Calculating against deadly disease

The risk of a full-blown cholera epidemic developing from just a few cases might be greater than experts previously thought.

Two differential equation-based models designed by Xueying (Snow) Wang, assistant professor of mathematics, provide a new and improved predictive framework for anticipating cholera outbreaks and planning for interventions. The models could be useful for combatting other diseases as well.

Wang is currently working with researchers in the Paul G. Allen School for Global Animal Health at WSU to apply her mathematical equations in developing early detection and containment methods for the Ebola virus in West Africa.

“Mathematics gives us a way to understand how human behavior influences disease distribution dynamics which can be extremely beneficial in terms of preemptive planning,” said Guy Palmer, director of the Allen School and a partner in Wang’s research. “If we can predict the number of infections that will result from an outbreak and how they will distribute the disease over space and time, we can more effectively allocate what limited resources are available to fight the disease.”

A growing problem

Cholera is an acute intestinal disease that can spread rapidly among people and can cause death in a few days if left untreated. It strikes hardest in underdeveloped regions that lack adequate hygiene and sanitation and have limited access to clean water and other resources. The last decade witnessed an increasing number of cholera outbreaks worldwide.

One of the largest eruptions of the disease in modern history occurred in post-earthquake Haiti in 2010-2012, when more than 530,000 cases were reported and more than 7,000 infected people died.

The worst African cholera outbreak in the past 20 years devastated Zimbabwe in 2008-2009, with nearly 100,000 reported cases and more than 4,000 deaths.

“These outbreaks, with their increased frequency and severity, indicate that our current knowledge in cholera dynamics and public health guidelines to control the disease are not adequate,” Wang said.

 

A novel solution

Cholera is typically transmitted directly from one infected human to another or indirectly from a contaminated food or water source to a human host.

To gain deeper understanding of how cholera spreads, researchers with the World Health Organization have used data about numbers and locations of infected people in past outbreaks to create mathematical models that predict how quickly cholera would reach something called the disease threshold, the point where enough individuals have been infected to sustain the disease within a population.

A standard assumption in almost all of these models is that cholera bacteria cannot persist in the absence of a human host or an influx of human waste. However, new evidence shows the growth and survival of free-living bacteria in the environment greatly influences the rate of cholera transmission. Additionally, previous modeling work assumes that cholera spreads outward in a uniform manner from the location of the initial infection. However, data from the Zimbabwe outbreak showed the transmission pattern varied widely throughout the country.

“There has been strong evidence that cholera can independently persist in the environment and that its spread is highly heterogeneous,” Wang said. “Consequently, taking into account both of these factors may play an essential role in shaping how a cholera epidemic pans out.”

Wang’s research attempts to address both of these issues. She uses a generalized differential equation model to simulate how cholera can persist in the environment without a human host and a partial differential equation model to represent the movement of humans and cholera bacteria in a spatially random environment.

The results of her work show that when the virus’s environmental reproduction rate and non-uniform spread are taken into account, the overall infection risk is far higher.

“The big implication here is that previous models may be underestimating the risk that an epidemic might occur,” Wang said. “While there are other sources of variability that still need to be addressed, our findings could provide useful guidelines for public health administrators to properly scale their efforts in cholera control.”