American Institute of Mathematical Sciences

• Previous Article
Initial value problem for fractional Volterra integro-differential equations with Caputo derivative
• DCDS-B Home
• This Issue
• Next Article
Periodic, almost periodic and almost automorphic solutions for SPDEs with monotone coefficients
December  2021, 26(12): 6463-6481. doi: 10.3934/dcdsb.2021029

Dynamics of a vector-host model under switching environments

 1 Department of Mathematics, The University of Alabama, Tuscaloosa, Alabama 35487-0350, USA 2 Faculty of Basic Sciences, Ho Chi Minh University of Transport, 2 Vo Oanh, Ho Chi Minh, Vietnam

** Corresponding author: Tran D. Tuong

Received  January 2020 Revised  November 2020 Published  December 2021 Early access  February 2021

Fund Project: This author is supported in part by NSF grant DMS-1853467

In this paper, the stochastic vector-host model has been proposed and analysed using nice properties of piecewise deterministic Markov processes (PDMPs). A threshold for the stochastic model is derived whose sign determines whether the disease will eventually disappear or persist. We show mathematically the existence of scenarios where switching plays a significant role in surprisingly reversing the long-term properties of deterministic systems.

Citation: Harrison Watts, Arti Mishra, Dang H. Nguyen, Tran D. Tuong. Dynamics of a vector-host model under switching environments. Discrete & Continuous Dynamical Systems - B, 2021, 26 (12) : 6463-6481. doi: 10.3934/dcdsb.2021029
References:

show all references

References:
Sample paths of $I_H(t)$ (Example 4.1). In the deterministic systems (LEFT) there is persistence in state 1 and extinction in state 2. In the switched system (RIGHT), the infection persists
Sample paths of $I_H(t)$ (Example 4.2). In both deterministic systems (LEFT), $I_H(t)$ converges exponentially fast to 0. Switching makes the disease persist (RIGHT)
Joint density of $(S_H(t),I_H(t),\xi_t)$ in state 1 (LEFT) and state 2 (RIGHT), according to the invariant measure (Example 4.2)
Sample paths of $I_H(t)$ (Example 4.3). In both deterministic systems, $I_H(t)$ converges to a positive equilibrium (LEFT). Switching allows for extinction (RIGHT)
 [1] Qingkai Kong, Zhipeng Qiu, Zi Sang, Yun Zou. Optimal control of a vector-host epidemics model. Mathematical Control & Related Fields, 2011, 1 (4) : 493-508. doi: 10.3934/mcrf.2011.1.493 [2] Yan-Xia Dang, Zhi-Peng Qiu, Xue-Zhi Li, Maia Martcheva. Global dynamics of a vector-host epidemic model with age of infection. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 1159-1186. doi: 10.3934/mbe.2017060 [3] Yanzhao Cao, Dawit Denu. Analysis of stochastic vector-host epidemic model with direct transmission. Discrete & Continuous Dynamical Systems - B, 2016, 21 (7) : 2109-2127. doi: 10.3934/dcdsb.2016039 [4] Yanxia Dang, Zhipeng Qiu, Xuezhi Li. Competitive exclusion in an infection-age structured vector-host epidemic model. Mathematical Biosciences & Engineering, 2017, 14 (4) : 901-931. doi: 10.3934/mbe.2017048 [5] Shangzhi Li, Shangjiang Guo. Persistence and extinction of a stochastic SIS epidemic model with regime switching and Lévy jumps. Discrete & Continuous Dynamical Systems - B, 2021, 26 (9) : 5101-5134. doi: 10.3934/dcdsb.2020335 [6] Tzy-Wei Hwang, Yang Kuang. Host Extinction Dynamics in a Simple Parasite-Host Interaction Model. Mathematical Biosciences & Engineering, 2005, 2 (4) : 743-751. doi: 10.3934/mbe.2005.2.743 [7] Keng Deng, Yixiang Wu. Extinction and uniform strong persistence of a size-structured population model. Discrete & Continuous Dynamical Systems - B, 2017, 22 (3) : 831-840. doi: 10.3934/dcdsb.2017041 [8] Kaifa Wang, Yang Kuang. Fluctuation and extinction dynamics in host-microparasite systems. Communications on Pure & Applied Analysis, 2011, 10 (5) : 1537-1548. doi: 10.3934/cpaa.2011.10.1537 [9] Sebastian J. Schreiber. On persistence and extinction for randomly perturbed dynamical systems. Discrete & Continuous Dynamical Systems - B, 2007, 7 (2) : 457-463. doi: 10.3934/dcdsb.2007.7.457 [10] Li Zu, Daqing Jiang, Donal O'Regan. Persistence and stationary distribution of a stochastic predator-prey model under regime switching. Discrete & Continuous Dynamical Systems, 2017, 37 (5) : 2881-2897. doi: 10.3934/dcds.2017124 [11] Xia Wang, Yuming Chen. An age-structured vector-borne disease model with horizontal transmission in the host. Mathematical Biosciences & Engineering, 2018, 15 (5) : 1099-1116. doi: 10.3934/mbe.2018049 [12] Daniel Franco, Chris Guiver, Phoebe Smith, Stuart Townley. A switching feedback control approach for persistence of managed resources. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021109 [13] Wen Jin, Horst R. Thieme. Persistence and extinction of diffusing populations with two sexes and short reproductive season. Discrete & Continuous Dynamical Systems - B, 2014, 19 (10) : 3209-3218. doi: 10.3934/dcdsb.2014.19.3209 [14] Wen Jin, Horst R. Thieme. An extinction/persistence threshold for sexually reproducing populations: The cone spectral radius. Discrete & Continuous Dynamical Systems - B, 2016, 21 (2) : 447-470. doi: 10.3934/dcdsb.2016.21.447 [15] Suqi Ma. Low viral persistence of an immunological model. Mathematical Biosciences & Engineering, 2012, 9 (4) : 809-817. doi: 10.3934/mbe.2012.9.809 [16] Naveen K. Vaidya, Feng-Bin Wang. Persistence of mosquito vector and dengue: Impact of seasonal and diurnal temperature variations. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021048 [17] Miaoran Yao, Yongxin Zhang, Wendi Wang. Bifurcation analysis for an in-host Mycobacterium tuberculosis model. Discrete & Continuous Dynamical Systems - B, 2021, 26 (4) : 2299-2322. doi: 10.3934/dcdsb.2020324 [18] Ling Xue, Caterina Scoglio. Network-level reproduction number and extinction threshold for vector-borne diseases. Mathematical Biosciences & Engineering, 2015, 12 (3) : 565-584. doi: 10.3934/mbe.2015.12.565 [19] S. R.-J. Jang. Allee effects in a discrete-time host-parasitoid model with stage structure in the host. Discrete & Continuous Dynamical Systems - B, 2007, 8 (1) : 145-159. doi: 10.3934/dcdsb.2007.8.145 [20] Miljana JovanoviĆ, Marija KrstiĆ. Extinction in stochastic predator-prey population model with Allee effect on prey. Discrete & Continuous Dynamical Systems - B, 2017, 22 (7) : 2651-2667. doi: 10.3934/dcdsb.2017129

2020 Impact Factor: 1.327

Tools

Article outline

Figures and Tables