Impact of incubation delay and stochastic perturbation on Dengue fever virus transmission model

ABSTRACT

Consider the fluctuation of environmental noise and the incubation period of virus, a stochastic vector-host model with incubation delay is proposed to describe the transmission of Dengue fever virus (DFVs) between humans and mosquitoes. By constructing suitable stochastic Lyapunov functional, the existence and uniqueness of global positive solutions of this model are proved. Furthermore, some sufficient conditions are obtained for the asymptotic pathwise estimation of solutions. In addition, we also consider the asymptotic pathwise estimation of solutions, the existence and uniqueness of stationary distribution of this model without delay, which imply that disease is stochastic persistent. Finally, numerical simulations explain the theoretical results and discuss the effects of stochastic perturbations and delays on DFVs transmission. Our results imply that the spread of DFVs presents many unpredictability under the influence of stochastic perturbation, and the reproduction number can no longer be used as a threshold condition for the extinction or persistence of disease. Moreover, ignoring the incubation delay will not only overestimate the risk of disease outbreaks but also underestimate the duration of diseases. Rational application of stochastic perturbations on disease transmission and incubation periods will play a very important role in vector-borne disease control.

KEYWORDS:

• Dengue fever transmission model
• stochastic perturbation
• Itô's formula
• incubation delay
• asymptotic pathwise estimation and stationary distribution

AMS CLASSIFICATIONS:

• 34A37
• 34D23
• 92D30

Acknowledgements

We are grateful to the editors and the anonymous referees for their careful reading and helpful comments which led to great improvement of our paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research is partially supported by the Natural Science Foundation of Xinjiang Uygur Autonomous Region [grant numbers 2021D01E12 and 2021D01C070], the National Natural Science Foundation of China [grant number 11961066].