A mathematical model of chikungunya dynamics and control: the major epidemic on Réunion Island

Abstract

Chikungunya is a re-emerging arboviral disease transmitted by Aedes spp. mosquitoes. Although principally endemic to Africa and Asia, recent outbreaks have occurred in Europe following introductions by returning travellers. A particularly large outbreak occurred on Réunion Island in 2006, the published data from which forms the basis of the current study. A simple, deterministic mathematical model of the transmission of the virus between humans and mosquitoes was constructed and parameterised with the up-to-date literature on infection biology. The model is fitted to the large Réunion epidemic, resulting in an estimate of 4.1 for the type reproduction number of chikungunya. Although simplistic, the model provided a close approximation of both the peak incidence of the outbreak and the final epidemic size. Sensitivity analysis using Monte Carlo simulation demonstrated the strong influence that both the latent period of infection in humans and the pre-patent period have on these two epidemiological outcomes. We show why separating these variables, which are epidemiologically distinct in chikungunya infections, is not only necessary for accurate model fitting but also important in informing control.

Figure 1. Compartmental construction of the epidemiological model for Chikungunya transmission.

Susceptible humans (S) are exposed to infection (E) before becoming infectious (I_a asymptomatically, or I symptomatically) and then recover (R). Susceptible mosquitoes (X) are exposed to infection (Y) before becoming infectious (Z). Transmission from mosquito-to-human and vice versa is denoted by the broken lines indicating a mosquito bite. Rates of change between compartments are denoted by corresponding Greek letters.

Figure 2. Mathematical model output (bars) fitted to weekly Chikungunya incidence data (circles) collected during the 2005–6 epidemic on Réunion island, Indian Ocean.

Figure 3. Spearman’s rank correlation coefficients demonstrating model output sensitivity to input parameters.

10,000 iterations of a Monte Carlo simulation were performed allowing each input parameter to vary by ±10% around its modal value.

Figure 4. Controlling a chikungunya epidemic.

Top, the reduction in the type reproduction number (R_T) as a function of vector control (increased mosquito mortality rate). Middle, the reduction in the type reproduction number as a function of quarantine (solid line, Q₁– pre-emptive isolation through screening or self-reporting mosquito bites, and, broken line, Q₂– isolation following symptoms onset). Bottom, the combinations of vector control with quarantining (solid line Q₁ and broken line Q₂) required to reduce the R_T below unity.