Model II: Medical Resource Is Limited
9.5 Conclusion
result shows that emergency budget required could be significantly increased with each 15 days of delay in intervention. For example, if intervention starts on July 1st and an emergency budget of ¥250 M is allocated, the cumulative unsatisfied demand is only 2821. However, if we postpone the intervention by half a month (July 16), the model solution requires an optimal budget of ¥494.6 M with an unsatisfied demand of 7012. What is worse, although there is ample emergency budget, the values of total unsatisfied demand in the following three scenarios are considerably large.
The impact of different intervention starting dates on the isolated wards capacity required is illustrated in Fig.9.5. It can be observed that the capacity required in all three areas show similar change trajectories. The capacity required increases sharply in the first several days. Beyond its peak, it decreases until the final planning horizon.
The later the intervention starts, the more isolated rooms will be required to suppress the disease spread. In summary, we suggest that intervention to an unexpected epi- demic should start as early as possible. This can significantly reduce the number of infected individuals, shrink the scale of isolated wards required, and finally save the valuable emergency budget.
Furthermore, we also conduct sensitivity analysis for three key parameters in our epidemic model. The results suggest that local government should try its best to reduce the transmission rate. Meanwhile, shorting the treatment time for infected persons could also reduce the total number of infected individuals. To reduce the transmission rate, several forcible quarantine measures should be carried out. In the meantime, self-quarantine for the exposed people and decreasing the contact with other susceptible individuals around are also effective strategies for controlling epidemic diffusion. Other monitoring measures such as taking a temperature test before boarding airplane or train could also help to alleviate epidemic diffusion risk.
As to short the treatment time, it could be realized by improving the corresponding medical techniques and this beyond our research scope.
0 10 20 30 40 50 60 0
2000 4000 6000 8000 10000
12000 JS-N area
Time
Number of isolated wards
July 1 July 16 July 31 August 15 August 30
0 10 20 30 40 50 60
0 2000 4000 6000 8000 10000 12000 14000
JS-C area
Time
Number of isolated wards
July 1 July 16 July 31 August 15 August 30
0 10 20 30 40 50 60
0 0.5 1 1.5 2 2.5x 10
4 JS-S area
Time
Number of isolated wards
July 1 July 16 July 31 August 15 August 30
(a)
(b)
(c)
Fig. 9.5 Capacity required with different intervention starting dates
start time. This can effectively help control the epidemic diffusion. Other differences between Büyüktahtakın et al. [1] and this study are listed as follows.
(1) Different infectious diseases have dissimilar diffusion dynamics, and thus we have different constraints for the integrated epidemic-logistics model. For exam- ple, individuals infected by H1N1 will first go into a latent (exposed) stage, dur- ing which they may have a low level of infectivity. However, the transmission dynamics of Ebola is totally different in Büyüktahtakın et al. [1]. Moreover, we consider a compartment of asymptomatic and partially infectious (see Fig.9.1), but we do not consider the deceased individuals because H1N1 is now a seasonal flu. While in the Ebola pandemic, funerals and how to bury the deceased individ- uals are important and unavoidable problems. Therefore, when we address the time discretized epidemic compartment model as the linear constraints, there will be total different constraints for the integrated epidemic-logistics model.
(2) Different infectious diseases can cause different public health emergencies, and thus we have different optimization objectives for the integrated epidemic- logistics model. As one can see, Büyüktahtakın’s objective is to minimize the total number of infected individuals and deaths of infected people who do not receive treatment. While in our study, the objective function is to minimize the total unsatisfied demand in all affected areas.
(3) In Büyüktahtakın et al. [1], the authors preset two kinds of ETC, 50-bed and 100- bed, and thus the capacity decision is a combinatorial optimization problem.
While in this study, we focus on when to open the new isolated wards and when to close the unused isolated wards. Moreover, our test demonstrates that the major cost for H1N1 intervention is the fixed cost. This is also different from Büyüktahtakın et al. [1], which suggested the major cost is the variable treatment cost and followed by the fixed cost. We think the difference of cost structure is caused by the different characteristics of the two diseases. As we all know, the treatment for Ebola patients is more complex and dangerous, and thus the variable treatment cost should be the major one. As to H1N1, it is now a seasonal flu with very low mortality rates due to advances in medical technologies. Therefore, the major cost for treating the infected individuals is the fixed cost.
Note that although there are several papers that study the integration of epidemic control and logistics planning in recent 5 years (i.e., [33, 39,41, 45]), many of them divide the continuous time into several independent decision-making periods and update forecasting for the number of infected individuals at the beginning of each period. Thus in essentially, the epidemic compartment model and the planning model are still independent from each other. Different from that, Büyüktahtakın et al. [1] integrated epidemic dynamics and the corresponding emergency logistics considerations into one optimization model. The key component was that no constant transition rate from compartment I to H. In this study, we retain the advantage of this modeling framework and thus our model could also forecast the development of H1N1 and depict the impact on different resource-allocation scenarios on the disease progression.
Future research could address some of the limitations in both the epidemiolog- ical and resource allocation portions of the proposed model. For example, other epidemics with other transmission characteristics could be incorporated into the optimization model. Moreover, cross-regional transmission with different transition rates and population structures could also be incorporated into the model. As to the resource allocation portion, future studies could also consider the influence of unsat- isfied demand, the emergency service level, or the potential delay in arrival time of the intervention budget.
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