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Models of infectious diseases in spatially heterogeneous environments
D J Rodríguez1, L Torres-Sorando
1Instituto de Zoología Tropical, Universidad Central de Venezuela, Apartado 47058, Caracas 1041-A, Venezuela. drodrig@strix.ciens.ucv.ve
Abstract:
Most models of dynamics of infectious diseases have assumed homogeneous mixing in the host population. However, it is increasingly recognized that heterogeneity can arise through many processes. It is then important to consider the existence of subpopulations of hosts, and that the contact rate within subpopulations is different than that between subpopulations. We study models with hosts distributed in subpopulations as a consequence of spatial partitioning. Two types of models are considered. In the first one there is direct transmission. The second one is a model of dynamics of a mosquito-borne disease, with indirect transmission, and applicable to malaria. The contact between subpopulations is achieved through the visits of hosts. Two types of visit are considered: a first one in which the visit time is independent of the distance travelled, and a second one in which visit time decreases with distance. There are two types of spatial arrangement: one dimensional, and two dimensional. Conditions for the establishment of the disease are obtained. Results indicate that the disease becomes established with greater difficulty when the degree of spatial partition increases, and when visit time decreases. In addition, when visit time decreases with distance, the establishment of the disease is more difficult when the spatial arrangement is one dimensional than when it is two dimensional. The results indicate the importance of knowing the spatial distribution and mobility patterns to understand the dynamics of infectious diseases. The consequences of these results for the design of public health policies are discussed.
Insights
Disease spread is harder when populations are spatially separated or mobility is limited. Understanding host distribution and movement is crucial for effective public health policies and infectious disease control.
Area of Science:
- Epidemiology
- Mathematical Modeling
- Spatial Analysis
Background:
- Traditional infectious disease models often assume homogeneous population mixing.
- Increasing evidence highlights the impact of population heterogeneity on disease dynamics.
- Spatial partitioning and varying contact rates between subpopulations are critical factors.
Purpose of the Study:
- To investigate infectious disease dynamics in spatially structured host populations.
- To analyze how spatial partitioning and host mobility affect disease establishment.
- To compare direct and indirect (malaria-like) transmission models in heterogeneous environments.
Main Methods:
- Development of two mathematical models: one for direct transmission, one for indirect (mosquito-borne) transmission.
- Incorporation of host movement between subpopulations, considering distance-dependent and independent visit times.
- Analysis of one-dimensional and two-dimensional spatial arrangements.
Main Results:
- Increased spatial partitioning and decreased visit times hinder disease establishment.
- Disease establishment is more challenging in one-dimensional arrangements compared to two-dimensional ones when visit time is distance-dependent.
- Host mobility patterns and spatial distribution significantly influence disease dynamics.
Conclusions:
- Spatial structure and host mobility are critical determinants of infectious disease spread.
- Public health policies must consider population distribution and movement patterns for effective disease control.
- Heterogeneity in host populations plays a vital role in epidemiological modeling.