# Forum for Science, Industry and Business

Search our Site:

## The math of malaria

21.06.2012
Malaria affects over 200 million individuals every year and kills hundreds of thousands of people worldwide.

The disease varies greatly from region to region in the species that cause it and in the carriers that spread it. It is easily transmitted across regions through travel and migration. This results in outbreaks of the disease even in regions that are essentially malaria-free, such as the United States.

Malaria has been nearly eliminated in the U.S. since the 1950s, but the country continues to see roughly 1,500 cases a year, most of them from travelers. Hence, the movement or dispersal of populations becomes important in the study of the disease.

In a paper published this month in the SIAM Journal on Applied Mathematics, authors Daozhou Gao and Shigui Ruan propose a mathematical model to study malaria transmission.

“Malaria is a parasitic vector-borne disease caused by the plasmodium parasite, which is transmitted to people via the bites of infected female mosquitoes of the genus Anopheles,” says Ruan. “It can be easily transmitted from one region to another due to extensive travel and migration.”

The life cycle of plasmodium involves incubation periods in two hosts, the human and the mosquito. Therefore, mathematical modeling of the spread of malaria usually focuses on the feedback dynamics from mosquito to human and back. Early models were 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.

Mathematical models that study transmission of malaria are 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 solution to controlling the disease is to arrive at a reproduction number at which the disease-free state can be established and maintained.

Previous studies used ordinary differential equations to model the transmission of malaria, in which human populations are classified as susceptible, exposed, infectious and recovered. Likewise, mosquito populations are divided into susceptible, exposed and infectious groups. The threshold below which the disease-free equilibrium can be maintained is determined by varying these parameters.

In order to analyze transmission rates of malaria between regions, multi-patch models are used, 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 authors in this paper model the transmission dynamics of malaria between humans and mosquitoes within a patch, and then go on to examine how population dispersal between patches or regions affects the spread of malaria in a two-patch model.

After deriving the reproduction number, they determine its dependence on human travel rates. Their analysis shows that 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. “A threshold for the persistence of malaria was obtained, below which the disease dies out and above which the disease persists,” explains Ruan. “Analysis of the threshold helps us design effective control measures to reduce disease transmission.”

The authors determine that malaria can 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. Numerical simulations are performed to corroborate these findings.

The paper thus concludes that human travel is a critical factor affecting the spread of malaria. “The analytical and numerical results confirm that human movement plays a significant role in the geographic spread of malaria among different regions,” says Ruan. Anti-malaria measures should involve more rigorous border screening and regulation, since exposed individuals who don’t exhibit symptoms of the disease—but are infectious—are hard to identify at screenings. “To control malaria, both regional and global strategies are needed,” he says.

Future directions for this research include testing the global stability of this model in more than two patches, and studying other influencers, such as climate. “Climate factors such as rainfall and temperature greatly influence the abundance and distribution of malaria vectors,” Ruan says. “It will be very interesting to study the impact of climate change on the transmission of malaria by considering periodic malaria models.”

Dr. Shigui Ruan is a professor and Daozhou Gao is a graduate student/ teaching assistant in the Department of Mathematics at The University of Miami. This work was partially supported by NSF grant DMS-1022728 and NIH grant R01GM093345.

Source article:

A Multipatch Malaria Model with Logistic Growth Populations

Shigui Ruan and Daozhou Gao, SIAM Journal on Applied Mathematics, 72(3), 819–841. (Online publish date: June 7, 2012)

Further information:
http://www.siam.org

### More articles from Health and Medicine:

Diabetes mellitus: A risk factor for early colorectal cancer
27.05.2020 | Nationales Centrum für Tumorerkrankungen (NCT) Heidelberg

Ultra-thin fibres designed to protect nerves after brain surgery
27.05.2020 | Martin-Luther-Universität Halle-Wittenberg

### Im Focus: New measurement exacerbates old problem

Two prominent X-ray emission lines of highly charged iron have puzzled astrophysicists for decades: their measured and calculated brightness ratios always disagree. This hinders good determinations of plasma temperatures and densities. New, careful high-precision measurements, together with top-level calculations now exclude all hitherto proposed explanations for this discrepancy, and thus deepen the problem.

Hot astrophysical plasmas fill the intergalactic space, and brightly shine in stellar coronae, active galactic nuclei, and supernova remnants. They contain...

### Im Focus: Biotechnology: Triggered by light, a novel way to switch on an enzyme

In living cells, enzymes drive biochemical metabolic processes enabling reactions to take place efficiently. It is this very ability which allows them to be used as catalysts in biotechnology, for example to create chemical products such as pharmaceutics. Researchers now identified an enzyme that, when illuminated with blue light, becomes catalytically active and initiates a reaction that was previously unknown in enzymatics. The study was published in "Nature Communications".

Enzymes: they are the central drivers for biochemical metabolic processes in every living cell, enabling reactions to take place efficiently. It is this very...

### Im Focus: New double-contrast technique picks up small tumors on MRI

Early detection of tumors is extremely important in treating cancer. A new technique developed by researchers at the University of California, Davis offers a significant advance in using magnetic resonance imaging to pick out even very small tumors from normal tissue. The work is published May 25 in the journal Nature Nanotechnology.

researchers at the University of California, Davis offers a significant advance in using magnetic resonance imaging to pick out even very small tumors from...

### Im Focus: I-call - When microimplants communicate with each other / Innovation driver digitization - "Smart Health“

Microelectronics as a key technology enables numerous innovations in the field of intelligent medical technology. The Fraunhofer Institute for Biomedical Engineering IBMT coordinates the BMBF cooperative project "I-call" realizing the first electronic system for ultrasound-based, safe and interference-resistant data transmission between implants in the human body.

When microelectronic systems are used for medical applications, they have to meet high requirements in terms of biocompatibility, reliability, energy...

### Im Focus: When predictions of theoretical chemists become reality

Thomas Heine, Professor of Theoretical Chemistry at TU Dresden, together with his team, first predicted a topological 2D polymer in 2019. Only one year later, an international team led by Italian researchers was able to synthesize these materials and experimentally prove their topological properties. For the renowned journal Nature Materials, this was the occasion to invite Thomas Heine to a News and Views article, which was published this week. Under the title "Making 2D Topological Polymers a reality" Prof. Heine describes how his theory became a reality.

Ultrathin materials are extremely interesting as building blocks for next generation nano electronic devices, as it is much easier to make circuits and other...

All Focus news of the innovation-report >>>

Anzeige

Anzeige