presentation for the ECMTB2022_Slides.pdf

lqs

1. Wolbachiainvasion in wild mosquito populations:
a modeling framework apt for dierent strains
Olga Vasilieva
1
, Jose L. Orozco-Gonzales
1
, Claudia P. Ferreira
2
,
Daiver Cardona-Salgado
3
, Lilian S. Sepulveda-Salcedo
3
,
1
Universidad del Valle, Cali { COLOMBIA
2
UNESP, Botucatu { BRAZIL
3
Universidad Autonoma de Occidente, Cali { COLOMBIA
The 12th European Conference on Mathematical and Theoretical Biology
ECMTB 2022
September 19-23, 2022 { Heidelberg, GERMANY
Olga Vasilieva (Univ. del Valle { Colombia) Wolbachiamodeling framework 1 / 17

2. Aedes aegyptimosquitoes and dengue infections6 NOVEMBER 2015 • VOL 350 ISSUE 6261 627SCIENCE sciencemag.org
MAP: ADAPTED FROM WORLD HEALTH ORGANIZATION BY P. HUEY/ SCIENCE
control remains elusive (5 ), underscoring the
need for a dengue vaccine.
Seven decades of dengue vaccine research
have shown how challenging it is to develop
a highly efficacious vaccine that protects
against all four serotypes (6 ). But now, the
first dengue vaccine is about to be licensed.
The vaccine developed by Sanofi Pasteur
(CYD-TDV) uses an infectious clone of the
live attenuated yellow fever 17D vaccine virus
to construct four chimeric viruses, each one
engineered to express the surface envelope
and premembrane proteins from one of the
four dengue serotypes (7 ).
Efficacy results for the CYD-TDV vaccine
come from two phase 3 trials in ~30,000
children aged 2 to 16 years, conducted in 10
highly endemic countries in Asia and Latin
America (8, 9 ). The pooled data from these
two trials showed an overall efficacy of 60%
against virologically confirmed dengue of
any severity due to any of the four serotypes
(10). However, efficacy differed by serotype,
was higher in individuals with prior dengue
infections, and increased with age. Among
children aged 9 years and older, efficacy was
higher (66%) than in younger children (45%).
Efficacy against severe dengue and hospi-
talization was substantial (93% and 81%, re-
spectively) in children aged 9 years or older,
compared with 45% and 56% in children
younger than 9 years.
The efficacy results are complex, and
the efficacy is modest; and elucidating the
reasons for this complexity is warranted.
Nonetheless, the efficacy results for severe
disease and hospitalizations look promising,
especially in older children. Reducing hospi-
talizations would be a major public health
victory in dengue control. Furthermore, re-
ducing overall infections may have a public
health impact beyond efficacy by reducing
virus circulation, thereby decreasing epi-
demic transmission.
Whether other dengue vaccine candidates
in the pipeline (including inactivated, live
attenuated, chimeric recombinant, subunit,
and DNA vaccines) (11) will have higher over-
all efficacy remains to be shown. For the mo-
ment, CYD-TDV is the only dengue vaccine
available. The moderate efficacy observed
underscores the need to integrate dengue
vaccination with improved vector control if
there is to be hope of controlling this disease.
This would have the added benefit of helping
to control otherAedes-transmitted diseases
such as chikungunya, zika, and yellow fever.
Of key importance is that a dengue vaccine
must be safe (12). Long-term safety data are
available from the third year of the phase 3
trials and from the third and fourth years of
a phase 2b long-term follow-up study of CYD-
TDV conducted in Thailand (10). Among
children aged 9 to 16 years, dengue hospi-
talizations were reduced for up to 3 years
after completion of the three-dose vaccine
regimen (10). However, the pooled relative
risk of dengue hospitalization in the younger
vaccinated group was 1.58 during the third
year, suggesting a trend to increased risk in
vaccinees that was not observed in the fourth
year (10). Further long-term follow-up of the
phase 3 study participants is ongoing. For the
time being, the transient reversed risk/ben-
efit ratio observed in the third year in young
children excludes this vaccine from being
used in children under the age of 9 years.
Because of the higher efficacy and the ab-
sence of safety concerns in older children, the
age group that would most benefit from the
use of this vaccine is hence individuals aged
9 years and older. Indeed, Sanofi Pasteur now
seeks licensure for CYD-TDV with an indica-
tion for persons in this age group.
The first dengue vaccine does not have the
hoped-for high and balanced efficacy over
all age groups. The quest to overcome these
shortcomings through different vaccine de-
velopment approaches has intensified. But
in the meantime, the question is, can we use
this vaccine, and if so, how? The answer will
depend on a broader perspective in evalu-
ating vaccines. Because the ultimate goal of
vaccination goes beyond efficacy, we need to
consider the capacity of a vaccination pro-
gram to reduce hospitalizations, thus mini-
mizing the pressure on health systems and
reducing health inequities. The burden and
age distribution of the disease in individual
countries will determine the impact of such
a program.
Thus, from a public health perspective,
available vaccines with demonstrated safety
even with only moderate efficacy should be
used to help control the ever-growing prob-
lem of dengue in countries where dengue
poses a major disease burden. In doing so, we
should adopt a “learn by doing” approach.
Post-licensure surveillance and research
will enhance understanding of vaccine ef-
fectiveness at the population level, quantify
the reduction in vaccine-preventable disease
incidence, assess long-term safety, aid in de-
termining the best timing for booster doses,
and measure the indirect effect of the vac-
cine. Integration with other strategies, in-
cluding improved clinical case management
and effective approaches to vector control,
will ensure a more substantial public health
impact in the long run. Lessons learned from
an integrated dengue vaccine introduction
will also pave the way for other vaccines that
only offer partial efficacy. ■
REFERENCES
1. S. Bhatt et al ., Nature 496, 504 (2013).
2. S. Yacoub, B. Wills, BMC Med. 12, 147 (2014).
3. S. B. Halstead, Science 239, 476 (1988).
4. C. P. Simmons, J. J. Farrar, N. van Vinh Chau, B. Wills, N.
Engl. J. Med. 366, 1423 (2012).
5. A. Wilder-Smith, D. J. Gubler, Med. Clin. North Am. 92, 1377
(2008).
6. S. J. Thomas, A. L. Rothman, Vaccine 10.1016/
j.vaccine.2015.05.095 (2015).
7. B. Guy, M. Saville, J. Lang, Hum. Vaccin. 6, 696 (2010).
8. M. R. Capeding et al ., Lancet 384, 1358 (2014).
9. L. Villar et al., N. Engl. J. Med. 372, 113 (2015).
10. S. R. Hadinegoro et al., N. Engl. J. Med. 373, 1195 (2015).
11. S. J. Thomas, T. P. Endy, Curr. Opin. Infect. Dis. 26, 429
(2013).
12. S. J. Thomas, N. Engl. J. Med. 372, 172 (2015).
13. http://apps.who.int/ithmap/
10.1126/science.aab4047
Aedes mosquito
Geographic distribution of Aedes
Countries that report dengue to WHO
Global dengue. More than 90 countries have reported cases of dengue to the World Health Organization in recent
years. The wide geographical distribution of the Aedes aegypti , the principal mosquito vector of dengue viruses
highlights the potential for further spread. [Map adapted from (13 )]
1
Lee Kong Chian School of Medicine, Nanyang Technological
University, Singapore.
2
Emerging Infectious Diseases Program,
Duke-NUS Graduate Medical School, Singapore.
E-mail: [email protected]
DA_1106Perspectives.indd 627 11/3/15 7:25 PM
Published byAAAS
IAe. aegyptifemales are transmitters of DENV
and other arboviruses
(they bite people)
IAe. aegyptimales do not transmit
arboviruses
(they do not bite people)
NO MOSQUITO = NO DENGUE
Image source:Wilder-Smith & Gubler, 2015, DOI: 10.1126/science.aab4047 Image source: https://www.peststrategies.com/
Olga Vasilieva (Univ. del Valle { Colombia) Wolbachiamodeling framework 2 / 17

3. What isWolbachia?
IWolbachiais a symbiotic bacterium naturally found
in up to 60-70% of insect species.
IWolbachiaisnotfound inAe. aegyptimosquitoes.
IWolbachiais transmitted maternally
(female99Keggs)
IWolbachiainducescytoplasmic incompatibility (CI-
phenotype)
I




Wolbachiasuppresses replication of dierent
viruses insideAe. aegyptifemales.
Image sources:Rosset al., 2020; DOI: 10.1002/ece3.6012 & https://www.nea.gov.sg/
Olga Vasilieva (Univ. del Valle { Colombia) Wolbachiamodeling framework 3 / 17

4. Major Wolbachia strains for the prevention ofAedes-borne diseases
Wolbachia strains
Key features
wMelPop wMel wAu
Virus inhibition or blockage (VI) High Medium High
Fitness cost (FC) High Low Low
Imperfect maternal transmission (IMT) High High High
Cytoplasmic incompatibility (CI) High High None
Wolbachia infection retention under thermal stress (WIR) Low Low High


Sources:Ant et al. [2018]; Homann et al. [2015]; Ogunlade et al. [2021]
TRADEOFF
=)
Olga Vasilieva (Univ. del Valle { Colombia) Wolbachiamodeling framework 4 / 17

5. Eect of high temperatures
Imperfect maternal transmission and cytoplasmic incompatibility
Wild population: females (~) and males (|)
Wolbachia-carrying population: females (~) and males (|)
Olga Vasilieva (Univ. del Valle { Colombia) Wolbachiamodeling framework 5 / 17

6. Extension of the model attributed to Escobar-Lasso and Vasilieva [2021]
Total mosquito
populationP(t)
8
>
>
>
>
>
>
>
<
>
>
>
>
>
>
>
:
Wolbachia-free
Pn(t)
8
<
:
MalesMn(t)
FemalesFn(t)
Wolbachia-carriers
Pw(t)
8
<
:
MalesMw(t)
FemalesFw(t)
Key assumptions for simplication
IWild andWolbachia-carrying mosquitoes exhibit (11) adult sex ratio [Axford et al.,
2016].
IWild andWolbachia-carrying male mosquitoes are equally capable to mate [Segoli et al.,
2014; Turley et al., 2013].
IWild female and male mosquitoes are often evenly distributed and have a similar lifespan
[Styer et al., 2007].
ILet us also suppose thatWolbachia-carrying males and females bear similar longevity.
Under these assumptions and in the line of other studies [Escobar-Lasso and Vasilieva, 2021;
Ferreira, 2020], we can then assume that
X(t) :=Mn(t) =Fn(t) andY(t) :=Mw(t) =Fw(t)8t0
Olga Vasilieva (Univ. del Valle { Colombia) Wolbachiamodeling framework 6 / 17

7. The modeling framework
8
>
>
>
<
>
>
>
:
dX
dt
=

nX
X+)Y
X+Y
+w(1)Y

e
(X+Y)
+!YnXJwild mosquitoes
dY
dt
=wY e
(X+Y)
!YwYJWolbachia-carriers
Parameters of the model:
nw{ average fecundity rate ofX;Y
nw{ death rates ofX;Y
>0 { competition parameter
2(0;1]
2[0;1] Wolbachiainfection;
!0 Wolbachiainfection due to thermal stress.
NOTE:w; wand; ; !are strain-dependent.
Olga Vasilieva (Univ. del Valle { Colombia) Wolbachiamodeling framework 7 / 17

8. Basic ospring numbers and possible equilibria
Qx:=
n
n
No. of
Qy:=
w
!+w
No. ofWolbachia-carriers Wolbachia-carrier
Qy;x:=
(1)w+!Qy
n
No. of Wolbachia-carrier
Equilibria of no interest
IExtinction equilibriumE0= (0;0) always exists; it is GAS ifQx1 andQy1;and
is repulsive otherwise.
IFully non-infected equilibriumEx=

X
]
;0

is a boundary equilibrium with
X
]
=
1

lnQx
that exists ifQx>1. It is LAS ifQy>1 and is GAS ifQy1.
Olga Vasilieva (Univ. del Valle { Colombia) Wolbachiamodeling framework 8 / 17

9. Coexistence equilibria
WhenQx>Qy>1, two coexistence equilibria arise under this condition:
Qc:=
Qy;x+Qy+Qx
Qx
>1
IUnstable coexistenceEu=

Xu;Yu

Xu=
lnQy
2
"

Qc1

+
r

Qc1

2
4
Qy;x
Qx
#
; Yu=
1

lnQyXu
IStable coexistenceEs=

Xs;Ys

Xs=
lnQy
2
"

Qc1


r

Qc1

2
4
Qy;x
Qx
#
; Ys=
1

lnQyXs
NOTE:stable coexistenceEs=

Xs;Ys

becomes aboundary equilibrium(Xs7!0) if
= 1 and!= 0 that is, whenQy;x= 0:
Olga Vasilieva (Univ. del Valle { Colombia) Wolbachiamodeling framework 9 / 17

10. wMel Wolbachiastrain: dynamics
Ideal case: 2 boundary LAS equilibria Stable coexistence (bistability)0 X
#
X
u X
0
Y
#
=Y
s
Y
u
Y 0 X
#
X
s X
u X
0
Y
s
Y
u
Y
= 1; = 1; != 0 = 0:95; = 0:98; != 0:1%
Unstable coexistence Wolbachia extinction0 X
#
X
s=X
u X
0
Y
s=Y
u
Y 0 X
#
X
0
Y
= 0:95; = 0:98; != 0:61% = 0:95; = 0:98; != 1%
Olga Vasilieva (Univ. del Valle { Colombia) Wolbachiamodeling framework 10 / 17

11. wMelPop Wolbachiastrain: dynamics
Ideal case: 2 boundary LAS equilibria Stable coexistence (bistability)0 X
#
X
u X
0
Y
#
=Y
s
Y
u
Y X
#
X
sX
u X
0
Y
s
Y
u
Y
= 1; = 1; != 0 = 0:99; = 0:95; != 0:015%
Unstable coexistence Wolbachia extinctionX
#
X
s=X
u X
0
Y
s=Y
u
Y 0 X
#
X
0
Y
= 0:99; = 0:95; != 0:083% = 0:99; = 0:95; != 0:5%
Olga Vasilieva (Univ. del Valle { Colombia) Wolbachiamodeling framework 11 / 17

12. wAu Wolbachiastrain: dynamics
Key feature ofwAustrain
This strain DOES NOT induce cytoplasmic incompatibility inAe. aegyptimosquitoes,
that is,
= 0
NO infection loss0 X
#
X
0
Y
= 1; = 0; != 0
NoWolbachiainvasion
NOTE:image source: https://es.dreamstime.com/
Olga Vasilieva (Univ. del Valle { Colombia) Wolbachiamodeling framework 12 / 17

13. SUMMARY: existence of the non-trivial equilibria
Maternal
transmission
(MT)
Infection
loss due to
thermal
stress
Cytoplasmic
incompatibility
(CI)
Existence of non-trivial equilibria

Wolbachia-free
(&#3627408511;
#
,??????)
Fully infected
(??????,&#3627408512;
#
)
Stable
coexistence
(&#3627408511;
??????,&#3627408512;
??????)

Unstable
coexistence
(&#3627408511;
??????,&#3627408512;
??????)

??????=1
(perfect)
??????=0
(absent)
??????=1
(perfect)




0<??????<1
(imperfect)
??????=0
(absent)



??????>0
(present)
??????=1
(perfect)
0<??????<1
(imperfect)
??????=0
(absent)
0<??????<1
(imperfect)
??????=0
(absent)
??????=1
(perfect)
0<??????<1
(imperfect)
??????=0
(absent)
??????>0
(present)
??????=1
(perfect)
0<??????<1
(imperfect)
??????=0
(absent)

Olga Vasilieva (Univ. del Valle { Colombia) Wolbachiamodeling framework 13 / 17

14. Conclusions
IThe proposed 2-dim modelretains the key propertiesof higher-
dimensional models ofWolbachiainvasion.
IThe proposed 2-dim systemhas rich dynamics and exhibits
numerous bifurcationsw.r.t. parameters(maternal trans-
mission),(cytoplasmic incompatibility), and!(infection loss
due to thermal stress).
IThe proposed 2-dim model allows to visualizeits phase portrait
for further identication of theattraction basinsof possible LAS
equilibria (bistability).
IThe proposed 2-dim model isapplicable to dierent Wol-
bachia strains(wMel,wMelPop, andwAu) that are currently
tested forWolbachia-based biocontrol ofAedes-borne diseases.
Olga Vasilieva (Univ. del Valle { Colombia) Wolbachiamodeling framework 14 / 17

15. Acknowledgements
INational Fund for Science, Technology, and Innovation (Autonomous
Heritage FundFrancisco Jose de Caldas), Project CI-71289 (Universidad
del Valle and Universidad Autonoma de Occidente, Cali, Colombia),
Contract No.: 80740-224-2021 issued by the Colombian Ministry of
Science, Technology, and Innovation (Minciencias)
IFundac~ao de Amparo a Pesquisa do Estado de S~ao Paulo | FAPESP,
Project No. 2020/10964-0 (Universidade Estadual Paulista { UNESP,
Botucatu SP, Brazil).
ISMB Landahl Travel Grant & ICETEXExpertos Internacionales
(Colombia)




























Olga Vasilieva (Univ. del Valle { Colombia) Wolbachiamodeling framework 15 / 17

16. References
T. Ant, C. Herd, V. Geoghegan, A. Homann, and S. Sinkins. TheWolbachiastrainwAu
provides highly ecient virus transmission blocking inAedes aegypti.PLoS Pathogens, 14(1):
e1006815, 2018.
J. Axford, P. Ross, H. Yeap, A. Callahan, and A. Homann. Fitness ofwAlbB Wolbachia
infection inAedes aegypti: parameter estimates in an outcrossed background and potential for
population invasion.The American Journal of Tropical Medicine and Hygiene, 94(3):507{516,
2016.
O. Escobar-Lasso and O. Vasilieva. A simplied monotone model ofWolbachiainvasion
encompassingAedes aegyptimosquitoes.Studies in Applied Mathematics, 146(3):565{585,
2021.
C. Ferreira.Aedes aegyptiandWolbachiainteraction: population persistence in an environment
changing.Theoretical Ecology, 13(2):137{148, 2020.
A. Homann, P.A Ross, and G. Rasic.Wolbachiastrains for disease control: ecological and
evolutionary considerations.Evolutionary applications, 8(8):751{768, 2015.
S. Ogunlade, M. Meehan, A. Adekunle, D. Rojas, O. Adegboye, and E. McBryde. A review:
Aedes-borne arboviral infections, controls andWolbachia-based strategies.Vaccines, 9(1):32,
2021.
M. Segoli, A. Homann, J. Lloyd, G. Omodei, and S. Ritchie. The eect of virus-blocking
Wolbachiaon male competitiveness of the dengue vector mosquito,Aedes aegypti.PLoS
neglected tropical diseases, 8(12):e3294, 2014.
L. Styer, S. Minnick, A. Sun, and T. Scott. Mortality and reproductive dynamics ofAedes aegypti
(Diptera: Culicidae) fed human blood.Vector-borne and zoonotic diseases, 7(1):86{98, 2007.
A. Turley, M. Zalucki, S. O'Neill, and E. McGraw. TransinfectedWolbachiahave minimal eects
on male reproductive success inAedes aegypti.Parasites & vectors, 6(1):1{10, 2013.
Olga Vasilieva (Univ. del Valle { Colombia) Wolbachiamodeling framework 16 / 17

17. Olga Vasilieva (Univ. del Valle { Colombia) Wolbachiamodeling framework 17 / 17