Article

# Fluctuations and oscillations in a simple epidemic model.

Departamento de Física and Centro de Física Teórica e Computacional, Faculdade de Ciências da Universidade de Lisboa, P-1649-003 Lisboa Codex, Portugal.

Physical Review E (Impact Factor: 2.31). 05/2009; 79(4 Pt 1):041922. DOI: 10.1103/PhysRevE.79.041922 Source: PubMed

- [Show abstract] [Hide abstract]

**ABSTRACT:**The time-covariance function captures the dynamics of biochemical fluctuations and contains important information about the underlying kinetic rate parameters. Intrinsic fluctuations in biochemical reaction networks are typically modelled using a master equation formalism. In general, the equation cannot be solved exactly and approximation methods are required. For small fluctuations close to equilibrium, a linearisation of the dynamics provides a very good description of the relaxation of the time-covariance function. As the number of molecules in the system decrease, deviations from the linear theory appear. Carrying out a systematic perturbation expansion of the master equation to capture these effects results in formidable algebra; however, symbolic mathematics packages considerably expedite the computation. The authors demonstrate that non-linear effects can reveal features of the underlying dynamics, such as reaction stoichiometry, not available in linearised theory. Furthermore, in models that exhibit noise-induced oscillations, non-linear corrections result in a shift in the base frequency along with the appearance of a secondary harmonic.IET Systems Biology 08/2012; 6(4):116-24. · 1.54 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The classic endemic model is used by Kuske et al. (2007) to study recurrence of childhood infections, which is a well-known but not well understood phenomenon. The conditions for recurrence that they derive are shown to agree with conditions for persistence.Journal of Theoretical Biology 08/2012; 313:212-6. · 2.35 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**A class of theoretical models seeks to explain rhythmic single cell data by postulating that they are generated by intrinsic noise in biochemical systems whose deterministic models exhibit only damped oscillations. The main features of such noise-induced oscillations are quantified by the power spectrum which measures the dependence of the oscillatory signal's power with frequency. In this paper we derive an approximate closed-form expression for the power spectrum of any monostable biochemical system close to a Hopf bifurcation, where noise-induced oscillations are most pronounced. Unlike the commonly used linear noise approximation which is valid in the macroscopic limit of large volumes, our theory is valid over a wide range of volumes and hence affords a more suitable description of single cell noise-induced oscillations. Our theory predicts that the spectra have three universal features: (i) a dominant peak at some frequency, (ii) a smaller peak at twice the frequency of the dominant peak and (iii) a peak at zero frequency. Of these, the linear noise approximation predicts only the first feature while the remaining two stem from the combination of intrinsic noise and nonlinearity in the law of mass action. The theoretical expressions are shown to accurately match the power spectra determined from stochastic simulations of mitotic and circadian oscillators. Furthermore it is shown how recently acquired single cell rhythmic fibroblast data displays all the features predicted by our theory and that the experimental spectrum is well described by our theory but not by the conventional linear noise approximation.Journal of Theoretical Biology 07/2013; · 2.35 Impact Factor

Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.