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Quiescence Generates Moving Average in a Stochastic Epidemiological Model with One Host and Two Parasites

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  • Usman Sanusi

    (Population Genetics, Department of Life Science Systems, School of Life Sciences, Technical University of Munich, 85354 Freising, Germany
    Department of Mathematics, Technical University of Munich, 85748 Garching, Germany
    Department of Mathematics and Statistics, Umaru Musa Yar’adua University, Dutsin-Ma Road, Katsina P.M.B. 2218, Nigeria)

  • Sona John

    (Population Genetics, Department of Life Science Systems, School of Life Sciences, Technical University of Munich, 85354 Freising, Germany
    Department of Mathematics, Technical University of Munich, 85748 Garching, Germany)

  • Johannes Mueller

    (Department of Mathematics, Technical University of Munich, 85748 Garching, Germany
    Institute for Computational Biology, Helmholtz Center Munich, 85764 Neuherberg, Germany)

  • Aurélien Tellier

    (Population Genetics, Department of Life Science Systems, School of Life Sciences, Technical University of Munich, 85354 Freising, Germany)

Abstract

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.

Suggested Citation

  • Usman Sanusi & Sona John & Johannes Mueller & Aurélien Tellier, 2022. "Quiescence Generates Moving Average in a Stochastic Epidemiological Model with One Host and Two Parasites," Mathematics, MDPI, vol. 10(13), pages 1-22, June.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2289-:d:852676
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    References listed on IDEAS

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    1. Blath, Jochen & Tóbiás, András, 2020. "Invasion and fixation of microbial dormancy traits under competitive pressure," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7363-7395.
    2. Frédéric M Hamelin & Linda J S Allen & Vrushali A Bokil & Louis J Gross & Frank M Hilker & Michael J Jeger & Carrie A Manore & Alison G Power & Megan A Rúa & Nik J Cunniffe, 2019. "Coinfections by noninteracting pathogens are not independent and require new tests of interaction," PLOS Biology, Public Library of Science, vol. 17(12), pages 1-25, December.
    3. Koopmann, Bendix & Müller, Johannes & Tellier, Aurélien & Živković, Daniel, 2017. "Fisher–Wright model with deterministic seed bank and selection," Theoretical Population Biology, Elsevier, vol. 114(C), pages 29-39.
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