Minimising severity of dengue serotype 1 infection by transmissible interfering particles

Transmissible interfering dengue particles (DENV–TIPs) are engineered dengue virus mutants which are defective and can replicate only with the help of dengue wild–type virus (DENV). In vitro studies have found that when DENV–TIPs and DENV coinfect a cell, they compete for viral genomes and cell proteins for replication and packaging, and DENV–TIPs outperform DENV in this process. Thus, it is hypothesised that DENV–TIPs may be used as a novel therapeutic agent. However, the effectiveness of DENV–TIPs as an antiviral agent is yet to be explored at an epidemiological scale. We present a mathematical model for the replication of DENV and DENV–TIPs as they interact with human host cells, accounting for the effectiveness of DENV–TIPs in blocking DENV from coinfected cells. We fit the model to sequentially measured plasma viral titre data from primary and secondary dengue serotype 1 infected patients in Vietnam. We show that variation in initial DENV load is sufficient to recreate the observed variation between patients. Parameter estimates, differing in primary and secondary infections, do not confirm a significant difference between these two types of infection. We use our model to investigate the potential impact of DENV–TIPs as an antiviral agent. We conclude that, when the effectiveness of DENV–TIPs in inhibiting DENV from coinfected cells is at least 80%, a dose as high as 1012 copies per millilitre of blood is required to reduce duration of infection and peak DENV serotype 1 infection level at any time point of infection. This work provides a quantitative understanding of the relationship between DENV–TIPs levels and their efficiency in clearing dengue viral infection. It will guide future development of mechanistic models of how DENV–TIPs might contribute as an antiviral agent in limiting natural dengue infection. Author summary Inhibition of dengue wild–type virus (DENV) by transmissible interfering dengue particles (DENV–TIPs) is seen in some in vitro studies, and it is hypothesised that DENV–TIPs may be used as a therapeutic agent. However, the efficiency of DENV–TIPs in limiting DENV infection in patients is yet to be explored at an epidemiological scale. Using data collected from dengue serotype 1 infected patients, we model how DENV replicates in an infected patient and how effective DENV–TIPs are in controlling that replication. Our results are of use in the evaluation of DENV–TIPs as a potential antiviral agent.

Dengue is a mosquito-borne viral disease in humans, with an estimated prevalence of 2 390 million per year, of which roughly 25% show clinical symptoms [1]. Approximately outperform WT-virus, producing DIPs mostly from the cell [18,19]. Inhibition of 48 WT-virus replication by DIPs is first identified more than 60 years ago with influenza 49 virus [20]. Since then, many in vitro studies have investigated the mechanism which 50 DIPs inhibit WT-virus replication [17,[21][22][23][24][25], and the potential for utilising DIPs as an 51 anti-viral agent [16,26,27]. 52 A recent study has found that infecting Aedes aegypti mosquitoes with blood sera 53 from DENV infected patients produced DIPs in mosquitoes which are identical to those 54 observed in patients, suggesting that DIPs may be transmitted between humans and 55 mosquitoes [28]. This study has also established that engineered DIPs (DENV-TIPs), 56 reduced the yield of DENV following coinfections of susceptible cells in vitro. These successful DENV transmission to mosquitoes [15], and that DENV-TIPs have the 62 potential to act as an anti-viral agent [28], it is important to investigate the dynamics of 63 DENV-TIPs and DENV as they interact with human hosts, and assess the effectiveness 64 of DENV-TIPS in shaping a patient's virus profile. Mathematical modelling of the DENV as they interact with human host cells, explicitly accounting for effectiveness of 75 DENV-TIPs in blocking DENV production from coinfected cells. We validate the 76 model using sequentially measured viral titre data from DENV1 infected patients, who 77 showed clinically apparent symptoms. The resulting parameter estimates guide the 78 determination of factors related to the variability observed in infection dynamics 79 between patients, but do not suggest a difference between primary and secondary 80 DENV1 infections. By using the estimated parameters we perform two simulation 81 studies to examine the potential impact of DENV-TIPs therapy. Our analyses allow us 82 to hypothesise a minimal DENV-TIPs dose required and an indication of how effective 83 DENV-TIPs must be in order to limit disease severity in DENV1 infected patients. 84 Materials and methods 85 The data 86 We use patient-level viral load data to validate the mathematical model. The data are 87 obtained from a previous experimental study on DENV transmission from humans to 88 mosquitoes [15]. The study in [15] concerns 208 adult dengue patients who visited the 89 Hospital for Tropical Diseases in Ho Chi Minh City, Vietnam. Patients were enrolled 90 within 72 hours of fever and experimentally exposed to field-derived Aedes aegypti 91 mosquitoes on 2 randomly chosen days during their first 4 days in the study. Virus 92 RNA in plasma was quantified by RT-PCR assay and each patient had once daily virus 93 measurement recorded for a maximum of 5 days. Measurements were recorded as copies 94 per millilitre (copies/ml) of plasma and patients were categorised according to their 95 infecting serotype (DENV1-4) and serology (primary, secondary). Serology of some 96 patients was not identified and thus marked as indeterminate. See [15] for details on 97 classifications of serotype and serology. The RT-PCR assay used had a limit of 98 detection (LOD) for each serotype, with 357 copies/ml as the LOD for both DENV1 99 and DENV3, 72 copies/ml for DENV2 and 720 copies/ml for DENV4. 100 We use data on DENV1 primary (n = 25) and secondary (n = 42) patients in our 101 analyses (Fig 1). There were 11 DENV1 cases whose serotype was indeterminate, so we 102 exclude these cases for model fitting. Plot of DENV1 profiles by fever day. Colours represent primary (red) and secondary (blue) profiles. Circles and triangles resemble measurements above and below LOD, respectively. Fever day 0 corresponds to the day of defervescence.
Mathematical model definition 104 Given that there are no experimental results determining how effective DENV-TIPs are 105 in shaping DENV dynamics of patients, we propose a novel within-host mathematical 106 model for the replication of DENV-TIPs and DENV as they interact with human host 107 cells, accounting for effectiveness of DENV-TIPs in blocking DENV production from The model is described by the following equations: An uninfected Susceptible cell is created at a constant rate, A, and can become 116 infected by a DENV or a DENV-TIP particle at rate β, via a mass action process,

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converting it to an I V or I T cell, respectively. An I B cell is created when a DENV-TIP 118 particle infects an I V cell or a DENV particle infects an I T cell at rate β, via a mass 119 action process, or a DENV particle mutates within an I V cell to produce a DENV-TIP 120 at rate µ. Parameters δ and γ represent death rates of an I V and I B cell, respectively. 121 A DENV or a DENV-TIP particle dies at rate κ. An I V type cell can produce only 122 DENV particles and the rate of this production is ω. An I T type cell does not produce 123 any particles. It is assumed that there is a one-to-one competition between DENV-TIPs 124 and DENV particles within an I B cell for viral proteins, and this competition may  naturally arising DIPs [28], and we assume the kinetic of DENV-TIPs within human 147 hosts will be the same as that of DIPs.

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Model (1) differs from the within-host dengue models analysed in [31,32,37], in 149 which the authors assumed that clearance of infected cells or free virus are mediated by 150 antibodies. Model (1) also differs from the models studied in [29,30], which examined 151 the roles of both innate and adaptive immunity play in clearing infected cells. None of 152 these models accommodated the dynamics of DENV-TIPs. As our focus is primarily on 153 examining the role which DENV-TIPs play in shaping DENV dynamic within patients, 154 we model neither innate nor adaptive immunity.

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Parameter estimation 156 Model (1) contains 9 parameters (A, β, δ, µ, γ, ω, κ, σ) and 6 initial conditions (S 0 , Table 1 provides the meaning of these parameters and initial 158 conditions, specifies whether they are estimated or assigned, and shows nominal values 159 used for parameters with reference where appropriate.

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The reason for assigning some parameters nominal values is because, in the absence of data on concentration of DENV-TIPs and the four types of cells considered in the model, not all parameters are identifiable. This is seen by performing an identifiablity analysis, similar to procedures outlined in [30,32]. SubstitutingŜ = S/A, initial population size of cells infected with only DENV (/ml) 0 I T0 initial population size of cells infected with only DENV-TIPs (/ml) 0 I B0 initial population size of coinfected cells (/ml) 0 V 0 initial inoculum of DENV (copies/ml) estimated T 0 initial inoculum of DENV-TIPs (copies/ml) 0 These equations reveal that parameters appearing in the sets Aβω(1 − σ) and Aβησ 161 cannot be uniquely identified. As measurements of DENV level for each patient are 162 available, β and initial DENV load (V 0 ) can be estimated independently. Therefore, we 163 fix parameters A, ω, σ and η at nominal values and estimate β, δ, µ, γ, κ and V 0 .

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Estimated parameters are fitted either common to all patients, specific to primary and 165 secondary groups, or specific to each patient. 166 We assign values for the rates of susceptible cell production (A), DENV production 167 (ω), and initial population size of susceptible cells (S 0 ) based on [31]. We assume that 168 patients' blood does not contain any infected cells or free DENV-TIPs, at the time they 169 April 15, 2020 9/42 become infected with free DENV. Hence, we set the initial population sizes of cells for these two parameters. We discuss the sensitivity of the assigned parameters to 175 DENV output, from the ODE, in the Results section.

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The only initial condition we fit in our statistical analysis is the initial amount of 177 free DENV (V 0 ), which we estimate as patient-specific. This is biologically intuitive, as 178 each patient may receive a different amount of DENV by infected mosquitoes when they 179 take blood meals from people and mosquitoes may be interrupted during feeding.

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Parameters β, δ, µ, γ, κ are fitted either common to all patients (table 2, model a) or 181 specific to primary and secondary groups (table 2, model b). Our goal in fitting these 182 two model variants is to determine which of these hypotheses best account for the 183 observed variation in viral load patterns in primary and secondary DENV1 infected 184 patients (Fig 1). Previous dengue studies allowed either the virus replication rate 185 (β) [29][30][31][32] or both β and the virus clearance rate (κ) [32] to vary by primary and 186 secondary infections, to test the ADE process. However, our aim in using model b is not 187 specifically to investigate the ADE process, but to test any potential biological 188 differences between primary and secondary infections which may be associated with 189 DENV-TIPs. β, δ, µ, γ, κ V 0 11608 (225.7) Common parameters are shared across all patients regardless of their group (primary or secondary). Also shown are the WAIC value for each model and its standard error.

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The DENV1 data are available as a function of time since the onset of symptoms.

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However, we intend to model DENV dynamic from the start of infection. To facilitate 192 this, it is required to estimate the incubation period (IP) or equivalently, the initial time 193 of infection. IP is defined as the time between DENV inoculation and the start of which we estimate. Thus, we do not aim to estimate the IP. Instead, following [30], we 196 use the estimate derived in [38] which used Bayesian time-to-event models to estimate 197 IP using observations from 35 dengue studies. This estimate is 5.9 days with 95% 198 confidence interval lying between 3 and 10 days. We add 6 days, which is the estimated 199 IP rounded to nearest whole number, prior to the first measurement of each patient.

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This amounts to starting infection randomly, for each patient. 201 We use a Bayesian approach for parameter estimation. Based on the dynamics of 202 virus profiles given in Fig 1 and following [30,32], we hypothesise that, for each patient, 203 the viremia measurements follow a log-normal distribution with mean given by the 204 logarithm of virus output from the ODE (1). The likelihood for the j-th patient is: In the likelihood, n j denotes the number of virus measurements for the j-th patient, 206 and v j (t k ) andv j (t k ) are the observed and modelled virus measurements, respectively, 207 for the j-th patient at time t k . We use a Gaussian probability density function, φ, to 208 calculate the probability of observing a virus measurement only if it lies above the LOD. 209 For measurements below the LOD, all we know is that they are at or below the LOD.

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Thus, we use the normal cumulative distribution function, Φ, to calculate the 211 probability of observing a data point at or below the LOD. The parameter quantifying 212 the standard deviation of the measurement error is σ e , which we estimate here. The full 213 log-likelihood is the sum of the log-likelihoods over all patients.

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In both models a and b, prior distributions for β, δ, µ, γ, κ are assumed to be 215 uniformly distributed with ranges chosen to include values which are previously 216 established and biologically plausible. The range set for δ, κ, γ, is from 1 to 10, which 217 includes the estimated value of 3.30 with credible interval of (3.07, 3.48) for δ and the 218 assigned value of 3.5 for κ in [31] for their virus neutralisation model. We expect the 219 value of γ to be close to but less than δ and thus seek an estimate of it within the same 220 range as δ. The range for β is from 2 × 10 −11 to 2 × 10 −10 , which includes the values of 221 3.83 × 10 −11 and 5 × 10 −11 assigned for primary and secondary infections, respectively, 222 in [31] for their virus neutralisation model. For µ, the range set is from 5 × 10 −5 to is assumed vague relative to the data and anticipated values, so is set to be normally distributed with mean 0 and standard deviation of 100. Similarly, the prior distribution 226 for σ e is assumed normally distributed with mean 1 and standard deviation of 2. across all patients within a group are compared.

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In order to assess how well the two model variants capture patient and group-level variations in virus dynamics, we use posterior predictive plots and the widely applicable information criterion (WAIC) measure [42]. The WAIC measure is commonly applied for estimating expected predictive accuracy from a fitted Bayesian model using the log-likelihood evaluated at the posterior simulations of the parameter values, and is asymptotically equivalent to leave-one-out cross validation [43]. Following the description in [43], we compute the WAIC measure using the log pointwise predictive density (lpd) and the estimated effective number of parameters (P ef f ) as: where J is the number of patients, S is the number of posterior samples, θ are the April 15, 2020 12/42 parameters, and v is the data [43]. The term (lpd − P ef f ) is the expected log pointwise predictive density (elpd). We estimate P ef f using the posterior variance of the log predictive density for each patient data, v j . That is, V S s = log(p(y j |θ s )), where V S s stands for the sample variance, which is given as V S s a s = S −1 S s (a s −ā) 2 . Finally, we sum over all patients to estimate the effective number of parameters. To assess the uncertainty of the WAIC estimate of prediction error, we compute its standard error using the individual components of elpd as: To compare the two fitted models, we estimate the difference in their predictive accuracy by the difference in elpd. The standard error of this difference is computed as: where elpd a and elpd b are the elpd measures of model a and model b, respectively. 240 We choose the WAIC measure over the deviance information criterion (DIC) because 241 the DIC has the limitation of relying on a point estimate rather than the full posterior 242 distribution. An alternative approach to compare the two models is to use the Bayes accurately and may be sensitive to prior specifications, so we avoid computing the BF. 246 For a detailed mathematical description of DIC and BF, we direct the interested reader 247 to [40].

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Effect of DENV-TIPs therapy 249 We use our ODE model (1)  if so, the smallest DENV-TIPs dose required for an effect.

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The effect of DENV-TIPs therapy is examined using two simulation studies. The starting from 100 copies/ml, increased by 2 fold on log10 scale until 10 12 copies/ml.

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In the second study, the patient is treated at two time points before DENV1 peaks 273  Table 1 for the assigned data. The value for µ is taken from the within-host dengue model studied in [35]. We 294 envisaged that the death rate of coinfected cells, γ, would be less than the death rate of 295 cells infected with only DENV1, δ, and so assigned for γ a value less than δ. With these 296 values, however, the computed DENV1 trajectory was substantially below the observed 297 DENV1 profiles (not shown). Thus, we fixed values for parameters A, σ and µ as

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Based on the the sensitivity plot of parameter A (Fig 2, subplot (b)), it appears that 306 DENV1 output is relatively insensitive to variability in parameter A (susceptible cell 307 production rate) between 100 and 1.4 × 10 6 (baseline value), but the peak starts to 308 occur earlier, with higher virus level at the peak for values above 1.4 × 10 6 . Moreover, 309 as A is increased, the DENV1 level stabilises at a constant value after the peak. (DENV-TIPs production rate from coinfected cells) (Fig 2, subplot (d)) and σ 316 (effectiveness of DENV-TIPs) (Fig 2, subplot (d)), supporting our option not to  Table 3. To assess potential differences between primary and secondary infections, we Parameters δ, γ, κ, β, µ are fitted common to all patients, and are summarised using posterior median and 95% credible interval in the curved parentheses. Initial viral load (V 0 ) is patient-specific and is summarised by taking the median of each posterior and the median of these medians is given with IQR in the squared parentheses.
compare parameter estimates for these two patient groups from model b (Table 4), 335 which allowed parameters δ, γ, κ, β, µ to vary between the two groups. These estimates 336 indicate that there may be some chance of the two types of infection coinciding due to a 337 large overlap in the 95% credible intervals across the group-specific parameters,  Parameters δ, γ, κ, β, µ are fitted as group-specific, V 0 is fitted as patient-specific. Parentheses have same meaning as given in Table 3. Measurement error, σ e is fitted common to all patients.
We examined the impact of DENV-TIPs therapy by implementing two simulation Our first simulation study concerns treatment of the patient on fever day −4, which is 348 assumed to be the day of symptoms onset as it falls around a time point of DENV1 349 peaks (Fig 5). Our second simulation study concerns treatment of the patient on two 350 selected days prior to symptoms onset (fever days −8 and −6, Fig 6 and Fig S3 Fig,   351 respectively) and two selected days post symptoms onset (fever days −2 and 0, Fig 7   352 and Fig S4 Fig, respectively). using the median summary of each estimated parameter from model a (Table 3), which 357 is favoured over model b, based on the elpd measures. We then administered

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The second simulation study shows that, when treatment is target prior to symptom 374 onset, a sharp reduction in duration of infection occurs for the dose with 10 12 copies/ml, 375 if σ is at least 0.7 (Fig 6 and Fig S3 Fig, subplots starting from first row third column 376 to the last subplot, the green solid curve), If σ is less than 0.7 and the dose administered 377 is 10 12 copies/ml, DENV1 level at peak is reduced, but duration of infection increases 378

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Similar to the results obtained for treatment prior to symptoms onset, the most 384 effective dose for treatment after symptoms onset is 10 12 copies/ml, but with σ being at 385 least 0.6 (Fig 7 and Fig S4 Fig, subplots starting from first row second column to the 386 last subplot, the green solid curve). A dose of 10 10 copies/ml given after symptom onset 387 also reduces duration of infection (Fig 7 and Fig S4 Fig, subplots starting from first row 388 second column to the last subplot, the orange solid curve), but to a lesser extent than 389 that for the 10 12 copies/ml dose. A dose of 10 8 copies/ml has no visible impact on 390 DENV1 profile (Fig 7 and Fig S4 Fig, the

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We examined the sensitivity of the assigned parameters to DENV1 output from the 413 ODE model. We found that the DENV1 output was relatively insensitive to variability 414 in the effectiveness parameter (σ) and the rate of production of DENV-TIPs from

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We did not find any substantive differences between primary and secondary DENV1 421 within-host dengue modelling studies [29][30][31][32]. Similarly, studies [29,32] established that 427 the virus clearance rate, κ, was significantly higher for secondary infection than that of 428 primary infection, due to an increased activation of the immune system that occurs in 429 secondary infection. 430 We note that our modelling approach is rather different from the approaches used 431 in [29][30][31][32]. These studies aimed to assess the roles of either adaptive immunity via 432 antibodies [31,32] or both innate and adaptive immunity via Type 1 interferon and

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T-cells [29,30], in shaping DENV dynamics, without considering a role of DENV-TIPs 434 in this process. On the other hand, we focused on investigating the role that 435 DENV-TIPs play in shaping DENV profiles, neglecting the role which immunity may 436 play in the process. There are also some differences between the data analysed in our 437 study and those used in these previous studies. Patients in their study were recruited 438 within 48 hours of fever onset, whilst patients in our study we used were recruited 439 within 72 hours of fever onset. Thus, DENV measurements around the peak were 440 available for many patients in their data while this information is not available for many 441 patients in the data we used. For example, in the [31] study, 38% of patients have 442 DENV1 measurements available around peak (S5 Fig, filled  In order to examine if the difference in results between our study and that of [31] 450 may be due to the differences in the two data sets, our ODE model was fitted separately 451 to the DENV1 primary and secondary data in [31] (S5 Fig). However, the results

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showed that there is a chance that the two types of infections coincide, due to the overlap in the credible intervals for parameters β, δ, γ, κ and µ, across the two groups 454 (S1 Table). Thus, the differences in results concerning the primary and secondary 455 groups in [31] and our analysis may not be due to the differences seen in the two data 456 sets, but may be due to the two mathematical modelling approaches used in the two 457 analyses. Hence, results obtained in [29][30][31][32] and ours must be interpreted with regard to 458 the context of application. DENV-TIPs dose administered is 10 12 copies/ml. 489 We note that our method of assessing the impact of DENV-TIPs therapy is different 490 from the anti-viral treatment applied in [32,44]. In both of these studies, the treatment 491 was specific to each patient, whilst in our approach, it was applied to a patient whose 492 infection dynamics may represent an average patient from the population, as we used 493 the median estimates of the posterior summary to simulate the DENV1 of this patient. 494 In [32], similar to our method, treatment was targeted at the time of onset of symptoms, 495 but, in general, the impact on secondary DENV1 cases was predicted to be less than on 496 primary DENV1 cases. Unlike this result, our estimated dose was equally effective for 497 both primary and secondary infections. In [44], various DENV-TIPs doses were 498 administered continuously to each patient until the DENV was cleared from the body. 499 For many DENV1 infected patients, it was required that doses as high as the DENV1 500 level at peak needed to be administered, for the entire duration of infection. In contrast 501 to this finding, our result showed that a single DENV-TIPs dose of 10 12 copies/ml, 502 administered on any day was sufficient to reduce severity of dengue for DENV1 patients. 503 To compare our method of assessing DENV-TIPs therapy with that applied in [32], 504 we investigated the impact of administering DENV-TIPs doses to ten DENV1 infected 505 patients, by varying the effectiveness parameter, σ, on the reported day of symptoms 506 (S6 Fig-S9 Fig), four days prior to the reported day of symptoms (S10 Fig-S12 Fig) and 507 two days after the reported day of symptoms (S13 Fig-S16 Fig). DENV-TIPs dose administered was 10 12 copies/ml. This provides the same conclusion 521 that we obtained from our first and second simulation studies.

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A shortcoming of our analysis is that we assumed that the effectiveness of 523 DENV-TIPs in blocking DENV from coinfected cells is the same, regardless of the 524 amount of DENV-TIPs and DENV present in the body (that is assigning a value from 525 0 to 1 for parameter σ). As a result, DENV production rate from coinfected cells (ω) is 526 scaled by a fixed amount. Ideally, DENV production rate from coinfected cells will 527 depend on the concentration of DENV-TIPs in these cells. This amounts to assuming 528 that if the rate of production of DENV from coinfected cells increases then the rate of 529 production of DENV-TIPs will be reduced and vice versa. These two assumptions may 530 be incorporated in the model by the use of monotonically decreasing and increasing hill 531 functions [45] which depends on the concentration of DENV-TIPs in the body.

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Although we did not incorporate any immune response in our ODE model, previous 533 within-host dengue studies showed that immunity plays a significant role in shaping 534 patients' DENV profiles [29][30][31][32]. Thus, modelling immunity along with DENV-TIPs 535 may reveal possible differences between primary and secondary infections, which we are 536 not able to establish here.

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Our results indicated some role for susceptible cell depletion around peak DENV 538 level, which could be due to the fact that the model fits are calibrated to cope with the 539 absence of data on DENV-TIPs and the four types of cells considered. Measurements of 540 these components would help to confirm the predicted dynamics.

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We fitted an ODE model to DENV1 primary and secondary data, accounting for   Table. Parameter estimates for the fits of model a separately to 592 DENV1 primary and secondary data in [31]. Parameters δ, γ, κ, β, µ are 593 summarised using posterior median and 95% credible interval in the curved parentheses. 594 Initial viral load (V 0 ) is patient-specific and is summarised by taking the median of