Bulletin of Mathematical Biology

, Volume 81, Issue 11, pp 4518–4563 | Cite as

Transmission Dynamics and Control Mechanisms of Vector-Borne Diseases with Active and Passive Movements Between Urban and Satellite Cities

  • Prince Harvim
  • Hong Zhang
  • Paul Georgescu
  • Lai ZhangEmail author
Special Issue: Mathematical Epidemiology


A metapopulation model which explicitly integrates vector-borne and sexual transmission of an epidemic disease with passive and active movements between an urban city and a satellite city is formulated and analysed. The basic reproduction number of the disease is explicitly determined as a combination of sexual and vector-borne transmission parameters. The sensitivity analysis reveals that the disease is primarily transmitted via the vector-borne mode, rather than via sexual transmission, and that sexual transmission by itself may not initiate or sustain an outbreak. Also, increasing the population movements from one city to the other leads to an increase in the basic reproduction number of the later city but a decrease in the basic reproduction number of the former city. The influence of other significant parameters is also investigated via the analysis of suitable partial rank correlation coefficients. After gauging the effects of mobility, we explore the potential effects of optimal control strategies relying upon several distinct restrictions on population movement.


Vector-borne disease Passive mobility Metapopulation model Sexual transmission Control mechanism 



L.Z. acknowledges the financial support by the PRC Grant NSFC (11571301,11871065), the NSF of Jiangsu Province (BK20181450), the Jiangsu Distinguished Professor Program, and the Yangzhou Talent Program ‘LvYangJinFeng’.

Author Contributions

P.H., H.Z. and P.G. developed the model structure; P.H., H.Z. and P.G. performed the modelling and model analyses; H.Z. further acknowledges the financial support by Qinlan Project of Jiangsu Province; P.H. and L.Z. developed the numerical analysis and simulations; all authors discussed the results and contributed to the writing of the manuscript.

Compliance with Ethical Standards

Conflicts of interest

The authors declare no conflicts of interest.

Data Accessibility

Estimation of parameters have been stated in the body of the paper and included in the reference section.


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Copyright information

© Society for Mathematical Biology 2019

Authors and Affiliations

  1. 1.Faculty of ScienceJiangsu UniversityZhenjiangPeople’s Republic of China
  2. 2.School of Economics and ManagementChangzhou Institute of TechnologyChangzhouPeople’s Republic of China
  3. 3.Department of MathematicsTechnical University of IaşiIasiRomania
  4. 4.School of Mathematical ScienceYangzhou UniversityYangzhouPeople’s Republic of China

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