TY - JOUR
T1 - Complex Dynamics of a host–parasite model with both horizontal and vertical transmissions in a spatial heterogeneous environment
AU - Cai, Yongli
AU - Kang, Yun
AU - Banerjee, Malay
AU - Wang, Weiming
N1 - Funding Information:
The first author would like to thank Prof. Shangbin Cui in Sun Yat-senUniversity for his helpful suggestions. This research was supported by Natural Science Foundation of China ( 11601179 , 61672013 & 61373005 ) and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China ( 16kJB110003 ). The research of Kang was partially supported by NSF-DMS (Award Number 1313312 ); NSF-IOS/DMS (Award Number 1558127 ) and The James S. McDonnell Foundation 21st Century Science Initiative in Studying Complex Systems Scholar Award (UHC Scholar Award 220020472 ).
PY - 2018/4
Y1 - 2018/4
N2 - In this paper, we investigate the dynamical outcomes of a host–parasite model incorporating both horizontal and vertical transmissions in a spatial heterogeneous environment analytically and numerically. Our study provides valuable insights in two aspects: Mathematically, we propose three threshold parameters, the demographic reproduction number Rd, the horizontal transmission reproduction number R0h and the vertical transmission reproduction number R0v, to identify the conditions that lead to disease-free dynamics, or susceptible-free dynamics, or endemic dynamics. Epidemiologically, we find that both host population movements and spatial heterogeneity strongly affect the disease dynamics of our proposed epidemic model: (1) the larger random mobility can result in 100% infection prevalence; and (2) the heterogeneity tends to enhance the persistence of the infected hosts with uninfected ones. As a consequence, our work suggests that, in order to control the invasion of the parasite, different preventive measures can be implemented in different regions.
AB - In this paper, we investigate the dynamical outcomes of a host–parasite model incorporating both horizontal and vertical transmissions in a spatial heterogeneous environment analytically and numerically. Our study provides valuable insights in two aspects: Mathematically, we propose three threshold parameters, the demographic reproduction number Rd, the horizontal transmission reproduction number R0h and the vertical transmission reproduction number R0v, to identify the conditions that lead to disease-free dynamics, or susceptible-free dynamics, or endemic dynamics. Epidemiologically, we find that both host population movements and spatial heterogeneity strongly affect the disease dynamics of our proposed epidemic model: (1) the larger random mobility can result in 100% infection prevalence; and (2) the heterogeneity tends to enhance the persistence of the infected hosts with uninfected ones. As a consequence, our work suggests that, in order to control the invasion of the parasite, different preventive measures can be implemented in different regions.
KW - Endemic
KW - Heterogeneity
KW - Parasite-free
KW - Susceptible-free
KW - Vertical transmission
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U2 - 10.1016/j.nonrwa.2017.10.001
DO - 10.1016/j.nonrwa.2017.10.001
M3 - Article
AN - SCOPUS:85032216879
SN - 1468-1218
VL - 40
SP - 444
EP - 465
JO - Nonlinear Analysis: Real World Applications
JF - Nonlinear Analysis: Real World Applications
ER -