Mathematical Model Studies Malaria Transmission

The model is based on the reproduction number, which defines the most important aspects of transmission for any infectious disease. Specifically, it is calculated by determining the expected number of infected organisms that can trace their infection directly back to a single organism after one disease generation.

The life cycle of the Malaria Plasmodium involves incubation periods in two hosts, human and infected female mosquitoes of the genus Anopheles. The mathematical modeling of the spread of malaria usually focuses on the feedback dynamics from mosquito to human and back, with early models based on malaria parasites' population biology and evolution. But increased computing power in recent years has allowed models for the disease to become more detailed and complex, allowing researchers to find the reproduction number threshold below which the disease-free equilibrium can be maintained.

To do so, multipatch models are used to analyze transmission rates of malaria between regions, where each region is a "patch." These models study how the reproduction number is affected by dispersal or movement of exposed and infectious individuals from region to region. The analysis showed that the reproduction number varies consistently with movement of exposed, infectious, and recovered humans; the same is seen to be true for the movement of infected mosquitoes.

The authors determined that malaria could potentially die out if movement of exposed, infectious, or recovered humans between two patches or regions remains weak; higher travel rates between the patches, however, can make malaria indigenous to both regions. They then conducted numerical simulations to corroborate these findings, and concluded that human travel is a critical factor affecting the spread of malaria. The study was published in the June 2012 issue of SIAM Journal on Applied Mathematics.

“The analytical and numerical results confirm that human movement plays a significant role in the geographic spread of malaria among different regions,” said study coauthor Shigui Ruan, PhD, of the department of mathematics. “A threshold for the persistence of malaria was obtained, below which the disease dies out and above which the disease persists. Analysis of the threshold helps us design effective control measures to reduce disease transmission.”

“Climate factors such as rainfall and temperature greatly influence the abundance and distribution of malaria vectors,” further added Dr. Ruan. “It will be very interesting to study the impact of climate change on the transmission of malaria by considering periodic malaria models.”

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