Could low-efficacy malaria vaccines increase secondary infections in endemic areas?
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1 Could low-efficacy malaria vaccines increase secondary infections in endemic areas? Robert Smith? The University of Ottawa
2 Malaria One of the most important human diseases throughout the tropical and sub-tropical regions of the world Source: NMCC Central Board of Health, 2000
3 Malaria One of the most important human diseases throughout the tropical and sub-tropical regions of the world More than 300 million acute illnesses each year Source: NMCC Central Board of Health, 2000
4 Malaria One of the most important human diseases throughout the tropical and sub-tropical regions of the world More than 300 million acute illnesses each year 1,000,000 deaths annually. Source: NMCC Central Board of Health, 2000
5 Symptoms Repeated episodes of fever
6 Symptoms Repeated episodes of fever Anemia
7 Symptoms Repeated episodes of fever Anemia Death.
8 Endemic areas 90% of malaria deaths occur in sub-saharan Africa
9 Endemic areas 90% of malaria deaths occur in sub-saharan Africa Mostly among young children Admissions to St. Kitzo-Matany hospital, Uganda
10 Endemic areas 90% of malaria deaths occur in sub-saharan Africa Mostly among young children Even when it doesn t kill, acute illness can devastate economies in the developing world. Admissions to St. Kitzo-Matany hospital, Uganda
11
12 Malaria vaccines The search for a malaria vaccine is now over 70 years old
13 Malaria vaccines The search for a malaria vaccine is now over 70 years old Recently, a candidate vaccine (RTS,S/AS01) completed Phase III trials
14 Malaria vaccines The search for a malaria vaccine is now over 70 years old Recently, a candidate vaccine (RTS,S/AS01) completed Phase III trials It cut the risk of developing severe malaria by 26%
15 Malaria vaccines The search for a malaria vaccine is now over 70 years old Recently, a candidate vaccine (RTS,S/AS01) completed Phase III trials It cut the risk of developing severe malaria by 26% The efficacy in infants was only 31%.
16 RTS,S/AS01 vaccine (Mosquirix) The time to first infection was cut by 45%
17 RTS,S/AS01 vaccine (Mosquirix) The time to first infection was cut by 45% Protection did not wane after 15 months
18 RTS,S/AS01 vaccine (Mosquirix) The time to first infection was cut by 45% Protection did not wane after 15 months Phase III trial completed in 2012
19 RTS,S/AS01 vaccine (Mosquirix) The time to first infection was cut by 45% Protection did not wane after 15 months Phase III trial completed in 2012 Currently in development commercially
20 RTS,S/AS01 vaccine (Mosquirix) The time to first infection was cut by 45% Protection did not wane after 15 months Phase III trial completed in 2012 Currently in development commercially Not expected on the market for a few years.
21 The downside Such vaccines hold great hope for containing the spread of the disease
22 The downside Such vaccines hold great hope for containing the spread of the disease However, they are likely to have poor efficacy, at least initially
23 The downside Such vaccines hold great hope for containing the spread of the disease However, they are likely to have poor efficacy, at least initially This may result in a net increase in infections.
24 Candidate vaccines Such vaccines permit infection but reduce parasite burden
25 Candidate vaccines Such vaccines permit infection but reduce parasite burden We call these disease-modifying vaccines.
26 Disease-modifying vaccines Disease-modifying vaccines may:
27 Disease-modifying vaccines Disease-modifying vaccines may: allow you to become infected
28 Disease-modifying vaccines Disease-modifying vaccines may: allow you to become infected reduce your duration of infection
29 Disease-modifying vaccines Disease-modifying vaccines may: allow you to become infected reduce your duration of infection lower your parasite burden.
30 Potential effects Potential effects from a malaria vaccine could include:
31 Potential effects Potential effects from a malaria vaccine could include: i. increasing the recovery rate
32 Potential effects Potential effects from a malaria vaccine could include: i. increasing the recovery rate ii. increasing the acquired immunity rate
33 Potential effects Potential effects from a malaria vaccine could include: i. increasing the recovery rate ii. increasing the acquired immunity rate iii. reducing the rate of infection.
34 Limitations Potential limitations of a vaccination program could include:
35 Limitations Potential limitations of a vaccination program could include: i. the vaccine may only be delivered to a proportion p of the population
36 Limitations Potential limitations of a vaccination program could include: i. the vaccine may only be delivered to a proportion p of the population ii. the vaccine may on take in a proportion ε of people vaccinated
37 Limitations Potential limitations of a vaccination program could include: i. the vaccine may only be delivered to a proportion p of the population ii. the vaccine may on take in a proportion ε of people vaccinated iii. the vaccine may wane at rate ω
38 Limitations Potential limitations of a vaccination program could include: i. the vaccine may only be delivered to a proportion p of the population ii. the vaccine may on take in a proportion ε of people vaccinated iii. the vaccine may wane at rate ω iv. the vaccine may have suboptimal efficacy ψ.
39 Efficacy A disease-modifying vaccine with 35% efficacy would:
40 Efficacy A disease-modifying vaccine with 35% efficacy would: stop infection 35% of the time
41 Efficacy A disease-modifying vaccine with 35% efficacy would: stop infection 35% of the time permit infection the remaining 65% of the time
42 Efficacy A disease-modifying vaccine with 35% efficacy would: stop infection 35% of the time permit infection the remaining 65% of the time lower your parasite burden once you became infected
43 Efficacy A disease-modifying vaccine with 35% efficacy would: stop infection 35% of the time permit infection the remaining 65% of the time lower your parasite burden once you became infected (so you re less likely to transmit the disease).
44 Four groups For any vaccine, there are four groups:
45 Four groups For any vaccine, there are four groups: a) those who never received the vaccine;
46 Four groups For any vaccine, there are four groups: a) those who never received the vaccine; b) those who received the vaccine but the vaccine did not take;
47 Four groups For any vaccine, there are four groups: a) those who never received the vaccine; b) those who received the vaccine but the vaccine did not take; c) those who received the vaccine, the vaccine took, but the vaccine waned over time; and
48 Four groups For any vaccine, there are four groups: a) those who never received the vaccine; b) those who received the vaccine but the vaccine did not take; c) those who received the vaccine, the vaccine took, but the vaccine waned over time; and d) those who received the vaccine, the vaccine took and for whom the vaccine did not wane over time.
49 Four groups For any vaccine, there are four groups: a) those who never received the vaccine; b) those who received the vaccine but the vaccine did not take; c) those who received the vaccine, the vaccine took, but the vaccine waned over time; and d) those who received the vaccine, the vaccine took and for whom the vaccine did not wane over time.
50 Vaccinated individuals Unvaccinated individuals = groups (a)-(c)
51 Vaccinated individuals Unvaccinated individuals = groups (a)-(c) Vaccinated individuals = group (d).
52 Vaccinated individuals Vaccinated individuals may have
53 Vaccinated individuals Vaccinated individuals may have a reduced rate of infection
54 Vaccinated individuals Vaccinated individuals may have a reduced rate of infection increased life expectancy
55 Vaccinated individuals Vaccinated individuals may have a reduced rate of infection increased life expectancy faster recovery.
56 Duration of infection Thus the duration of infection for vaccinated individuals may
57 Duration of infection Thus the duration of infection for vaccinated individuals may decrease (due to higher recovery rates)
58 Duration of infection Thus the duration of infection for vaccinated individuals may decrease (due to higher recovery rates) increase (due to fewer deaths).
59 The model "#$! "!! "! + & & & ' & ) & % & ' &!!!#* "#$ $ &! "#$ $. "! "#$! " /. " " "!"#$ #*!"#$!"#$!! ""#$! ) ( + ( % (!! ""#$!!! ""#$! ' ( "#$! $ (,!!%- "!! "! & ( ' (
60 The model!!!#* "#$ "#$! "!! + & " '! & ) & % ' & & $ & & &!! "#$ "#$ UNVACCINATED $! ". /. " " " "!"#$ #*!"#$!"#$!! ""#$! ) ( + ( % (!! ""#$!!! ""#$! ' ( "#$! $ (,!!%- "!! "! & ( ' (
61 The model!!!#* "#$ "#$! "!! + & " '! & ) & % ' & & $ & & &!! "#$ "#$ UNVACCINATED $! ". /. " " " "!"#$ #*!"#$!"#$!! ""#$! ) ( + ( % (!! ""#$!!! ""#$! ' ( "#$! $ (,!!%- "!! "! & ( ' ( VACCINATED
62 The model!!!#* "#$ "#$! "!! + & " '! & ) & % ' & & $ & & &!! "#$ "#$ UNVACCINATED $! ". /. " " " " MOSQUITOS!"#$ #*!"#$!"#$!! ""#$! ) ( + ( % (!! ""#$!!! ""#$! ' ( "#$! $ (,!!%- "!! "! & ( ' ( VACCINATED
63 The model population!!!#* "#$ "#$! "!! + & " '! & ) & % ' & & $ & & &!! "#$ "#$ $. " UNVACCINATED! " /. " " " MOSQUITOS!"#$ #*!"#$!"#$!! ""#$! ) ( + ( % (!! ""#$!!! ""#$! ' ( "#$! $ (,!!%- "!! "! & ( ' ( VACCINATED
64 The model population!!!#* "#$ "#$! "!! + & " '! & ) & % ' & & $ & & &!! "#$ "#$! " /. " "!"#$ #*!! ""#$! ) ( $. " UNVACCINATED take + (!"#$ % (!! ""#$!!"#$!! ""#$! "#$! $ (,!!%- "!! "! & ( ' ( " ' ( MOSQUITOS VACCINATED
65 The model population!!!#* "#$ "#$! "!! + & " '! & ) & % ' & & $ & & &!! "#$ "#$! " /. " "!"#$ #*!! ""#$! ) ( $. " UNVACCINATED take proportion vaccinated + (!"#$ % (!! ""#$!!"#$!! ""#$! "#$! $ (,!!%- "!! "! & ( ' ( " ' ( MOSQUITOS VACCINATED
66 The model population!!!#* "#$ "#$! "!! + & " '! & ) & % ' & & $ & & &!! "#$ "#$! " /. " "!"#$ #*!! ""#$! ) ( $. " UNVACCINATED waning take proportion vaccinated + (!"#$ % (!! ""#$!!"#$!! ""#$! "#$! $ (,!!%- "!! "! & ( ' ( " ' ( MOSQUITOS VACCINATED
67 The model population susceptible!!!#* "#$ "#$! "!! + & " '! & ) & % ' & & $ & & &!! "#$ "#$ UNVACCINATED waning take proportion vaccinated $! ". /. " " " "!"#$ #*!! ""#$! ) ( + (!"#$ % (!! ""#$!!"#$!! ""#$! ' ( "#$! $ (,!!%- "!! "! & ( ' ( MOSQUITOS VACCINATED
68 The model population susceptible!!!#* "#$ "#$! "!! + & " '! & ) & % ' & & $ & infected & &!! "#$ "#$ UNVACCINATED waning take proportion vaccinated $! ". /. " " " "!"#$ #*!! ""#$! ) ( + (!"#$ % (!! ""#$!!"#$!! ""#$! ' ( "#$! $ (,!!%- "!! "! & ( ' ( MOSQUITOS VACCINATED
69 The model population susceptible!!!#* "#$ "#$! "!! + & " '! & ) & % ' & & $ & infected immune & &!! "#$ "#$ UNVACCINATED waning take proportion vaccinated $! ". /. " " " "!"#$ #*!! ""#$! ) ( + (!"#$ % (!! ""#$!!"#$!! ""#$! ' ( "#$! $ (,!!%- "!! "! & ( ' ( MOSQUITOS VACCINATED
70 The model population susceptible!!!#* "#$ "#$! "!! + & " '! & ) & % ' & & $ & infected immune & &!! "#$ "#$ susceptible mosqitoes UNVACCINATED waning take proportion vaccinated $! ". /. " " " "!"#$ #*!! ""#$! ) ( + (!"#$ % (!! ""#$!!"#$!! ""#$! ' ( "#$! $ (,!!%- "!! "! & ( ' ( MOSQUITOS VACCINATED
71 The model population susceptible!!!#* "#$ "#$! "!! + & " '! & ) & % ' & & $ & infected immune & &!! "#$ "#$ susceptible mosqitoes UNVACCINATED waning take $! ". /. " " " "!"#$ #*!! ""#$!!"#$!! ""#$!!"#$!! ""#$! proportion vaccinated "#$! $ (,!!%- "!! &"! infected mosqitoes ( ) ( + ( % ( ' ( ' ( MOSQUITOS VACCINATED
72 The model population susceptible!!!#* "#$ "#$! "!! + & " '! & ) & % ' & & $ & infected immune & &!! infecton rate "#$ "#$ susceptible mosqitoes UNVACCINATED waning take $! ". /. " " " "!"#$ #*!! ""#$!!"#$!! ""#$!!"#$!! ""#$! proportion vaccinated "#$! $ (,!!%- "!! &"! infected mosqitoes ( ) ( + ( % ( ' ( ' ( MOSQUITOS VACCINATED
73 The model population susceptible!!!#* "#$ "#$! "!! + & " '! & ) & % ' & & $ & infected immune & &!! infecton rate "#$ "#$ susceptible mosqitoes UNVACCINATED waning take $! ". /. " " " "!"#$ #*!! ""#$!!"#$!! ""#$!!"#$!! ""#$! proportion vaccinated "#$! $ (,!!%- "!! &"! infected mosqitoes ( ) ( + ( % ( ' ( ' ( recovery MOSQUITOS VACCINATED
74 The model population susceptible!!!#* "#$ "#$! "!! + & " '! & ) & % ' & & $ & infected immune & &!! infecton rate "#$ "#$ susceptible mosqitoes UNVACCINATED waning take $! ". /. " " " "!"#$ #*!! ""#$!!"#$!! ""#$!!"#$!! ""#$! proportion vaccinated "#$! $ (,!!%- "!! &"! infected mosqitoes ( ) ( + ( % ( ' ( ' ( recovery acquired immunity MOSQUITOS VACCINATED
75 The model population susceptible!!!#* "#$ "#$! "!! + & " '! & ) & % ' & & $ & infected immune & &!! infecton rate "#$ "#$ susceptible mosqitoes UNVACCINATED waning take $! ". /. " " " "!"#$ #*!! ""#$!!"#$!! ""#$!!"#$!! ""#$! proportion vaccinated "#$! $ (,!!%- "!! &"! infected mosqitoes ( ) ( + ( % ( ' ( ' ( recovery acquired immunity MOSQUITOS VACCINATED loss of immunity
76 The model population susceptible!!!#* "#$ "#$! "!! + & " '! & ) & % ' & & $ & infected immune & &!! infecton rate "#$ "#$ susceptible mosqitoes UNVACCINATED waning take $! ". /. " " " "!"#$ #*!! ""#$!!"#$!! ""#$!!"#$!! ""#$! proportion vaccinated "#$! $ (,!!%- "!! &"! infected mosqitoes ( ) ( + ( % ( ' ( ' ( recovery acquired immunity MOSQUITOS VACCINATED efficacy. loss of immunity
77 The ODEs dm dt = Ω β M Y U M β M Y V M µ M M dn dt = β MY U M + β M Y V M µ M N dx U dt = (1 ɛp)π µx U β U NX U + ωx V + h U Y U + δ U Q U dx V dt = ɛpπ µx V (1 ψ)β V NX V ωx V + h V Y V + δ V Q V dy U dt = β U NX U (µ + γ U + α U + h U )Y U + ωy V dy V dt = (1 ψ)β V X V (µ + γ V + α V + h V )Y V ωy V dq U dt = α U Y U (µ + δ U )Q U + ωq V dq V dt = α V Y V (µ + δ V )Q V ωq V.
78 Basic reproductive numbers
79 Basic reproductive numbers The average number of secondary infections caused by an infected unvaccinated individual is R 0
80 Basic reproductive numbers The average number of secondary infections caused by an infected unvaccinated individual is R 0 The average number of secondary infections caused by an infected vaccinated individual is R V.
81 Population reproductive number The total number of secondary infections caused by a single individual is
82 Population reproductive number The total number of secondary infections caused by a single individual is R p = SR V +(1-S)R 0 R 0 =reproductive number (unvaccinated) R V =reproductive number (vaccinated)
83 Population reproductive number The total number of secondary infections caused by a single individual is R p = SR V +(1-S)R 0 S = proportion successfully vaccinated. R 0 =reproductive number (unvaccinated) R V =reproductive number (vaccinated)
84 Vaccine coverage level When R p = 1, SR V + (1-S)R 0 = 1 R j =reproductive numbers (pop, vacc, unvacc) ω=waning ε=take S=proportion vaccinated pc=coverage µ=background death rate
85 Vaccine coverage level When R p = 1, SR V + (1-S)R 0 = 1 Thus R j =reproductive numbers (pop, vacc, unvacc) ω=waning ε=take S=proportion vaccinated pc=coverage µ=background death rate
86 Vaccine coverage level When R p = 1, SR V + (1-S)R 0 = 1 Thus S = p cµ µ + = 1 R 0 R V R 0 p c = (µ + )(1 R 0) µ(r V R 0 ) R j =reproductive numbers (pop, vacc, unvacc) ω=waning ε=take S=proportion vaccinated pc=coverage µ=background death rate
87 Vaccine coverage level When R p = 1, SR V + (1-S)R 0 = 1 Thus S = p cµ µ + = 1 R 0 R V R 0 p c = (µ + )(1 R 0) µ(r V R 0 ) R j =reproductive numbers (pop, vacc, unvacc) ω=waning ε=take S=proportion vaccinated pc=coverage µ=background death rate
88 Vaccine coverage level When R p = 1, SR V + (1-S)R 0 = 1 Thus S = p cµ µ + = 1 R 0 R V R 0 p c = (µ + )(1 R 0) µ(r V R 0 ) is the threshold vaccine coverage level. R j =reproductive numbers (pop, vacc, unvacc) ω=waning ε=take S=proportion vaccinated pc=coverage µ=background death rate
89 Eradication? Vaccination programs whose coverage levels exceed pc are likely to eradicate the disease pc=critical coverage level
90 Eradication? Vaccination programs whose coverage levels exceed pc are likely to eradicate the disease However, this may not be achievable in real terms. pc=critical coverage level
91 First, do no harm Disease-modifying vaccines run the risk of increasing the number of secondary infections
92 First, do no harm Disease-modifying vaccines run the risk of increasing the number of secondary infections This may happen due to increasing the average duration of infection
93 First, do no harm Disease-modifying vaccines run the risk of increasing the number of secondary infections This may happen due to increasing the average duration of infection This may occur if many more people survive to become infected later.
94 Increasing secondary infections The number of secondary infections will increase if Rp > R0 R j =reproductive numbers (pop, vacc, unvacc) Ψ=efficacy S=proportion vaccinated βj=rate of infection ξj=duration
95 Increasing secondary infections The number of secondary infections will increase if Rp > R0 Thus R j =reproductive numbers (pop, vacc, unvacc) Ψ=efficacy S=proportion vaccinated βj=rate of infection ξj=duration
96 Increasing secondary infections The number of secondary infections will increase if Rp > R0 Thus (1 S)R 0 + SR V > R 0 V U > 1 V (1 ) 2 U. R j =reproductive numbers (pop, vacc, unvacc) Ψ=efficacy S=proportion vaccinated βj=rate of infection ξj=duration
97 Increasing secondary infections The number of secondary infections will increase if Rp > R0 Thus (1 S)R 0 + SR V > R 0 V U > 1 V (1 ) 2 U. R j =reproductive numbers (pop, vacc, unvacc) Ψ=efficacy S=proportion vaccinated βj=rate of infection ξj=duration
98 Increasing secondary infections The number of secondary infections will increase if Rp > R0 Thus (1 S)R 0 + SR V > R 0 V U > 1 V (1 ) 2 U. relative rate of infection R j =reproductive numbers (pop, vacc, unvacc) Ψ=efficacy S=proportion vaccinated βj=rate of infection ξj=duration
99 Increasing secondary infections The number of secondary infections will increase if Rp > R0 Thus (1 S)R 0 + SR V > R 0 V U > 1 V (1 ) 2 U. relative rate of infection R j =reproductive numbers (pop, vacc, unvacc) Ψ=efficacy S=proportion vaccinated βj=rate of infection ξj=duration vaccine efficacy
100 Increasing secondary infections The number of secondary infections will increase if Rp > R0 Thus (1 S)R 0 + SR V > R 0 V U > 1 V (1 ) 2 U. relative rate of infection R j =reproductive numbers (pop, vacc, unvacc) Ψ=efficacy S=proportion vaccinated βj=rate of infection ξj=duration vaccine efficacy relative duration of infection
101 relative rate of infection vaccine efficacy (%) Increase in secondary infections Decrease in secondary infections relative duration of infection 3 4
102 Decreasing rate and duration If the rate and duration of infection both decrease, the number of secondary infections will always decrease relative rate of infection vaccine efficacy (%) Increase in secondary infections Decrease in secondary infections relative duration of infection 3 4
103 Decreasing rate and duration If the rate and duration of infection both decrease, the number of secondary infections will always decrease relative rate of infection rate and duration both decrease vaccine efficacy (%) Increase in secondary infections Decrease in secondary infections relative duration of infection 3 4
104 Decreasing rate and duration If the rate and duration of infection both decrease, the number of secondary infections will always decrease (Not terribly surprising.) relative rate of infection rate and duration both decrease vaccine efficacy (%) Increase in secondary infections Decrease in secondary infections relative duration of infection 3 4
105 A duration shoulder For a given vaccine efficacy, there is a duration shoulder relative rate of infection vaccine efficacy (%) Increase in secondary infections Decrease in secondary infections relative duration of infection 3 4
106 A duration shoulder For a given vaccine efficacy, there is a duration shoulder relative rate of infection duration shoulder 50 vaccine efficacy (%) Increase in secondary infections Decrease in secondary infections relative duration of infection 3 4
107 A duration shoulder For a given vaccine efficacy, there is a duration shoulder A small increase in the duration of infection will still decrease the number of secondary infections relative rate of infection duration shoulder 50 vaccine efficacy (%) Increase in secondary infections Decrease in secondary infections relative duration of infection 3 4
108 A duration shoulder For a given vaccine efficacy, there is a duration shoulder A small increase in the duration of infection will still decrease the number of secondary infections This is true even if the rate of infection is unchanged. relative rate of infection duration shoulder 50 vaccine efficacy (%) Increase in secondary infections Decrease in secondary infections relative duration of infection 3 4
109 Beyond the shoulder If the duration of infection is significantly increased, then it is crucial that the rate of infection be decreased accordingly relative rate of infection vaccine efficacy (%) Increase in secondary infections Decrease in secondary infections relative duration of infection 3 4
110 Beyond the shoulder If the duration of infection is significantly increased, then it is crucial that the rate of infection be decreased accordingly relative rate of infection beyond the shoulder 50 vaccine efficacy (%) Increase in secondary infections Decrease in secondary infections relative duration of infection 3 4
111 Beyond the shoulder If the duration of infection is significantly increased, then it is crucial that the rate of infection be decreased accordingly Thus is crucial for low-efficacy vaccines. relative rate of infection beyond the shoulder 50 vaccine efficacy (%) Increase in secondary infections Decrease in secondary infections relative duration of infection 3 4
112 An example A 20% efficacious vaccine could accomodate an increase in the duration of infection by as much as 1.56 times thhe current duration of infection relative rate of infection vaccine efficacy (%) Increase in secondary infections Decrease in secondary infections relative duration of infection 3 4
113 An example A 20% efficacious vaccine could accomodate an increase in the duration of infection by as much as 1.56 times thhe current duration of infection Even if there is no 1 reduction in the rate of infection, the net result will still be a 60 decrease in secondary infections relative rate of infection vaccine efficacy (%) 1 2 Increase in secondary infections Decrease in secondary infections relative duration of infection 3 4
114 Reducing the infection rate However, a 20% efficacious vaccine that increased the duration of infection by a factor of 4 would lead to an increase in secondary infections... relative rate of infection vaccine efficacy (%) Increase in secondary infections Decrease in secondary infections relative duration of infection 3 4
115 Reducing the infection rate However, a 20% efficacious vaccine that increased the duration of infection by a factor of 4 would lead to an increase in secondary infections......unless the rate of infection for the vaccinated population were reduced to 40% of the current rate of infection. relative rate of infection vaccine efficacy (%) Increase in secondary infections Decrease in secondary infections relative duration of infection 3 4
116 Conclusions An imperfect malaria vaccine can eradicate the disease, if the coverage levels are sufficiently high
117 Conclusions An imperfect malaria vaccine can eradicate the disease, if the coverage levels are sufficiently high Duration of infection decreases secondary infections always decrease
118 Conclusions An imperfect malaria vaccine can eradicate the disease, if the coverage levels are sufficiently high Duration of infection decreases secondary infections always decrease Small increases in the duration of infection can be tolerated, but larger increases must be accompanied by a reduction in the rate of infection
119 Conclusions An imperfect malaria vaccine can eradicate the disease, if the coverage levels are sufficiently high Duration of infection decreases secondary infections always decrease Small increases in the duration of infection can be tolerated, but larger increases must be accompanied by a reduction in the rate of infection This is critical for low-efficacy vaccines.
120 A further consequence These results primarily apply to areas where malaria is endemic
121 A further consequence These results primarily apply to areas where malaria is endemic A disease-modifying malaria vaccine with a high duration of infection...
122 A further consequence These results primarily apply to areas where malaria is endemic A disease-modifying malaria vaccine with a high duration of infection... (for example, one which reduced mortality, but had no effect on the recovery rates)
123 A further consequence These results primarily apply to areas where malaria is endemic A disease-modifying malaria vaccine with a high duration of infection... (for example, one which reduced mortality, but had no effect on the recovery rates)...might be quite desirable for the developed world, if the prospect of reinfection is negligible.
124 Recommendation Low-efficacy vaccines that result in high durations of infection must significantly lower the rate of infection if they are to be used in endemic areas.
125 Key reference R.J. Smith?, Could low-efficacy malaria vaccines increase secondary infections in endemic areas? (Mathematical Modeling of Biological Systems, Volume II (2007). A. Deutsch, R. Bravo de la Parra, R. de Boer, O. Diekmann, P. Jagers, E. Kisdi, M. Kretzschmar, P. Lansky and H. Metz (eds). Birkhäuser, Boston, 3-10)
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