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April
2018, 15(2): 337-359.
doi: 10.3934/mbe.2018015
The potential impact of a prophylactic vaccine for Ebola in Sierra Leone
Rhodes College, Department of Mathematics & Computer Science, 2000 N. Parkway, Memphis, TN 38112, USA |
The 2014 outbreak of Ebola virus disease (EVD) in West Africa was multinational and of an unprecedented scale primarily affecting the countries of Guinea, Liberia, and Sierra Leone. One of the qualities that makes EVD of high public concern is its potential for extremely high mortality rates (up to 90%). A prophylactic vaccine for ebolavirus (rVSV-ZEBOV) has been developed, and clinical trials show near-perfect efficacy. We have developed an ordinary differential equations model that simulates an EVD epidemic and takes into account (1) transmission through contact with infectious EVD individuals and deceased EVD bodies, (2) the heterogeneity of the risk of becoming infected with EVD, and (3) the increased survival rate of infected EVD patients due to greater access to trained healthcare providers. Using fitted parameter values that closely simulate the dynamics of the 2014 outbreak in Sierra Leone, we utilize our model to predict the potential impact of a prophylactic vaccine for the ebolavirus using various vaccination strategies including ring vaccination. Our results show that an rVSV-ZEBOV vaccination coverage as low as 40% in the general population and 95% in healthcare workers will prevent another catastrophic outbreak like the 2014 outbreak from occurring.
Keywords:
Ebolavirus,
prophylactic vaccine,
vaccine coverage,
ring vaccination,
ordinary differential equations,
epidemiology,
population dynamics,
Sierra Leone.
Mathematics Subject Classification:
Primary: 92B05, 92D30; Secondary: 92-08.
Citation:
Erin N. Bodine, Connor Cook, Mikayla Shorten. The potential impact of a prophylactic vaccine for Ebola in Sierra Leone. Mathematical Biosciences & Engineering,
2018, 15
(2)
: 337-359.
doi: 10.3934/mbe.2018015
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|
Figure 2.
Timeline showing the implementation of different control strategies over the course of the outbreak. The date for time $t=0$ is 30 days prior to the initial date that the CDC began recording outbreak data.
Figure 3.
Flow diagram of the model given in System (1). Shaded compartments indicate high risk of exposure (red), low risk of exposure (orange), and ability to transmit EVD (yellow). Green arrows indicate movement into the population, blue arrows indicate background death, and dashed line arrows indicate vaccination.
Figure 5.
$\mathcal{R}_A(t)$ for response periods $[0,95]$ (red), $[95,202]$ (blue), $[202,248]$ (orange), $[248,460]$ (green), and $[460,647]$ (purple).
Figure 6.
Matrix plots displaying the sensitivity of the parameters $\alpha$ , $x$ , $\nu$ , and $\rho_L$ to the cumulative number of infected individuals (CI) during a ring vaccination scenario with $\epsilon=1$ , $\rho_H={\raise0.5ex\hbox{$\scriptstyle 0.95$}\kern-0.1em/\kern-0.15em\lower0.25ex\hbox{$\scriptstyle 21$}}$ , and $\hat{\rho}={\raise0.5ex\hbox{$\scriptstyle 0.99$}\kern-0.1em/\kern-0.15em\lower0.25ex\hbox{$\scriptstyle 7$}}$ .
Table 1.
Parameters and values used in the model.
| Parameter | Units | Value | Description | Source | |
| Fitted Parameters | |
See Table 3 | transmission rate from infectious individuals to high risk susceptible individuals | ||
| |
See Table 3 | transmission rate from infectious individuals to low risk susceptible individuals | |||
| |
See Table 3 | transmission rate from infectious individuals to susceptible healthcare workers | |||
| See Table 3 | transmission rate from deceased individuals to high risk susceptible individuals | ||||
| See Table 3 | transmission rate from deceased individuals to low risk susceptible individuals | ||||
| See Table 3 | transmission rate from deceased individuals to susceptible healthcare workers | ||||
| See Table 3 | transmission rate from recovering, still infectious individuals to low risk individuals | ||||
| -- | See Table 3 | proportion of symptomatic individuals who go to hospitals | |||
| -- | See Table 3 | scaling constant where |
|||
| Vax | -- | |
proportion of individuals in whom the vaccine is effective | [31] | |
| -- | See Section 5 | proportion of low susceptible population ( |
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| -- | See Section 5 | proportion of high susceptible population ( |
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| -- | See Section 5 | proportion of healthcare workers ( |
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| See section 3 | migration rate of healthcare workers into the population | ||||
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natural death rate per day per 1,000 individuals | [16] | |||
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natural birth rate per day per 1,000 individuals | [16] | |||
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rate at which individuals become symptomatic and infectious | [45] | |||
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infectious period of individuals who are not in hospitals | [50] | |||
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infectious period of individuals who are in hospitals | ||||
| -- | |
proportion of individuals who die from Ebola | [12] | ||
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number of healthcare workers in the population prior to outbreak | [16] | |||
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burial rate of deceased individuals who were not in hospitals | ||||
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burial rate of deceased individuals who were in hospitals | [50] | |||
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rate at which recovering and still infectious individuals become non-infectious | [18,15] | |||
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rate at which individuals move from low risk to high risk susceptible populations | ||||
| rate at which individuals move from high risk to low risk susceptible populations | |||||
| Parameter | Units | Value | Description | Source | |
| Fitted Parameters | |
See Table 3 | transmission rate from infectious individuals to high risk susceptible individuals | ||
| |
See Table 3 | transmission rate from infectious individuals to low risk susceptible individuals | |||
| |
See Table 3 | transmission rate from infectious individuals to susceptible healthcare workers | |||
| See Table 3 | transmission rate from deceased individuals to high risk susceptible individuals | ||||
| See Table 3 | transmission rate from deceased individuals to low risk susceptible individuals | ||||
| See Table 3 | transmission rate from deceased individuals to susceptible healthcare workers | ||||
| See Table 3 | transmission rate from recovering, still infectious individuals to low risk individuals | ||||
| -- | See Table 3 | proportion of symptomatic individuals who go to hospitals | |||
| -- | See Table 3 | scaling constant where |
|||
| Vax | -- | |
proportion of individuals in whom the vaccine is effective | [31] | |
| -- | See Section 5 | proportion of low susceptible population ( |
|||
| -- | See Section 5 | proportion of high susceptible population ( |
|||
| -- | See Section 5 | proportion of healthcare workers ( |
|||
| See section 3 | migration rate of healthcare workers into the population | ||||
| |
natural death rate per day per 1,000 individuals | [16] | |||
| |
natural birth rate per day per 1,000 individuals | [16] | |||
| |
rate at which individuals become symptomatic and infectious | [45] | |||
| |
infectious period of individuals who are not in hospitals | [50] | |||
| |
infectious period of individuals who are in hospitals | ||||
| -- | |
proportion of individuals who die from Ebola | [12] | ||
| |
number of healthcare workers in the population prior to outbreak | [16] | |||
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burial rate of deceased individuals who were not in hospitals | ||||
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burial rate of deceased individuals who were in hospitals | [50] | |||
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rate at which recovering and still infectious individuals become non-infectious | [18,15] | |||
| |
rate at which individuals move from low risk to high risk susceptible populations | ||||
| rate at which individuals move from high risk to low risk susceptible populations | |||||
Table 3.
Values of fitted parameters for each response period. The range of the uniform distribution for each parameter for each response period is shown above the fitted parameter value.
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Table 2.
Weight equation parameter values for each response period.
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0.015 | 0.030 | 0.060 | 0.013 | 0.013 |
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40 | 20 | 10 | 50 | 45 |
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0.015 | 0.030 | 0.060 | 0.013 | 0.013 |
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Table 4.
$\bar{\mathcal{R}}_A(t)$ for each response period.
| Response period | |
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3.31 |
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1.88 |
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0.90 |
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0.27 |
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0.16 |
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3.31 |
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1.88 |
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0.90 |
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0.27 |
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0.16 |
Table 5.
Impact of prophylactic vaccine distributed during the outbreak on cumulative infections and deaths
| Cumulative Infections | Cumulative Deaths | |||||
| at tf | Prevented | at tf | Prevented | |||
| Baseline |
14436 | 0 | 4416 | 0 | ||
| Start vax at | 8863 | 5573 | 2738 | 1678 | ||
| 12583 | 1853 | 3837 | 579 | |||
| 13225 | 1211 | 4050 | 366 | |||
| 14325 | 111 | 4392 | 24 | |||
| Start vax at | 5138 | 9298 | 1656 | 2760 | ||
| 11075 | 3361 | 3343 | 1073 | |||
| 12168 | 2268 | 3708 | 708 | |||
| 14173 | 263 | 4357 | 59 | |||
| Start vax at | 13999 | 437 | 4283 | 133 | ||
| 14285 | 151 | 4369 | 47 | |||
| 14351 | 85 | 4391 | 25 | |||
| 14429 | 7 | 4415 | 1 | |||
| Start vax at | 8821 | 5615 | 2726 | 1690 | ||
| 12553 | 1883 | 3827 | 589 | |||
| 13211 | 1225 | 4046 | 370 | |||
| 14323 | 113 | 4391 | 25 | |||
| Cumulative Infections | Cumulative Deaths | |||||
| at tf | Prevented | at tf | Prevented | |||
| Baseline |
14436 | 0 | 4416 | 0 | ||
| Start vax at | 8863 | 5573 | 2738 | 1678 | ||
| 12583 | 1853 | 3837 | 579 | |||
| 13225 | 1211 | 4050 | 366 | |||
| 14325 | 111 | 4392 | 24 | |||
| Start vax at | 5138 | 9298 | 1656 | 2760 | ||
| 11075 | 3361 | 3343 | 1073 | |||
| 12168 | 2268 | 3708 | 708 | |||
| 14173 | 263 | 4357 | 59 | |||
| Start vax at | 13999 | 437 | 4283 | 133 | ||
| 14285 | 151 | 4369 | 47 | |||
| 14351 | 85 | 4391 | 25 | |||
| 14429 | 7 | 4415 | 1 | |||
| Start vax at | 8821 | 5615 | 2726 | 1690 | ||
| 12553 | 1883 | 3827 | 589 | |||
| 13211 | 1225 | 4046 | 370 | |||
| 14323 | 113 | 4391 | 25 | |||
Table 6.
Effect of vaccination prior to an initial outbreak (1 infected). Vaccination coverage of healthcare workers is 0% when $x=0$ and 95% otherwise.
| Vaccination strategy for |
||||||||
| CI | CI | CI | CI | |||||
| 0 | 4156370 | 495 | 3743965 | 516 | 650846 | 492 | 2643460 | 492 |
| 0.10 | 3064971 | 648 | 2506362 | 694 | 1853742 | 644 | 1845334 | 644 |
| 0.20 | 1866043 | 974 | 1026659 | 1138 | 1040091 | 987 | 1030788 | 988 |
| 0.29 | 764174 | 1990 | 37 | 103 | 188898 | 2267 | 188898 | 2267 |
| 0.30 | 646329 | 2270 | 33 | 0 | 82717 | 2546 | 82717 | 2546 |
| 0.31 | 529673 | 2657 | 29 | 0 | 19911 | 2502 | 19911 | 2502 |
| 0.32 | 414210 | 3213 | 25 | 0 | 3866 | 2091 | 3866 | 2091 |
| 0.33 | 300060 | 4090 | 23 | 0 | 954 | 1570 | 954 | 1570 |
| 0.34 | 171811 | 5697 | 20 | 0 | 325 | 1023 | 325 | 1023 |
| 0.35 | 13195 | 7300 | 18 | 0 | 147 | 0 | 147 | 0 |
| 0.36 | 431 | 0 | 16 | 0 | 81 | 0 | 81 | 0 |
| 0.40 | 26 | 0 | 20 | 0 | 23 | 0 | 23 | 0 |
| 0.50 | 7 | 0 | 7 | 0 | 7 | 0 | 7 | 0 |
| 0.60 | 4 | 0 | 4 | 0 | 4 | 0 | 4 | 0 |
| 0.70 | 2 | 0 | 2 | 0 | 2 | 0 | 2 | 0 |
| 0.80 | 2 | 0 | 2 | 0 | 2 | 0 | 2 | 0 |
| 0.90 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
| Vaccination strategy for |
||||||||
| CI | CI | CI | CI | |||||
| 0 | 4156370 | 495 | 3743965 | 516 | 650846 | 492 | 2643460 | 492 |
| 0.10 | 3064971 | 648 | 2506362 | 694 | 1853742 | 644 | 1845334 | 644 |
| 0.20 | 1866043 | 974 | 1026659 | 1138 | 1040091 | 987 | 1030788 | 988 |
| 0.29 | 764174 | 1990 | 37 | 103 | 188898 | 2267 | 188898 | 2267 |
| 0.30 | 646329 | 2270 | 33 | 0 | 82717 | 2546 | 82717 | 2546 |
| 0.31 | 529673 | 2657 | 29 | 0 | 19911 | 2502 | 19911 | 2502 |
| 0.32 | 414210 | 3213 | 25 | 0 | 3866 | 2091 | 3866 | 2091 |
| 0.33 | 300060 | 4090 | 23 | 0 | 954 | 1570 | 954 | 1570 |
| 0.34 | 171811 | 5697 | 20 | 0 | 325 | 1023 | 325 | 1023 |
| 0.35 | 13195 | 7300 | 18 | 0 | 147 | 0 | 147 | 0 |
| 0.36 | 431 | 0 | 16 | 0 | 81 | 0 | 81 | 0 |
| 0.40 | 26 | 0 | 20 | 0 | 23 | 0 | 23 | 0 |
| 0.50 | 7 | 0 | 7 | 0 | 7 | 0 | 7 | 0 |
| 0.60 | 4 | 0 | 4 | 0 | 4 | 0 | 4 | 0 |
| 0.70 | 2 | 0 | 2 | 0 | 2 | 0 | 2 | 0 |
| 0.80 | 2 | 0 | 2 | 0 | 2 | 0 | 2 | 0 |
| 0.90 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
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2018 Impact Factor: 1.313
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