Habitat fragmentation promotes malaria persistence
The authors study a multipatch malaria model based on the Ross-Macdonald model with identical patches. They show that the basic reproduction number of the multipatch model is always greater than or equal to that of the model with a single patch. This is shown by establishing an eigenvalue inequality on the product of a class of nonnegative matrices, applying a theorem on line-sum symmetric matrices. The result suggests that habitat fragmentation leads to an increased level of the disease. The risk of infection is the smallest in case of the distribution of mosquitoes being proportional to that of humans. The results also emphasize the importance to consider the spatial structure when one studies the spread of an infectious disease. Otherwise, one might underestimate the risk of outbreaks and disease persistence and also the efforts needed to eliminate the disease. Numerical examples are also shown for the case of two patches. These results show that the reproduction number can obtain arbitrarily large values if the travel pattern is chosen appropriately. The authors also raise several important questions regarding further research on the topic.
scientific article; zbMATH DE number 7135096