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On qualitative analysis of the nonstationary delayed model of coexistence of two-strain virus: Stability, bifurcation, and transition to chaos.

ABSTRACT: The model of interaction of two strains of the virus is considered in the paper. The model is based on a nonstationary system of differential equations with delays and takes into account populations of susceptible, first-time and re-infected individuals across two strains. For small values of the delays, the conditions of global asymptotic stability are obtained with the help of Lyapunov functionals technique. In some special cases the exponential estimates are constructed. On the basis of numerical modeling complex chaotic solutions of the model are obtained. Their investigation is performed with help of nonlinear characteristics, namely bifurcation maps based on Poincare sections and the maximal Lyapunov exponent were obtained.

SUBMITTER: Martsenyuk V

PROVIDER: S-EPMC7566851 | biostudies-literature | 2021 Jan

REPOSITORIES: biostudies-literature

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On qualitative analysis of the nonstationary delayed model of coexistence of two-strain virus: Stability, bifurcation, and transition to chaos.

Martsenyuk Vasyl V Augustynek Krzysztof K Urbas Andrzej A

International journal of non-linear mechanics 20201016

The model of interaction of two strains of the virus is considered in the paper. The model is based on a nonstationary system of differential equations with delays and takes into account populations of susceptible, first-time and re-infected individuals across two strains. For small values of the delays, the conditions of global asymptotic stability are obtained with the help of Lyapunov functionals technique. In some special cases the exponential estimates are constructed. On the basis of numer ...[more]

PMID: 33100373

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Project description:This paper investigates a RVF epidemic model by qualitative analysis and numerical simulations. Qualitative analysis have been used to explore the stability dynamics of the equilibrium points while visualization techniques such as bifurcation diagrams, Poincaré maps, maxima return maps and largest Lyapunov exponents are numerically computed to confirm further complexity of these dynamics induced by the seasonal forcing on the mosquitoes oviposition rates. The obtained results show that ordinary differential equation models with external forcing can have rich dynamic behaviour, ranging from bifurcation to strange attractors which may explain the observed fluctuations found in RVF empiric outbreak data, as well as the non deterministic nature of RVF inter-epidemic activities. Furthermore, the coexistence of the endemic equilibrium is subjected to existence of certain number of infected Aedes mosquitoes, suggesting that Aedes have potential to initiate RVF epidemics through transovarial transmission and to sustain low levels of the disease during post epidemic periods. Therefore we argue that locations that may serve as RVF virus reservoirs should be eliminated or kept under control to prevent multi-periodic outbreaks and consequent chains of infections. The epidemiological significance of this study is: (1) low levels of birth rate (in both Aedes and Culex) can trigger unpredictable outbreaks; (2) Aedes mosquitoes are more likely capable of inducing unpredictable behaviour compared to the Culex; (3) higher oviposition rates on mosquitoes do not in general imply manifestation of irregular behaviour on the dynamics of the disease. Finally, our model with external seasonal forcing on vector oviposition rates is able to mimic the linear increase in livestock seroprevalence during inter-epidemic period showing a constant exposure and presence of active transmission foci. This suggests that RVF outbreaks partly build upon RVF inter-epidemic activities. Therefore, active RVF surveillance in livestock is recommended.

Dataset Information

On qualitative analysis of the nonstationary delayed model of coexistence of two-strain virus: Stability, bifurcation, and transition to chaos.

Publications

On qualitative analysis of the nonstationary delayed model of coexistence of two-strain virus: Stability, bifurcation, and transition to chaos.

Similar Datasets

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