tetano
Editor, Senior Moderator
Bull Math Biol
. 2026 Oct 12;88(11):203.
doi: 10.1007/s11538-026-01689-1.
Lusha Shi 1 2 3 , Shuai Shen 4 , Lili Liu 2 3 , Xiaohong Zhang 5 , Zhen Jin 6 7
Affiliations Expand
Human mobility plays an important role in the disease spatial transmission. In this paper, a multi-patch SEIR Influenza model incorporating long-term population migration and daily commuting was formulated to describe Influenza interregional spreading. Mathematically, the explicit expression for basic reproduction number was derived by the next-generation matrix method, and the globally asymptotically stability of disease free equilibrium and the unique positive equilibrium were rigorously proved. Numerically, taking the end of 2025 influenza epidemic in Shanxi province as an example, the model was fitted by using influenza surveillance data, census data, and Baidu migration data from the 11 cities. A Logistic decay form of transmission rate is introduced to characterize the effects of intervention time and intervention strength. The numerical results showed a good fitting and indicate that the provincial basic reproduction number is 2.5877, while the city-level values range from 1.13-2.85. Sensitivity analysis further showed that the initial transmission intensity, infectious period, and intervention time are key factors affecting Influenza spreading, and local transmission contributes more to epidemic spread than inter-city mobility, which implies that reducing local transmission is more effective when controlling disease spreading. Moreover, under some certain conditions, early targeted control in hotspot cities can achieve effects comparable to or even better than province-wide uniform control. These findings provide theoretical support and quantitative evidence for understanding interregional influenza transmission and designing region-specific prevention and control strategies.
Keywords: Epidemic threshold; Influenza; Multi-patch model; Population mobility pattern; Prevention and control measures.
. 2026 Oct 12;88(11):203.
doi: 10.1007/s11538-026-01689-1.
Dynamics and Numerical Analysis of a Multi-Patch Influenza Transmission Model with Population Migration and Daily Commuting
Lusha Shi 1 2 3 , Shuai Shen 4 , Lili Liu 2 3 , Xiaohong Zhang 5 , Zhen Jin 6 7
Affiliations Expand
- PMID: 42862423
- DOI: 10.1007/s11538-026-01689-1
Abstract
Human mobility plays an important role in the disease spatial transmission. In this paper, a multi-patch SEIR Influenza model incorporating long-term population migration and daily commuting was formulated to describe Influenza interregional spreading. Mathematically, the explicit expression for basic reproduction number was derived by the next-generation matrix method, and the globally asymptotically stability of disease free equilibrium and the unique positive equilibrium were rigorously proved. Numerically, taking the end of 2025 influenza epidemic in Shanxi province as an example, the model was fitted by using influenza surveillance data, census data, and Baidu migration data from the 11 cities. A Logistic decay form of transmission rate is introduced to characterize the effects of intervention time and intervention strength. The numerical results showed a good fitting and indicate that the provincial basic reproduction number is 2.5877, while the city-level values range from 1.13-2.85. Sensitivity analysis further showed that the initial transmission intensity, infectious period, and intervention time are key factors affecting Influenza spreading, and local transmission contributes more to epidemic spread than inter-city mobility, which implies that reducing local transmission is more effective when controlling disease spreading. Moreover, under some certain conditions, early targeted control in hotspot cities can achieve effects comparable to or even better than province-wide uniform control. These findings provide theoretical support and quantitative evidence for understanding interregional influenza transmission and designing region-specific prevention and control strategies.
Keywords: Epidemic threshold; Influenza; Multi-patch model; Population mobility pattern; Prevention and control measures.