The global scientific community has intensified efforts to develop, test, and commercialize pharmaceutical products to deal with the COVID-19 pandemic. Trials for both antivirals and vaccines are in progress; candidates include existing repurposed drugs that were originally developed for other ailments. Once these products are shown to be effective, their production will need to be ramped up rapidly to keep pace with the growing demand as the pandemic progresses. It is highly likely that the drugs will be in short supply in the interim, which leaves policy makers and medical personnel with the difficult task of determining how to allocate them. Under such conditions, mathematical models can provide valuable decision support. In particular, useful models can be derived from process integration (PI) techniques that deal with tight resource constraints. In this paper, a linear programming (LP) model is developed to determine the allocation of COVID-19 drugs that minimizes patient mortality, taking into account additional hospital capacity constraints. Two hypothetical case studies are solved to illustrate the computational capability of the model, which can generate an allocation plan with outcomes that are superior to simple ad hoc allocation.
Process integration models for emerging challenges: Optimal allocation of antivirals under resource constraints
https://doi.org/10.21203/rs.3.rs-24325/v1
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Pharmaceutical shortage
Resource allocation
COVID-19
mathematical programming
disease outbreak
Sustainable Development Goal
Table 4. Available resources
|
Resource |
Number of units |
|
Home Care |
Unlimited |
|
Hospital Beds |
100 |
|
Intensive Care Units |
20 |
Table 5. Mortality Rates by severity level and resource
|
|
No adequate care |
With adequate Care |
|
Mild |
0.0 |
0.0 |
|
Moderate |
0.2 |
0.05 |
|
Critical |
1.0 |
0.50 |
Table 6. Severity of infected individuals and their access to proper care for Scenario 1.1
|
Severity |
With proper care |
No proper care |
Total |
|
Mild |
800 |
0 |
800 |
|
Moderate |
100 |
50 |
150 |
|
Critical |
20 |
30 |
50 |
Table 7. Allocation of Antivirals for Scenario 1.2
|
|
Mild |
Moderate |
Critical |
Total antiviral used |
|
No antiviral |
700 |
0 |
0 |
NA |
|
Antiviral A |
33 |
50 |
17 |
100 |
|
Antiviral B |
67 |
100 |
33 |
200 |
|
Total infected |
800 |
150 |
50 |
|
Table 8. Severity of infected symptomatic individuals and their access to proper care for Scenario 1.2
|
Severity |
With proper care |
No proper care |
Total |
|
Mild |
905 |
0 |
905 |
|
Moderate |
88 |
0 |
88 |
|
Critical |
17 |
0 |
17 |
Table 9. Allocation of Antivirals for Scenario 1.3
|
|
Mild |
Moderate |
Critical |
Total antiviral |
|
No antiviral |
700 |
0 |
0 |
NA |
|
Antiviral A |
50 |
0 |
50 |
50 |
|
Antiviral B |
50 |
150 |
0 |
150 |
|
Total infected symptomatic |
800 |
150 |
50 |
|
Table 10. Severity of infected symptomatic individuals and their access to proper care for Scenario 1.3
|
Severity |
With proper care |
No proper care |
Total |
|
Mild |
912 |
0 |
912 |
|
Moderate |
78 |
0 |
78 |
|
Critical |
10 |
0 |
10 |
Table 11. Summary of Results
|
|
Scenario 1.1 |
Scenario 1.2 |
Scenario 1.3 |
|||
|
Antiviral A |
Antiviral B |
Antiviral A |
Antiviral B |
Antiviral A |
Antiviral B |
|
|
Mild |
0 |
0 |
0 |
0 |
0 |
0 |
|
Moderate |
0 |
0 |
50 |
100 |
0 |
150 |
|
Critical |
0 |
0 |
17 |
33 |
50 |
0 |
|
No proper care |
80 |
0 |
0 |
|||
|
Proper care |
920 |
1,000 |
1,000 |
|||
|
Deaths |
55 |
13 |
9 |
|||
Table 12. Optimal allocation of antivirals at different levels of supply availablity in Scenario 2.1
|
Fractional Availability |
Deaths |
Mild |
Moderate |
Critical |
||||||
|
No Antiviral |
Antiviral A |
Antiviral B |
No Antiviral |
Antiviral A |
Antiviral B |
No Antiviral |
Antiviral A |
Antiviral B |
||
|
0.1 |
16,527 |
32,577 |
0 |
0 |
45,087 |
0 |
0 |
8,708 |
9,597 |
0 |
|
0.2 |
10,841 |
32,577 |
0 |
0 |
44,094 |
0 |
994 |
105 |
18,200 |
0 |
|
0.3 |
9,421 |
32,577 |
0 |
0 |
34,602 |
0 |
10,486 |
0 |
18,305 |
0 |
|
0.4 |
8,217 |
32,577 |
0 |
0 |
25,005 |
0 |
20,083 |
0 |
18,305 |
0 |
|
0.5 |
7,076 |
32,577 |
0 |
0 |
15,408 |
0 |
29,680 |
0 |
18,305 |
0 |
|
0.6 |
6,030 |
32,577 |
0 |
0 |
5,811 |
0 |
39,276 |
0 |
18,305 |
0 |
|
0.7 |
5,400 |
32,577 |
0 |
0 |
42 |
0 |
45,046 |
0 |
18,305 |
0 |
|
0.8 |
5,397 |
32,577 |
0 |
0 |
0 |
0 |
45,087 |
0 |
18,305 |
0 |
|
0.9 |
5,397 |
32,577 |
0 |
0 |
0 |
0 |
45,087 |
0 |
18,305 |
0 |
|
1 |
5,397 |
32,577 |
0 |
0 |
0 |
0 |
45,087 |
0 |
18,305 |
0 |
Table 13. Optimal patient outcomes at different levels of hospital resource availability in Scenario 2.2
|
Fractional Availability |
Deaths |
Access to hospital resources |
||
|
0.1 |
8,349 |
Home |
Bed |
ICU |
|
0.2 |
7,868 |
66,392 |
2,806 |
149 |
|
0.3 |
7,397 |
66,392 |
5,534 |
291 |
|
0.4 |
6,945 |
66,392 |
8,209 |
432 |
|
0.5 |
6,538 |
66,392 |
10,751 |
572 |
|
0.6 |
6,246 |
66,392 |
12,996 |
713 |
|
0.7 |
5,991 |
66,392 |
14,473 |
854 |
|
0.8 |
5,786 |
66,392 |
15,712 |
992 |
|
0.9 |
5,581 |
66,392 |
16,633 |
1,126 |
|
1 |
5,397 |
66,392 |
17,553 |
1,259 |