Fig 1.
Smallpox disease progression overview when no countermeasure is implemented.
The symbol S denotes susceptible, A and B denote early and late incubation respectively, P denotes prodrome, C and E denote early and late rash respectively, R denotes recovered and D denotes dead. The suffix h denotes immunocompetency, and c denotes immunodeficiency e.g., Sh, Sc respectively denote immunocompetent and immunodeficient susceptible, etc. Table 4 in Appendix A.1 of S1 Appendix contains all the relevant abbreviations we used to represent each state. The states in blue color are the susceptibles (not yet infected but they are prone to infection) while those in light green color are still in incubation period, hence they are not infectious. The states in dark red are infectious while those in gold have recovered and black denotes dead. In addition, the yellow arrows show interactional changes, namely susceptibles transitioning to the incubation state after contracting the virus from infectious individuals. The blue arrows indicate a non-interactional change, namely the natural progression of the disease.
Fig 2.
Smallpox disease progression overview for “drug only” scenario.
The state in orange color denotes the preempted state. The red arrows denote preemption via drugs. Every other state and transition has the same meaning as described in the caption for Fig 1.
Fig 3.
Smallpox disease progression overview for vaccine only scenario.
Building on the definitions of states in Fig 1, the suffixes a and b respectively denote willingness to receive vaccine and otherwise e.g., Sah, Sac respectively denote immunocompetent and immunodeficient susceptibles that are willing to vaccinate. Similarly, Sbh, Sbc respectively denote immunocompetent and immunodeficient susceptibles that are not willing to vaccinate. The states in the top two rows and the transitions between them are identical to those in the bottom two rows except for the index “a” being replaced by “b”. The difference in this index represents a partition of these states based on the willingness to vaccinate. Sans this partition, the states and the transitions are similar to those in Fig 2—specifically, the states in the top two rows and the transitions between them, and those in the bottom two rows, by themselves, are similar to the states and the transitions in Fig 2 (except that the transition to the preempted state happens from a larger set of states in Fig 2). Table 7 in Appendix A.3 of S1 Appendix contains all the relevant abbreviations in this scenario. The states in blue color are the susceptibles (not yet infected but they are prone to infection) while those in light green color are still in incubation period, hence they are not infectious. The states in dark red are infectious while those in gold have recovered, those in yellow are immunized, and black denotes dead. In addition, the yellow arrows show susceptibles transitioning to the incubation state after contracting the virus. The blue arrows indicate the natural progression of the disease. The red arrows denote preemption via vaccination while the black arrows indicate opinion evolution.
Fig 4.
Smallpox disease progression overview for both drug and vaccine scenario.
The states colored orange are the preempted states. Every other state and transition has the same meaning as described in the caption for Fig 3.
Fig 5.
(a) Star topology. (b) Linear topology.
Fig 6.
Relationship between fatality and opinion spread rate (single cluster).
(a) Number of individuals infected at the initial time is 1,000. (b) Number of individuals infected at the initial time is 10,000.
Fig 7.
Fatality versus opinion spread rate for different numbers and stages of initial infections in a single cluster (both drug and vaccine scenario).
Fig 8.
Relationship between fatality and opinion spread rate (multiple clusters).
(a) Star topology, κ = 0.01. (b) Star topology, κ = 0.8. (c) Linear topology, κ = 0.01. (d) Linear topology, κ = 0.8.
Fig 9.
Relationship between fatality and opinion spread rate when non-cooperatives convert cooperatives.
(a) Single cluster (initial cooperativity = 0.8). (b) Single cluster (initial cooperativity = 0.2). (c) Star topology (initial cooperativity = 0.8). (d) Star topology (initial cooperativity = 0.2). (e) Linear topology (initial cooperativity = 0.8). (f) Linear topology (initial cooperativity = 0.2).
Fig 10.
Relationship between fatality and preemption scale factor.
(a) Star topology, α = 0.001. (b) Star topology, α = 0.8. (c) Linear topology, α = 0.001. (d) Linear topology, α = 0.8.
Fig 11.
Percentage decrease in fatality as a function of preemption scale factor.
a) Star topology. (b) Linear topology.
Fig 12.
Relationship between fatality and mobility rate.
(a) Star topology. (b) Linear topology.
Fig 13.
Relationship between fatality and initial distribution of cooperatives.
(a) Initial cooperatives are uniformly distributed across clusters (initial cooperativity = 0.25). (b) Initial cooperatives are only in the central cluster (initial cooperativity = 0.25).
Fig 14.
Fatalities under four countermeasure application scenarios for various values of infection spread rates and initial cooperativities for single cluster.
(a) Relationship between fatality and disease spread rate. (b) Relationship between fatality and initial cooperativity.
Fig 15.
Fatalities under four countermeasure application scenarios for various values of infection spread rates and initial cooperativities for multiple clusters.
(a) Relationship between total fatality and disease spread rate (star topology). (b) Relationship between total fatality and initial cooperativity (linear topology).
Fig 16.
Relationship between fatalities and antiviral drug availability.
(a) Single cluster. (b) Star topology. (c) Linear topology.
Table 1.
The three tables respectively compare the actual fatality count and linear interpolations for the “both drug and vaccine scenario” for 1) single cluster (Fig 16a), 2) star topology (Fig 16b), and 3) linear topology (Fig 16c).
In these tables, the first column (A) represents the number of individuals in millions, who have been administered the drugs, the second column (B) provides the actual fatality counts, the third column (C) provides the fatality counts of a linear interpolation (i.e., straight line with the entries marked in bold as end-points), the fourth column provides the percentage errors, i.e., 100 × (B − C)/B.
Fig 17.
Policies for drug deployment (star topology).
(a) Initially infected individuals are in the central cluster. (b) Initially infected individuals are distributed uniformly across clusters.
Fig 18.
Policies for drug deployment (linear topology).
(a) Initially infected individuals are in a peripheral cluster. (b) Initially infected individuals are distributed uniformly across clusters.
Table 2.
The four tables respectively compare the actual fatality count and linear interpolations for policy 1 “both drug and vaccine scenario” and 1) eight cluster star topology—Central (Fig 17a) 2) eight cluster star topology—Uniform (Fig 17b) 3) five cluster linear topology—Peripheral (Fig 18a) 4) five cluster linear topology—Uniform (Fig 18b).
The columns A, B, C have the same significance as in Table 1.
Table 3.
The five tables respectively compare the per cluster fatality counts for the “both drug and vaccine” scenario for different opinion spread rates (α) (Table 3a and 3b), preemption scale factor (λ) (Table 3c), mobility rates (κ) (Table 3d), and drug supply (m) (Table 3e). In these tables, the first column (P) represents Normalized linear, the second column (Q) represents Normalized star, and the third column (R) provides Q − P, the fourth column, Change = 100 × R/P.
Fig 19.
Health care load against drug availability.
(a) Linear topology. (b) Star topology.
Fig 20.
The symbol S denotes susceptibles, L denotes individuals in the latent stage, P stands for pre-symptomatic, Is denotes symptomatic stage, Ia denotes asymptomatic stage, H stands for hospitalized, R denotes recovered, and D stands for dead. The suffixes c and n respectively stand for cooperatives and non-cooperatives e.g., Sc and Sn denote cooperative and non-cooperative susceptible individuals respectively. Similarly, Ica and Ina stand for cooperative asymptomatic and non-cooperative asymptomatic individuals respectively.