Implication of vaccination against dengue for zika outbreak

ABSTRACT Zika virus co-circulates with dengue in tropical and sub-tropical regions. Cases of co-infection by dengue and Zika have been reported, the implication of this co-infection for an

integrated intervention program for controlling both dengue and Zika must be addressed urgently. Here, we formulate a mathematical model to describe the transmission dynamics of co-infection

of dengue and Zika with particular focus on the effects of Zika outbreak by vaccination against dengue among human hosts. Our analysis determines specific conditions under which vaccination

against dengue can significantly increase the Zika outbreak peak, and speed up the Zika outbreak peak timing. Our results call for further study about the co-infection to direct an

integrated control to balance the benefits for dengue control and the damages of Zika outbreak. SIMILAR CONTENT BEING VIEWED BY OTHERS SHIFTING PATTERNS OF DENGUE THREE YEARS AFTER ZIKA

VIRUS EMERGENCE IN BRAZIL Article Open access 20 January 2024 INTERACTIONS BETWEEN TIMING AND TRANSMISSIBILITY EXPLAIN DIVERSE FLAVIVIRUS DYNAMICS IN FIJI Article Open access 15 March 2021

INTER-PROVINCIAL DISPARITY OF COVID-19 TRANSMISSION AND CONTROL IN NEPAL Article Open access 25 June 2021 INTRODUCTION Dengue and Zika are both vector-borne diseases in tropical and

sub-tropical regions with a common vector, dengue and Zika both belong to the family Flaviviridae and genus Flavivirus. Dengue is a prevalent disease being transmitted by the bite of a

mosquito infected with one of the four serotypes1,2 while Zika is an emerging disease. Zika virus was first isolated in Uganda in 19473, and there was an outbreak of Zika in Yap, Federated

States of Micronesia4 in 2007, and in French Polynesia5 till 2013. By the end of January 2016, autochthonous circulation of Zika was reported in more than 20 countries or territories in

South, Central, and North America and the Caribbean6,7,8,9,10,11,12, leading to the declaration of WHO that Zika virus is a global public health emergency13. Recent clinical and experimental

evidences support immunological cross-reactivity between dengue and Zika14,15,16,17. In particular, these evidences show that plasma to dengue was able to drive antibody-dependent

enhancement of Zika infection. Co-circulation of multiple serotypes of dengue and dengue-Zika co-circulation have previously been reported in refs 18, 19, 20. In particular, co-infection of

dengue and Zika were observed in two patients during the Zika outbreak in New Caledonia in 201418, and in two patients during the Zika outbreak in Tuparetama of Brazil in 201519. The

co-circulation could be a potentially series public concern given that more than a third of the world’s population lives in countries where dengue is endemic21, with the dengue belt covering

Central America, most of South America, sub-Saharan Africa, India, and South East Asia. Relevant to this co-infection is the development of vaccine products against dengue by _Sanofi

Pasteur_, and the clinical trials by Butantan and Takeda. Thus, it is an important urgent issue for public health decision makers to know how dengue immunization program impacts Zika

transmission when co-circulation becomes wide spread. Specially, under which conditions implemented dengue immunization control programs may boost the outbreak of Zika is no longer a

thought-provoking issue. Developing a framework to address this issue through a mathematical model is the main objective of this study. Much progress has been made for modelling dengue

infection dynamics including the role of cross-reactive antibodies for the four different dengue serotypes as discussed in the review paper22. The dengue transmission dynamics becomes very

complex because of the co-circulating serotypes in many endemic areas, and the absence of long-term cross-immunity23,24,25,26. In 1997, Feng _et al_.27 proposed a two-stain model with the

vector population being subdivided into a susceptible class and two serotype-specific infectious classes and the host populations being described by the SIR-type model for each serotype.

Esteva and Vargas28 considered a further model by including an explicit state for individuals who recovered from primary infections. Nuraini _et al_.29 and Sriprom _et al_.30 extended

Esteva’s model by accounting for two separate symptomatic and asymptomatic compartments for secondary infections. A four-serotype model was considered in these papers31,32,33. Different from

these previous studies, recently developed mathematical models have emphasized the evaluation of the impact of co-circulation of the four serotypes mainly among hosts34,35,36,37,38,39,40.

In contrast to dengue, the epidemiology of Zika among humans remains poorly understood, despite some recent outbreaks of modelling activities41,42,43,44. We should mention that mathematical

models of co-infection of two infectious diseases among humans have been developed in many different settings45, including co-infection of HIV with TB46,47,48,49,50,51, HCV52,53, two strains

of HIV54, HDV and HBV55, multi-strains of influenza56,57. To our best knowledge, our work here is the first attempt to develop a mathematical model to address the co-infection of dengue and

Zika and its implication to Zika prevalence. Our purpose here is to propose a mathematical model of co-infection of dengue and Zika with particular focus on the potential impact and

implication for Zika outbreak of vaccination against dengue in humans. PRELIMINARIES We stratify the total human population, _N__h_(_t_), into: _S_(_t_): the number of humans susceptible to

both dengue and Zika at time _t_; _I__d_(_a, t_): the number of dengue-infected humans with infection age _a_ at time _t_, who can also be infected by Zika virus and move to _I__dz_(_a, b,

t_); _I__z_(_b, t_): the number of Zika-infected humans with infection age _b_ at time _t_, who can also be infected by dengue and move to _I__dz_(_a, b, t_); _I__dz_(_a, b, t_): the number

of dengue and Zika-infected humans with dengue infection age _a_ and Zika infection age _b_ at time _t_; _R__d_(_t_): the number of humans recovered from dengue at time _t_, who can also be

infected by Zika and move to ; _R__z_(_t_): the number of humans recovered from Zika at time _t_, who can also be infected by dengue and move to ; : the number of Zika-infected humans with

Zika-infection age _b_, at time _t_, who are immune to dengue; : the number of dengue-infected humans with dengue-infection age _a_, at time _t_, who are immune to Zika; _R__dz_(_t_): the

number of humans recovered from dengue and Zika at time _t_, who can neither be infected by dengue nor Zika. Mosquito population _N__m_ is divided into _S__m_, _I__md_, _I__mz_, _I__mdz_,

representing the density of mosquitos who are susceptible, infected with dengue only, infected with Zika only, infected with both dengue and Zika. The transmission diagram of co-infection of

dengue and Zika among humans and mosquitos is shown in Fig. 1. We start with an intuitive view about the effects of vaccination against dengue among humans on the outbreak of Zika through a

very simple static transmission model illustrated in Fig. 2. Here the susceptible humans (_S_) can be infected with Zika virus via three different routes, namely Let the initial number of

susceptible humans (_S_) be _S_0. If we do not inoculate against dengue, then the final average number of humans infected with Zika virus through the above three routes (i.e. _I__z_,

_I__dz_, ) can be calculated as Therefore, the total number of humans infected with Zika virus should be Now we assume that the coverage rate of dengue vaccine is _P__c_ and the efficacy

rate of dengue vaccine is _P_0. Then the effective coverage rate of dengue vaccine is _P__v_ = _P_0_P__c_. The portion of susceptible humans successfully inoculated with dengue vaccine will

directly transfer to the compartment _R__d_. Therefore, the final average numbers of _I__z_, _I__dz_ and become Then, the total number of humans infected with Zika virus after vaccination

against dengue should be Comparing equation (2) with equation (4), we can see that with the implementation of vaccination of dengue the final numbers of _I__z_ and _I__dz_ decrease while the

final number of increases. To determine whether the total number of humans infected with Zika is increased or not, we let where is the ratio at which the part of the susceptible humans

inoculated with dengue vaccine are infected with Zika, is the total ratio at which the susceptible humans are infected with Zika through the above mentioned three routes described in (1). It

follows from equation (6) that if (i.e. , as shown in the red region of Fig. 3(A)), then the higher ratio the susceptible humans are inoculated with dengue vaccine, the more the total

number of humans are infected with Zika virus compared with the case without dengue vaccination, as shown in Fig. 3(B,C); if (i.e. , as shown in the green region of Fig. 3(A)), inoculating

dengue vaccine can decrease relatively the total number of humans infected with Zika virus, as shown in Fig. 3(B,D). This discussion, based on a static infection outcome analysis, suggests a

likely scenario that, under certain conditions, vaccination against dengue can significantly boost the outbreak of Zika. Our analysis below is to theoretically and numerically examine these

conditions with our proposed transmission dynamics model. MODEL FORMULATION We assume a SI-type model for dengue and Zika co-infection for the mosquito population. The model equations for

mosquitos give Here, Λ is the recruitment rate of mosquitos, and the definitions for other parameters are listed in Table 1. We assume SIR-type model for dengue and Zika co-infection in

human population and formulate the following age-structured model to describe the dynamics of co-infection of dengue and Zika among humans: Here _γ__d_(_a_) is the recover rate at which

individuals in the compartment _I__d_ with dengue-infection age _a_ recover to the class _R__d_, _γ__z_(_b_) denotes the recover rate at which individuals in the class _I__z_ with

Zika-infection age _b_ move to the compartment _R__z_, represents the recover rate at which individuals in the class with Zika-infection age _b_ recover to the compartment _R__dz_, and is

the recover rate at which individuals in the class with dengue-infection age _a_ move to compartment _I__dz_, _γ__dz_(_a, b_) denotes the recover rate at which individuals in the class

_I__dz_ with time-since-infection _a_ for dengue and time-since-infection _b_ for Zika recover to the compartment _R__dz_ directly, _γ__dz_(_a_) represents the recover rate at which

individuals in the class _I__dz_ transit to the compartment due to recovery of dengue, and _γ__dz_(_b_) is the recover rate at which individuals in the class _I__dz_ transit to the

compartment due to recovery of Zika. The definitions for other parameters independent of infection ages are given in Table 1. Here, the condition _I__dz_(0, 0, _t_) = 0 means that the

susceptible individuals can not be infected with dengue and Zika in the same time. We assume that and Define , i.e. the total number of humans who are infected with dengue at time _t_, and

can further be infected by Zika. Then, we have Further, if we assume that the recover rate _γ__d_(_a_) is independent of dengue-infection age _a_, that is, _γ__d_, we have . Then formula (9)

yields Similarly, if the recover rate _γ__z_(_b_) is independent of Zika-infection age _b_, the total number of humans infected with Zika, given by , reads With similar calculation, we can

get the derivative of the compartment _I__dz_(_t_) as follows: Also, when we assume that the recover rates _γ__dz_(_a, b_), _γ__dz_(_a_) and _γ__dz_(_b_) are all constants, denoted by and ,

respectively, then formula (12) gives Moreover, define the total number of humans who are immune to dengue but infected with Zika as and the total number of humans who are immune to Zika but

infected with dengue as . By assuming the recover rates and being independent of infection ages (i.e., and ), we easily obtain that and Based on the above assumptions and discussions, the

double age-structured model is reduced to the following ODE model: We call model (16) with model (7) as system _S_*. It follows from model (16) that the total number of humans _N__h_(_t_) is

a constant, denoted by _N__h_. Let and _I__md_ = _I__mz_ = _I__mdz_ = 0. Then we can show that system _S_* has a disease-free equilibrium, which gives Using the next generation matrix

introduced in papers58,59, we can calculate the basic reproduction number for system _S_*, denoted by _R_0 (see electronic supplementary information for details). This is the spectral radius

of the next generation matrix and given by Here, and are the basic reproduction numbers for the dengue-only model and Zika-only model, respectively. Consequently, when _R__z_ > 1 (_R__d_

 > 1), then there is an outbreak of Zika (dengue) while the number of Zika (dengue) infections will directly decrease to zero if _R__z_ < 1 (_R__d_ < 1). MAIN RESULTS In this

section, we carry out numerical simulations for the dynamic system _S_* in order to examine effect of dengue vaccination on the outbreak of Zika. In our simulations, we vary three parameters

_β__dz_, _β__rz_ and Λ, and fix all the other parameter values as follows: Let the initial values _IV_(0) for system _S_* be given by Let the effective coverage rate of vaccination against

dengue among humans be _P__v_. When inoculating dengue vaccine to humans at the outset of the outbreak of dengue and Zika, the initial conditions of model _S_* become as with while other

vector components remaining unchanged. We first simulate system _S_* by fixing the parameters _β__dz_ and _β__rz_ as 0.18 and 0.05, respectively. We examine the variation of with parameter Λ

with or without inoculating dengue vaccine, as shown in Fig. 4. As we can see, when the parameter Λ varies in the interval from 10000 to 1000000 vaccination against dengue can lead to two

opposite results for the outbreak of Zika. That is, when Λ is relatively low, the effect of dengue vaccine on the outbreak of Zika is not noticeable. However, if Λ increases to relatively

large, vaccination against dengue among humans will significantly boost the outbreak of Zika with a much higher outbreak peak compared with that without vaccination. The lower and upper

bounds of this parameter value are determined from intensive numerical simulations to clearly illustrate these two opposite scenarios. In particular, we plot solutions to system _S_* (shown

in Figs 5 and 6) with Λ being fixed as 10000 and 1000000 (the lower and higher boundary value of the interval of Λ chosen in Fig. 4), respectively. Figures 5(H) and 6(H) demonstrate these

two opposite situations: dengue vaccination results in the number of human infected with Zika either decline or increase. It follows from Figs 5 and 6 that vaccination against dengue among

humans will always reduce the number of humans infected with dengue (including the compartments _I__d_, , and _I__dz_), and hence leads to a reduction in the total number of humans infected

with dengue (i.e. ). However, vaccination against dengue may increase the number of individuals in the compartment . This explains the two opposite results about the effects of the dengue

vaccination on the Zika outbreak. Note that when Λ = 1000000, with which vaccination against dengue can significantly boost the Zika outbreak, we can calculate that _R__d_ = _R__z_ = 2.82,

within the range of basic reproduction numbers for dengue and Zika in the literatures42,60,61,62,63,64. Further, we examine the effects of the effective coverage rate _P__v_ on the outbreak

of Zika. Fix parameters _β__dz_ = 0.05, _β__rz_ = 0.18, Λ = 10000 and let the parameter _P__v_ vary, Fig. 7(A) shows that a higher effective coverage rate of vaccination can result in a much

higher peak of the outbreak of Zika. Moreover, if we choose Λ = 1000000, then we observe that with a higher rate of vaccination against dengue not only the peak of the outbreak of Zika can

be significantly increased, but also the Zika outbreak peak much earlier, as shown in Fig. 7(B). Considering the number of the accumulated Zika infections, we obtained two similar opposite

results. Figure 7(C) shows that with a higher rate of vaccination against dengue the number of accumulated Zika infections will increase significantly, while Fig. 7(D) illustrates that

vaccination against dengue may reduce the number of the accumulated Zika infections. In Fig. 7(D) we assumed that _β__rz_ = _β__z_ = 0.05 while in Fig. 7(C) we assumed that 0.18 = _β__rz_ 

> _β__z_ = 0.05 based on the emerging clinical evidence of enhancement14,15,16,17. Comparisons between these scenarios clearly indicate, under the conditions reflected by the parameter

values, that dengue vaccination may indeed lead to significant increase in Zika infections. CONCLUSION AND DISCUSSION There are increasing evidence of co-infection of dengue and Zika. Due to

similar transmission routes with the same host species, some intervention strategies such as vector control are effective for curbing both dengue and Zika. However, other interventions such

as vaccination against one virus may be harmful to the control of another, specially when enhancement occurs to favor the spread of the virus not covered with vaccine. Our study examined

the implication of this enhancement for Zika outbreaks when vaccination against dengue in humans is applied. We initially formulated a very simple static transmission model to give an

intuitive illustration that vaccination against dengue among humans may significantly boost Zika transmission among the population. In order to theoretically verify this illustration, we

then proposed a dynamic model to describe the dynamics of co-infection of dengue and Zika. More specifically, we developed a novel model with double age-structures for dengue and Zika,

extending the general age-structure model65,66,67 by incorporating compartments with specific dengue-infection and Zika-infection age. Under certain stage-specific homogenetical assumptions

about the virus dynamics characteristics, we simplified our double age-structured model to an ODE model, for which the basic reproduction number can be calculated. We also numerically

investigated the dynamics of model _S_* and obtained some observations which are in agreement with the conclusions from the analysis of our static transmission model in Section 2. Figure 4

shows that vaccination against dengue among humans may result in the total number of humans infected with Zika virus decline or increase, depending on the parameter Λ, the recruitment rate

of mosquitos. In particular, it significantly enlarges the peak of the outbreak of Zika when Λ is relatively large. It follows from Figs 5 and 6 that this enlarged outbreak of Zika by

vaccination against dengue is due to multiple factors. Vaccination against dengue can reduce the numbers of _I__z_ and _I__dz_ while it always increases the number of . Thus the balance of

increase in the number of and decrease in the number of _I__z_ and _I__dz_ determines whether the total number of infected with Zika increase or not. Further, we observed that a higher rate

of vaccination against dengue can also results in a higher and earlier peak of the outbreak of Zika, as shown in Fig. 7(A,B). Comparing Fig. 7(B) with Fig. 7(A), we observe that the

conclusion that vaccination against dengue can boost Zika outbreak remains true for a wide range of mosquito index values (when the recruitment rate of mosquito decreases from 1000000 to

10000). This conclusion is also shown in Fig. S2 (electronic supplementary information) when the mosquito mortality rate _μ__m_ varies. Comparison between Fig. 7(B) and Fig. 7(A) however

also shows that reducing the mosquito indices can significantly decrease the magnitude of Zika outbreak as the number of Zika cases at the peak time can be reduced substantially. Therefore,

given the simultaneous impact on both dengue and Zika outbreaks, vector control should be always implemented regardless of the availability of vaccine. Figure 7(C,D) further confirm that the

accumulated Zika infections may be greater for a greater rate of vaccination of dengue vaccine to human. Sensitive analyses show that parameters _β__z_, _β__dz_, Λ and _μ__m_ can

significantly affect the outbreak of Zika, in terms of both the accumulated Zika infections and the daily number of Zika infections (see electronic supplementary information for details).

Most existing studies on the multi-serotype models of vector-host transmission of dengue focus on the importance of subsequent infections with different dengue serotypes. It was assumed that

the patients can be subsequently infected by another serotypes after recovering from one serotype. In our consideration of dengue-Zika co-infection, we extended these models by adding a new

compartment of humans as well as mosquitos infected by both of Zika and dengue simultaneously. From our numerical analysis, the parameter _β__dz_ (i.e. the transmission rate of the

compartment of mosquitos infected with dengue and Zika to susceptible humans), which is related to the newly added compartment _I__mdz_, can have important influences on the dynamics of the

co-infection model. For the models of co-infection of HIV with TB and HCV, a SI-type model is usually assumed as the basic model for each disease. In comparison with these models, our model

with SIR-type for humans is different to handle the asymmetric vector-host interaction as discussed in ref. 27, and to allow recovered (or vaccinated) individuals from one virus to have

higher risk of infection by another. Our analysis indicates that with a big recruitment rate of mosquitos Λ vaccination against dengue among humans can significantly boost the Zika outbreak

(as shown in Fig. 6(H)), and cause the Zika outbreak peak coming early with a bigger mosquito to humans transmission rate _β__rz_ and lower _β__dz_ (as shown in Fig. 7(B)). It is important

to note that a safe, effective and affordable dengue vaccine against the four strains offers an important tool to reach the WHO goal of reducing dengue morbidity by at least 25% and

mortality by at least 50% by 202068. The first dengue vaccine, Dengvaxiar(CYD-TDV) (developed by _Sanofi Pasteur_), was licensed in Mexico in 201569; and two dengue vaccine candidates

(developed by Butantan and Takeda) entered the Phase III trails in early 201670,71,72. Our study should not serve as a discouragement to the development of these dengue vaccine products, but

rather we determine conditions under which dengue vaccination can contribute to the prevention and control of dengue without inducing significant increase in Zika infection. Most published

works focus on the benefits of the control strategies (such as treatments for only one or both diseases) to both diseases involved in the co-infection. For example, Derouich and Boutayeb73

considered a model of two subsequent infections of dengue at separate time intervals with continuous vaccination. They concluded that vaccination can be a control strategy for dengue.

However, with consideration of co-infection and the current development of dengue vaccine, our results suggest that additional study on co-infection is urgently and critically needed.

ADDITIONAL INFORMATION HOW TO CITE THIS ARTICLE: Tang, B. _et al_. Implication of vaccination against dengue for Zika outbreak. _Sci. Rep._ 6, 35623; doi: 10.1038/srep35623 (2016).

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computer simulation. Appl. Math. Comput. 177, 528–544 (2006). MathSciNet  MATH  Google Scholar  Download references ACKNOWLEDGEMENTS This project was supported by the National Natural

Science Foundation of China (NSFC, 11571273, 11631012(YX)), by the Fundamental Research Funds for the Central Universities (08143042 (YX)), by the Canada Research Chair Program, the Natural

Sciences and Engineering Research Council of Canada (JW), and the International Development Research Center (Ottawa, Canada, 104519-010). AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * School

of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049, P.R. China Biao Tang & Yanni Xiao * Centre for Disease Modelling, York Institute for Health Research,

York University, Toronto, M3J 1P3, ON, Canada Biao Tang & Jianhong Wu Authors * Biao Tang View author publications You can also search for this author inPubMed Google Scholar * Yanni

Xiao View author publications You can also search for this author inPubMed Google Scholar * Jianhong Wu View author publications You can also search for this author inPubMed Google Scholar

CONTRIBUTIONS B.T., Y.X. and J.W. designed the study and carried out the analysis. B.T. performed numerical simulations. B.T., Y.X. and J.W. contributed to writing the paper. ETHICS

DECLARATIONS COMPETING INTERESTS The authors declare no competing financial interests. ELECTRONIC SUPPLEMENTARY MATERIAL SUPPLEMENTARY INFORMATION RIGHTS AND PERMISSIONS This work is

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Implication of vaccination against dengue for Zika outbreak. _Sci Rep_ 6, 35623 (2016). https://doi.org/10.1038/srep35623 Download citation * Received: 11 July 2016 * Accepted: 04 October

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