of quiescence as a bet-hedging strategy against disease stochastic extinction, and are relevant for predicting infectious disease dynamics in small populations.

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arXiv2022

Age structure, replicator equation, and the prisoner's dilemma

We investigate the evolutionary dynamics of an age-structured population under weak frequency-dependent selection. It turns out that the weak selection is affected in a non-trivial way by the life-history trait. We can disentangle the dynamics, based on the appearance of different time scales. These time scales, which seem to form a universal structure in the interplay of weak selection and life-history traits, allow us to reduce the infinite dimensional model to a one-dimensional modified replicator equation. The modified replicator equation is then used to investigate cooperation (the prisoner's dilemma) by means of adaptive dynamics. We identify conditions under which age structure is able to promote cooperation. At the end we discuss the relevance of our findings.

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arXiv2022

Quiescence generates moving average in a stochastic epidemiological model with one host and two parasites

Mathematical modelling of epidemiological and coevolutionary dynamics is widely being used to improve disease management strategies of infectious diseases. Many diseases present some form of intra-host quiescent stage, also known as covert infection, while others exhibit dormant stages in the environment. As quiescent/dormant stages can be resistant to drug, antibiotics, fungicide treatments, it is of practical relevance to study the influence of these two life-history traits on the coevolutionary dynamics. We develop first a deterministic coevolutionary model with two parasite types infecting one host type and study analytically the stability of the dynamical system. We specifically derive a stability condition for a five-by-five system of equations with quiescence. Second, we develop a stochastic version of the model to study the influence of quiescence on stochasticity of the system dynamics. We compute the steady state distribution of the parasite types which follows a multivariate normal distribution. Furthermore, we obtain numerical solutions for the covariance matrix of the system under symmetric and asymmetric quiescence rates between parasite types. When parasite strains are identical, quiescence increases the variance of the number of infected individuals at high transmission rate and vice versa when the transmission rate is low. However, when there is competition between parasite strains with different quiescent rates, quiescence generates a moving average behaviour which dampen off stochasticity and decreases the variance of the number of infected hosts. The strain with the highest rate of entering quiescence determines the strength of the moving average and the magnitude of reduction of stochasticity. Thus, it is worth investigating simple models of multi-strain parasite under quiescence/dormancy to improve disease management strategies.

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arXiv2016

Deterministic evolution of an asexual population under the action of beneficial and deleterious mutations on additive fitness landscapes

We study a continuous time model for the frequency distribution of an infinitely large asexual population in which both beneficial and deleterious mutations occur and the fitness is additive. When beneficial mutations are ignored, the exact solution for the frequency distribution is known to be a Poisson distribution. Here we include beneficial mutations and obtain exact expressions for the frequency distribution at all times using an eigenfunction expansion method. We find that the stationary distribution is non-Poissonian and related to the Bessel function of the first kind. We also provide suitable approximations for the stationary distribution and the time to relax to the steady state. Our exact results, especially at mutation-selection equilibrium, can be useful in developing semi-deterministic approaches to understand stochastic evolution.

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arXiv2015

Exploiting the adaptation dynamics to predict the distribution of beneficial fitness effects

Adaptation of asexual populations is driven by beneficial mutations and therefore the dynamics of this process, besides other factors, depend on the distribution of beneficial fitness effects. It is known that on uncorrelated fitness landscapes, this distribution can only be of three types: truncated, exponential and power law. We performed extensive stochastic simulations to study the adaptation dynamics on rugged fitness landscapes, and identified two quantities that can be used to distinguish the underlying distribution of beneficial fitness effects. The first quantity studied here is the fitness difference between successive mutations that spread in the population, which is found to decrease in the case of truncated distributions, remain nearly a constant for exponentially decaying distributions and increase when the fitness distribution decays as a power law. The second quantity of interest, namely, the rate of change of fitness with time also shows quantitatively different behaviour for different beneficial fitness distributions. The patterns displayed by the two aforementioned quantities are found to hold for both low and high mutation rates. We discuss how these patterns can be exploited to determine the distribution of beneficial fitness effects in microbial experiments.

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arXiv2015

Effect of drift, selection and recombination on the equilibrium frequency of deleterious mutations

We study the stationary state of a population evolving under the action of random genetic drift, selection and recombination in which both deleterious and reverse beneficial mutations can occur. We find that the equilibrium fraction of deleterious mutations decreases as the population size is increased. We calculate exactly the steady state frequency in a nonrecombining population when population size is infinite and for a neutral finite population, and obtain bounds on the fraction of deleterious mutations. We also find that for small and very large populations, the number of deleterious mutations depends weakly on recombination, but for moderately large populations, recombination alleviates the effect of deleterious mutations. An analytical argument shows that recombination decreases disadvantageous mutations appreciably when beneficial mutations are rare as is the case in adapting microbial populations, whereas it has a moderate effect on codon bias where the mutation rates between the preferred and unpreferred codons are comparable.

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