By Lina Sorg
The rapid, geographic spread of infectious disease presents a continuous threat to daily life. Because many serious infections and vector-borne diseases—notably, malaria and dengue fever—lack effective vaccines, disease control measures instead aim to directly reduce transmission, thus minimizing the need for treatment. For example, mosquito management (through insecticide sprays) is the main control measure for the mosquito-borne dengue virus, as it reduces the number of adult insects able to spread the disease.
In a minisymposium about infectious diseases at the 2017 SIAM Conference on Applications of Dynamical Systems, Alun Lloyd of North Carolina State University modeled the surprisingly perverse consequences of disease control measures for an endemic infection. His research pertains to standardized infection ratio (SIR)-type infections, in which patients are permanently immune after recovery. Lloyd’s model incorporates the basic reproductive number (for the susceptible population), effective reproductive number (for the partially-susceptible population), transmission parameters, and recovery rate. “An absolutely key point to emphasize is that if the system has an endemic equilibrium—a positive steady state—the effective reproductive number at that state is 1,” he said.
However, susceptibles begin to build up in the body as transmission declines during this period. “You’re storing up some sort of trouble for yourself down the line,” Lloyd said. “A large outbreak may often be seen after the honeymoon. And some control measures can cause transient oscillations whose peaks exceed the pre-control endemic level.” Essentially, if one chooses poor control measures, a damaging post-control outbreak can occur. The incidence of large peaks is particularly troubling in certain infections, such as dengue fever. “Increasing that maximum peak can be a big problem,” Lloyd said. “It overwhelms the local health systems.”
Next, Lloyd explored the consequences of seasonality in a seasonally-forced SIR model. He incorporated weak seasonality, in the form of passive annual oscillations, to avoid the dynamical complexities associated with strong seasonality. The seasonally-forced model yields larger peak RCI values than the standard SIR model. “We see the effects even more strongly here,” he said. “The dynamics and magnitude of the divorce effect depend on timing.”
The results of Lloyd’s model have valuable implications for the control of dengue and other mosquito-borne illnesses in clinical trials. Because weak control can significantly reduce the incidence of an endemic infection, researchers must take great care when analyzing the results of short-term trials. A post-control outbreak could occur several years after the implementation and subsequent termination of a control measure, long after researchers have stopped observing the effects. “Vector control trials are more complicated than a standard clinical trial because people move in and out of the intervention area,” Lloyd said. Thus, it is essential to monitor the dynamics of susceptibles over a lengthy period of time before drawing any conclusions.
Ultimately, Lloyd’s SIR-based approach indicates that certain transient control measures have counterintuitive consequences that could actually exceed the number of disease cases that would have occurred had no intervention been employed. He is currently conducting an empirical investigation of the divorce effect in Zika virus and dengue fever, and searching for mitigation methods to increase the likelihood of transient control success.