Detecting a trend change in cross-border epidemic transmission

Abstract

A method for a system of Langevin equations is developed for detecting a trend change in cross-border epidemic transmission. The equations represent a standard epidemiological SIR compartment model and a meta-population network model. The method analyzes a time series of the number of new cases reported in multiple geographical regions. The method is applicable to investigating the efficacy of the implemented public health intervention in managing infectious travelers across borders. It is found that the change point of the probability of travel movements was one week after the WHO worldwide alert on the SARS outbreak in 2003. The alert was effective in managing infectious travelers. On the other hand, it is found that the probability of travel movements did not change at all for the flu pandemic in 2009. The pandemic did not affect potential travelers despite the WHO alert.

Keywords: Change point; Epidemic transmission; Langevin equation; Meta-population network; Public health intervention; SIR compartment model.

Fig. 1

Fraction of correct detection of the change in $\alpha$ and $\gamma$ from synthesized datasets of $D=30$ and $\Delta t=1$ for random digraphs of $N=30$ with the initial condition of $I_0\left(t_0\right)=200$. The parameters $\alpha$ and $\gamma$ do not change at all. (a) Marginalized likelihood selector for the change in $\alpha$, (b) maximal likelihood selector for $\alpha$, (c) marginalized likelihood selector for $\gamma$, (d) maximal likelihood selector for $\gamma$.

Fig. 2

Fraction of correct detection of the change in $\alpha$ and $\gamma$ from synthesized datasets of $D=30$ and $\Delta t=1$ for random digraphs of $N=30$ with the initial condition of $I_0\left(t_0\right)=200$. The parameter $\alpha$ decreases from ${\alpha }_1=0.075$ to ${\alpha }_2={\alpha }_1-\Delta \alpha$ at $t_c^{\left[\alpha \right]}=0.5(D-1)\Delta t=14.5$, but $\beta =0.025$ and $\gamma =0.1$ do not change. The ratio of change $\Delta \alpha /{\alpha }_1$ is 0.2, 0.4, 0.6, or 0.8. (a) Marginalized likelihood selector for the change in $\alpha$, (b) maximal likelihood selector for $\alpha$, (c) marginalized likelihood selector for $\gamma$, (d) maximal likelihood selector for $\gamma$.

Fig. 3

Fraction of correct detection when $\alpha$ decreases at $t_c^{\left[\alpha \right]}=0.2(D-1)\Delta t=5.8$. The other experimental conditions are the same as those for Fig. 2.

Fig. 4

Fraction of correct detection when $\gamma$ changes at $t_c^{\left[\gamma \right]}=0.2(D-1)\Delta t$. The other experimental conditions are the same as those for Fig. 2.

Fig. 5

Fraction of correct detection when $\gamma$ decreases at $t_c^{\left[\gamma \right]}=0.2(D-1)\Delta t$, and $\alpha$ decreases by $\Delta \alpha /{\alpha }_1=0.6$ at $t_c^{\left[\alpha \right]}=0.5(D-1)\Delta t$ as well. The other experimental conditions are the same as those for Fig. 2.