Mathematical modeling of within-host Zika virus dynamics

A multiscale model of the action of a capsid assembly modulator for the treatment of chronic hepatitis B

Chronic hepatitis B virus (HBV) infection is strongly associated with increased risk of liver cancer and cirrhosis. While existing treatments effectively inhibit the HBV life cycle, viral rebound occurs rapidly following treatment interruption. Consequently, functional cure rates of chronic HBV infection remain low and there is increased interest in a novel treatment modality, capsid assembly modulators (CAMs). Here, we develop a multiscale mathematical model of CAM treatment in chronic HBV infection. By fitting the model to participant data from a phase I trial of the first-generation CAM vebicorvir, we estimate the drug's dose-dependent effectiveness and identify the physiological mechanisms that drive the observed biphasic decline in HBV DNA and RNA, and mechanistic differences between HBeAg-positive and negative infection. Finally, we demonstrate analytically and numerically that HBV RNA is more sensitive than HBV DNA to increases in CAM effectiveness.

Prediction of long-term humoral response induced by the two-dose heterologous Ad26.ZEBOV, MVA-BN-Filo vaccine against Ebola

The persistence of the long-term immune response induced by the heterologous Ad26.ZEBOV, MVA-BN-Filo two-dose vaccination regimen against Ebola has been investigated in several clinical trials. Longitudinal data on IgG-binding antibody concentrations were analyzed from 487 participants enrolled in six Phase I and Phase II clinical trials conducted by the EBOVAC1 and EBOVAC2 consortia. A model based on ordinary differential equations describing the dynamics of antibodies and short- and long-lived antibody-secreting cells (ASCs) was used to model the humoral response from 7 days after the second vaccination to a follow-up period of 2 years. Using a population-based approach, we first assessed the robustness of the model, which was originally estimated based on Phase I data, against all data. Then we assessed the longevity of the humoral response and identified factors that influence these dynamics. We estimated a half-life of the long-lived ASC of at least 15 years and found an influence of geographic region, sex, and age on the humoral response dynamics, with longer antibody persistence in Europeans and women and higher production of antibodies in younger participants.

SARS-CoV-2 viral dynamic modeling to inform model selection and timing and efficacy of antiviral therapy

Mathematical models of viral dynamics have been reported to describe adequately the dynamic changes of severe acute respiratory syndrome-coronavirus 2 viral load within an individual host. In this study, eight published viral dynamic models were assessed, and model selection was performed. Viral load data were collected from a community surveillance study, including 2155 measurements from 162 patients (124 household and 38 non-household contacts). An extended version of the target-cell limited model that includes an eclipse phase and an immune response component that enhances viral clearance described best the data. In general, the parameter estimates showed good precision (relative standard error <10), apart from the death rate of infected cells. The parameter estimates were used to simulate the outcomes of a clinical trial of the antiviral tixagevimab-cilgavimab, a monoclonal antibody combination which blocks infection of the target cells by neutralizing the virus. The simulated outcome of the effectiveness of the antiviral therapy in controlling viral replication was in a good agreement with the clinical trial data. Early treatment with high antiviral efficacy is important for desired therapeutic outcome.

Antibody Dynamics Simulation-A Mathematical Exploration of Clonal Deletion and Somatic Hypermutation

We have employed mathematical modeling techniques to construct a comprehensive framework for elucidating the intricate response mechanisms of the immune system, facilitating a deeper understanding of B-cell clonal deletion and somatic hypermutation. Our improved model introduces innovative mechanisms that shed light on positive and negative selection processes during T-cell and B-cell development. Notably, clonal deletion is attributed to the attenuated immune stimulation exerted by self-antigens with high binding affinities, rendering them less effective in eliciting subsequent B-cell maturation and differentiation. Secondly, our refined model places particular emphasis on the crucial role played by somatic hypermutation in modulating the immune system's functionality. Through extensive investigation, we have determined that somatic hypermutation not only expedites the production of highly specific antibodies pivotal in combating microbial infections but also serves as a regulatory mechanism to dampen autoimmunity and enhance self-tolerance within the organism. Lastly, our model advances the understanding of the implications of antibody in vivo evolution in the overall process of organismal aging. With the progression of time, the age-associated amplification of autoimmune activity becomes apparent. While somatic hypermutation effectively delays this process, mitigating the levels of autoimmune response, it falls short of reversing this trajectory entirely. In conclusion, our advanced mathematical model offers a comprehensive and scholarly approach to comprehend the intricacies of the immune system. By encompassing novel mechanisms for selection, emphasizing the functional role of somatic hypermutation, and illuminating the consequences of in vivo antibody evolution, our model expands the current understanding of immune responses and their implications in aging.

A target-cell limited model can reproduce influenza infection dynamics in hosts with differing immune responses

We consider a hierarchy of ordinary differential equation models that describe the within-host viral kinetics of influenza infections: the IR model explicitly accounts for an immune response to the virus, while the simpler, target-cell limited TEIV and TV models do not. We show that when the IR model is fitted to pooled experimental murine data of the viral load, fraction of dead cells, and immune response levels, its parameters values can be determined. However, if, as is common, only viral load data are available, we can estimate parameters of the TEIV and TV models but not the IR model. These results are substantiated by a structural and practical identifiability analysis. We then use the IR model to generate synthetic data representing infections in hosts whose immune responses differ. We fit the TV model to these synthetic datasets and show that it can reproduce the characteristic exponential increase and decay of viral load generated by the IR model. Furthermore, the values of the fitted parameters of the TV model can be mapped from the immune response parameters in the IR model. We conclude that, if only viral load data are available, a simple target-cell limited model can reproduce influenza infection dynamics and distinguish between hosts with differing immune responses.

Modeling the stochastic within-host dynamics SARS-CoV-2 infection with discrete delay

In this paper, a new mathematical model that describes the dynamics of the within-host COVID-19 epidemic is formulated. We show the stochastic dynamics of Target-Latent-Infected-Virus free within the human body with discrete delay and noise. Positivity and uniqueness of the solutions are established. Our study shows the extinction and persistence of the disease inside the human body through the stability analysis of the disease-free equilibrium [Formula: see text] and the endemic equilibrium [Formula: see text], respectively. Moreover, we show the impact of delay tactics and noise on the extinction of the disease. The most interesting result is even if the deterministic system is inevitably pandemic at a specific point, extinction will become possible in the stochastic version of our model.

Stage duration distributions and intraspecific competition: a review of continuous stage-structured models

Stage structured models, by grouping individuals with similar demographic characteristics together, have proven useful in describing population dynamics. This manuscript starts from reviewing two widely used modeling frameworks that are in the form of integral equations and age-structured partial differential equations. Both modeling frameworks can be reduced to the same differential equation structures with/without time delays by applying Dirac and gamma distributions for the stage durations. Each framework has its advantages and inherent limitations. The net reproduction number and initial growth rate can be easily defined from the integral equation. However, it becomes challenging to integrate the density-dependent regulations on the stage distribution and survival probabilities in an integral equation, which may be suitably incorporated into partial differential equations. Further recent modeling studies, in particular those by Stephen A. Gourley and collaborators, are reviewed under the conditions of the stage duration distribution and survival probability being regulated by population density.

Multiscale Model of Antiviral Timing, Potency, and Heterogeneity Effects on an Epithelial Tissue Patch Infected by SARS-CoV-2

We extend our established agent-based multiscale computational model of infection of lung tissue by SARS-CoV-2 to include pharmacokinetic and pharmacodynamic models of remdesivir. We model remdesivir treatment for COVID-19; however, our methods are general to other viral infections and antiviral therapies. We investigate the effects of drug potency, drug dosing frequency, treatment initiation delay, antiviral half-life, and variability in cellular uptake and metabolism of remdesivir and its active metabolite on treatment outcomes in a simulated patch of infected epithelial tissue. Non-spatial deterministic population models which treat all cells of a given class as identical can clarify how treatment dosage and timing influence treatment efficacy. However, they do not reveal how cell-to-cell variability affects treatment outcomes. Our simulations suggest that for a given treatment regime, including cell-to-cell variation in drug uptake, permeability and metabolism increase the likelihood of uncontrolled infection as the cells with the lowest internal levels of antiviral act as super-spreaders within the tissue. The model predicts substantial variability in infection outcomes between similar tissue patches for different treatment options. In models with cellular metabolic variability, antiviral doses have to be increased significantly (>50% depending on simulation parameters) to achieve the same treatment results as with the homogeneous cellular metabolism.

Bluetongue Research at a Crossroads: Modern Genomics Tools Can Pave the Way to New Insights

Bluetongue virus (BTV) is an arthropod-borne, segmented double-stranded RNA virus that can cause severe disease in both wild and domestic ruminants. BTV evolves via several key mechanisms, including the accumulation of mutations over time and the reassortment of genome segments.Additionally, BTV must maintain fitness in two disparate hosts, the insect vector and the ruminant. The specific features of viral adaptation in each host that permit host-switching are poorly characterized. Limited field studies and experimental work have alluded to the presence of these phenomena at work, but our understanding of the factors that drive or constrain BTV's genetic diversification remains incomplete. Current research leveraging novel approaches and whole genome sequencing applications promises to improve our understanding of BTV's evolution, ultimately contributing to the development of better predictive models and management strategies to reduce future impacts of bluetongue epizootics.

Nonlinear growth and mathematical modelling of COVID-19 in some African countries with the Atangana-Baleanu fractional derivative

We analyse the time-series evolution of the cumulative number of confirmed cases of COVID-19, the novel coronavirus disease, for some African countries. We propose a mathematical model, incorporating non-pharmaceutical interventions to unravel the disease transmission dynamics. Analysis of the stability of the model's steady states was carried out, and the reproduction number R 0 , a vital key for flattening the time-evolution of COVID-19 cases, was obtained by means of the next generation matrix technique. By dividing the time evolution of the pandemic for the cumulative number of confirmed infected cases into different regimes or intervals, hereafter referred to as phases, numerical simulations were performed to fit the proposed model to the cumulative number of confirmed infections for different phases of COVID-19 during its first wave. The estimated R 0 declined from 2.452-9.179 during the first phase of the infection to 1.374-2.417 in the last phase. Using the Atangana-Baleanu fractional derivative, a fractional COVID-19 model is proposed and numerical simulations performed to establish the dependence of the disease dynamics on the order of the fractional derivatives. An elasticity and sensitivity analysis of R 0 was carried out to determine the most significant parameters for combating the disease outbreak. These were found to be the effective disease transmission rate, the disease diagnosis or case detection rate, the proportion of susceptible individuals taking precautions, and the disease infection rate. Our results show that if the disease infection rate is less than 0.082/day, then R 0 is always less than 1; and if at least 55.29% of the susceptible population take precautions such as regular hand washing with soap, use of sanitizers, and the wearing of face masks, then the reproduction number R 0 remains below unity irrespective of the disease infection rate. Keeping R 0 values below unity leads to a decrease in COVID-19 prevalence.

In vivo kinetics of SARS-CoV-2 infection and its relationship with a person's infectiousness

The within-host viral kinetics of SARS-CoV-2 infection and how they relate to a person's infectiousness are not well understood. This limits our ability to quantify the impact of interventions on viral transmission. Here, we develop viral dynamic models of SARS-CoV-2 infection and fit them to data to estimate key within-host parameters such as the infected cell half-life and the within-host reproductive number. We then develop a model linking viral load (VL) to infectiousness and show a person's infectiousness increases sublinearly with VL and that the logarithm of the VL in the upper respiratory tract is a better surrogate of infectiousness than the VL itself. Using data on VL and the predicted infectiousness, we further incorporated data on antigen and RT-PCR tests and compared their usefulness in detecting infection and preventing transmission. We found that RT-PCR tests perform better than antigen tests assuming equal testing frequency; however, more frequent antigen testing may perform equally well with RT-PCR tests at a lower cost but with many more false-negative tests. Overall, our models provide a quantitative framework for inferring the impact of therapeutics and vaccines that lower VL on the infectiousness of individuals and for evaluating rapid testing strategies.

Determining reliable parameter estimates for within-host and within-vector models of Zika virus

In this paper, we introduce three within-host and one within-vector models of Zika virus. The within-host models are the target cell limited model, the target cell limited model with natural killer (NK) cells class, and a within-host-within-fetus model of a pregnant individual. The within-vector model includes the Zika virus dynamics in the midgut and salivary glands. The within-host models are not structurally identifiable with respect to data on viral load and NK cell counts. After rescaling, the scaled within-host models are locally structurally identifiable. The within-vector model is structurally identifiable with respect to viremia data in the midgut and salivary glands. Using Monte Carlo Simulations, we find that target cell limited model is practically identifiable from data on viremia; the target cell limited model with NK cell class is practically identifiable, except for the rescaled half saturation constant. The within-host-within-fetus model has all fetus-related parameters not practically identifiable without data on the fetus, as well as the rescaled half saturation constant is also not practically identifiable. The remaining parameters are practically identifiable. Finally we find that none of the parameters of the within-vector model is practically identifiable.

Dengue virus is sensitive to inhibition prior to productive replication

Uncovering vulnerable steps in the life cycle of viruses supports the rational design of antiviral treatments. However, information on viral replication dynamics obtained from traditional bulk assays with host cell populations is inherently limited as the data represent averages over a multitude of unsynchronized replication cycles. Here, we use time-lapse imaging of virus replication in thousands of single cells, combined with computational inference, to identify rate-limiting steps for dengue virus (DENV), a widespread human pathogen. Comparing wild-type DENV with a vaccine candidate mutant, we show that the viral spread in the mutant is greatly attenuated by delayed onset of productive replication, whereas wild-type and mutant virus have identical replication rates. Single-cell analysis done after applying the broad-spectrum antiviral drug, ribavirin, at clinically relevant concentrations revealed the same mechanism of attenuating viral spread. We conclude that the initial steps of infection, rather than the rate of established replication, are quantitatively limiting DENV spread.

OntoRepliCov: an Ontology-Based Approach for Modeling the SARS-CoV-2 Replication Process

Understanding the replication machinery of viruses contributes to suggest and try effective antiviral strategies. Exhaustive knowledge about the proteins structure, their function, or their interaction is one of the preconditions for successfully modeling it. In this context, modeling methods based on a formal representation with a high semantic expressiveness would be relevant to extract proteins and their nucleotide or amino acid sequences as an element from the replication process. Consequently, our approach relies on the use of semantic technologies to design the SARS-CoV-2 replication machinery. This provides the ability to infer new knowledge related to each step of the virus replication. More specifically, we developed an ontology-based approach enriched with reasoning process of a complete replication machinery process for SARS-CoV-2. We present in this paper a partial overview of our ontology OntoRepliCov to describe one step of this process, namely, the continuous translation or protein synthesis, through classes, properties, axioms, and SWRL (Semantic Web Rule Language) rules.

Generation of multicellular spatiotemporal models of population dynamics from ordinary differential equations, with applications in viral infection

BACKGROUND

The biophysics of an organism span multiple scales from subcellular to organismal and include processes characterized by spatial properties, such as the diffusion of molecules, cell migration, and flow of intravenous fluids. Mathematical biology seeks to explain biophysical processes in mathematical terms at, and across, all relevant spatial and temporal scales, through the generation of representative models. While non-spatial, ordinary differential equation (ODE) models are often used and readily calibrated to experimental data, they do not explicitly represent the spatial and stochastic features of a biological system, limiting their insights and applications. However, spatial models describing biological systems with spatial information are mathematically complex and computationally expensive, which limits the ability to calibrate and deploy them and highlights the need for simpler methods able to model the spatial features of biological systems.

RESULTS

In this work, we develop a formal method for deriving cell-based, spatial, multicellular models from ODE models of population dynamics in biological systems, and vice versa. We provide examples of generating spatiotemporal, multicellular models from ODE models of viral infection and immune response. In these models, the determinants of agreement of spatial and non-spatial models are the degree of spatial heterogeneity in viral production and rates of extracellular viral diffusion and decay. We show how ODE model parameters can implicitly represent spatial parameters, and cell-based spatial models can generate uncertain predictions through sensitivity to stochastic cellular events, which is not a feature of ODE models. Using our method, we can test ODE models in a multicellular, spatial context and translate information to and from non-spatial and spatial models, which help to employ spatiotemporal multicellular models using calibrated ODE model parameters. We additionally investigate objects and processes implicitly represented by ODE model terms and parameters and improve the reproducibility of spatial, stochastic models.

CONCLUSION

We developed and demonstrate a method for generating spatiotemporal, multicellular models from non-spatial population dynamics models of multicellular systems. We envision employing our method to generate new ODE model terms from spatiotemporal and multicellular models, recast popular ODE models on a cellular basis, and generate better models for critical applications where spatial and stochastic features affect outcomes.

Kinetics of Asian and African Zika virus lineages over single-cycle and multi-cycle growth in culture: Gene expression, cell killing, virus production, and mathematical modeling

Since 2014, an Asian lineage of Zika virus has caused outbreaks, and it has been associated with neurological disorders in adults and congenital defects in newborns. The resulting threat of the Zika virus to human health has prompted the development of new vaccines, which have yet to be approved for human use. Vaccines based on the attenuated or chemically inactivated virus will require large-scale production of the intact virus to meet potential global demands. Intact viruses are produced by infecting cultures of susceptible cells, a dynamic process that spans from hours to days and has yet to be optimized. Here, we infected Vero cells adhesively cultured in well-plates with two Zika virus strains: a recently isolated strain from the Asian lineage, and a cell-culture-adapted strain from the African lineage. At different time points post-infection, virus particles in the supernatant were quantified; further, microscopy images were used to quantify cell density and the proportion of cells expressing viral protein. These measurements were performed across multiple replicate samples of one-step infections every four hours over 60 h and for multi-step infections every four to 24 h over 144 h, generating a rich data set. For each set of data, mathematical models were developed to estimate parameters associated with cell infection and virus production. The African-lineage strain was found to produce a 14-fold higher yield than the Asian-lineage strain in one-step growth and a sevenfold higher titer in multi-step growth, suggesting a benefit of cell-culture adaptation for developing a vaccine strain. We found that image-based measurements were critical for discriminating among different models, and different parameters for the two strains could account for the experimentally observed differences. An exponential-distributed delay model performed best in accounting for multi-step infection of the Asian strain, and it highlighted the significant sensitivity of virus titer to the rate of viral degradation, with implications for optimization of vaccine production. More broadly, this study highlights how image-based measurements can contribute to the discrimination of virus-culture models for the optimal production of inactivated and attenuated whole-virus vaccines.

A near analytic solution of a stochastic immune response model considering variability in virus and T-cell dynamics

Biological processes at the cellular level are stochastic in nature, and the immune response system is no different. Therefore, models that attempt to explain this system need to also incorporate noise or fluctuations that can account for the observed variability. In this work, a stochastic model of the immune response system is presented in terms of the dynamics of T cells and virus particles. Making use of the Green's function and the Wilemski-Fixman approximation, this model is then solved to obtain the analytical expression for the joint probability density function of these variables in the early and late stages of infection. This is then also used to calculate the average level of virus particles in the system. Upon comparing the theoretically predicted average virus levels to those of COVID-19 patients, it is hypothesized that the long-lived dynamics that are characteristics of such viral infections are due to the long range correlations in the temporal fluctuations of the virions. This model, therefore, provides an insight into the effects of noise on viral dynamics.

Mechanistic Modeling of SARS-CoV-2 and Other Infectious Diseases and the Effects of Therapeutics

Modern viral kinetic modeling and its application to therapeutics is a field that attracted the attention of the medical, pharmaceutical, and modeling communities during the early days of the AIDS epidemic. Its successes led to applications of modeling methods not only to HIV but a plethora of other viruses, such as hepatitis C virus (HCV), hepatitis B virus and cytomegalovirus, which along with HIV cause chronic diseases, and viruses such as influenza, respiratory syncytial virus, West Nile virus, Zika virus, and severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which generally cause acute infections. Here we first review the historical development of mathematical models to understand HIV and HCV infections and the effects of treatment by fitting the models to clinical data. We then focus on recent efforts and contributions of applying these models towards understanding SARS-CoV-2 infection and highlight outstanding questions where modeling can provide crucial insights and help to optimize nonpharmaceutical and pharmaceutical interventions of the coronavirus disease 2019 (COVID-19) pandemic. The review is written from our personal perspective emphasizing the power of simple target cell limited models that provided important insights and then their evolution into more complex models that captured more of the virology and immunology. To quote Albert Einstein, "Everything should be made as simple as possible, but not simpler," and this idea underlies the modeling we describe below.

Early events in hepatitis B infection: the role of inoculum dose

The relationship between the inoculum dose and the ability of the pathogen to invade the host is poorly understood. Experimental studies in non-human primates infected with different inoculum doses of hepatitis B virus have shown a non-monotonic relationship between dose magnitude and infection outcome, with high and low doses leading to 100% liver infection and intermediate doses leading to less than 0.1% liver infection, corresponding to CD4 T-cell priming. Since hepatitis B clearance is CD8 T-cell mediated, the question of whether the inoculum dose influences CD8 T-cell dynamics arises. To help answer this question, we developed a mathematical model of virus-host interaction following hepatitis B virus infection. Our model explains the experimental data well, and predicts that the inoculum dose affects both the timing of the CD8 T-cell expansion and the quality of its response, especially the non-cytotoxic function. We find that a low-dose challenge leads to slow CD8 T-cell expansion, weak non-cytotoxic functions, and virus persistence; high- and medium-dose challenges lead to fast CD8 T-cell expansion, strong cytotoxic and non-cytotoxic function, and virus clearance; while a super-low-dose challenge leads to delayed CD8 T-cell expansion, strong cytotoxic and non-cytotoxic function, and virus clearance. These results are useful for designing immune cell-based interventions.

Lassa viral dynamics in non-human primates treated with favipiravir or ribavirin

Lassa fever is an haemorrhagic fever caused by Lassa virus (LASV). There is no vaccine approved against LASV and the only recommended antiviral treatment relies on ribavirin, despite limited evidence of efficacy. Recently, the nucleotide analogue favipiravir showed a high antiviral efficacy, with 100% survival obtained in an otherwise fully lethal non-human primate (NHP) model of Lassa fever. However the mechanism of action of the drug is not known and the absence of pharmacokinetic data limits the translation of these results to the human setting. Here we aimed to better understand the antiviral effect of favipiravir by developping the first mathematical model recapitulating Lassa viral dynamics and treatment. We analyzed the viral dynamics in 24 NHPs left untreated or treated with ribavirin or favipiravir, and we put the results in perspective with those obtained with the same drugs in the context of Ebola infection. Our model estimates favipiravir EC50 in vivo to 2.89 μg.mL-1, which is much lower than what was found against Ebola virus. The main mechanism of action of favipiravir was to decrease virus infectivity, with an efficacy of 91% at the highest dose. Based on our knowledge acquired on the drug pharmacokinetics in humans, our model predicts that favipiravir doses larger than 1200 mg twice a day should have the capability to strongly reduce the production infectious virus and provide a milestone towards a future use in humans.

Evolving viral and serological stages of Zika virus RNA-positive blood donors and estimation of incidence of infection during the 2016 Puerto Rican Zika epidemic: an observational cohort study

BACKGROUND

Puerto Rico began screening blood donations for Zika virus RNA with nucleic acid amplification tests (NAATs) on April 3, 2016, because of an emerging Zika virus outbreak. We followed up positive donors to assess the dynamics of viral and serological markers during the early stages of Zika virus infection and update the estimate of infection incidence in the Puerto Rican population during the outbreak.

METHODS

Blood donations from volunteer donors in Puerto Rico were screened for the presence of Zika virus RNA using the cobas Zika NAAT. Positive donations were further tested to confirm infection, estimate viral load, and identify Zika virus-specific IgM antibodies. Individuals with positive blood donations were invited to attend follow-up visits. Donations with confirmed infection (defined as detection of Zika virus RNA or IgM on additional testing of index or follow-up samples) were assessed for stage of infection according to Zika virus RNA detectability in simulated minipools, viral load, and Zika virus IgM status. A three-step process was used to estimate the mean duration of NAAT reactivity of Zika virus in human plasma from individuals identified pre-seroconversion with at least one follow up visit and to update the 2016 incidence estimate of Zika virus infection.

FINDINGS

Between April 3 and Dec 31, 2016, 53 112 blood donations were screened for Zika virus, of which 351 tested positive, 339 had confirmed infections, and 319 could be staged. Compared with IgM-positive index donations (n=110), IgM-negative index donations (n=209) had higher mean viral loads (1·1 × 10⁶vs 8·3 × 10⁴ international units per mL) and were more likely to be detected in simulated minipools (93% [n=194] vs 26% [n=29]). The proportions of donations with confirmed infections that had viral RNA detected only in individual-donation NAATs (ie, not in simulated minipools) and were IgM positive increased as the epidemic evolved. The estimated mean duration of NAAT detectability in the 140 donors included in the follow-up study was 11·70 days (95% CI 10·06-14·36). Applying this detection period to the observed proportion of donations that were confirmed NAAT positive yielded a Zika virus seasonal incidence estimate of 21·1% (95% CI 18·1-24·1); 768 101 infections in a population of 3 638 773 in 2016.

INTERPRETATION

Characterisation of early Zika virus infection has implications for blood safety because infectivity of blood donations and utility of screening methods likely correlate with viral load and serological stage of infection. Our findings also have implications for diagnostic testing, public health surveillance, and epidemiology, and we estimate that around 21% of the Puerto Rican population was infected during the 2016 outbreak.

FUNDING

Biomedical Advanced Research and Development Authority, National Heart, Lung, and Blood Institute.

Leveraging Computational Modeling to Understand Infectious Diseases

Purpose of Review

Computational and mathematical modeling have become a critical part of understanding in-host infectious disease dynamics and predicting effective treatments. In this review, we discuss recent findings pertaining to the biological mechanisms underlying infectious diseases, including etiology, pathogenesis, and the cellular interactions with infectious agents. We present advances in modeling techniques that have led to fundamental disease discoveries and impacted clinical translation.

Recent Findings

Combining mechanistic models and machine learning algorithms has led to improvements in the treatment of Shigella and tuberculosis through the development of novel compounds. Modeling of the epidemic dynamics of malaria at the within-host and between-host level has afforded the development of more effective vaccination and antimalarial therapies. Similarly, in-host and host-host models have supported the development of new HIV treatment modalities and an improved understanding of the immune involvement in influenza. In addition, large-scale transmission models of SARS-CoV-2 have furthered the understanding of coronavirus disease and allowed for rapid policy implementations on travel restrictions and contract tracing apps.

Summary

Computational modeling is now more than ever at the forefront of infectious disease research due to the COVID-19 pandemic. This review highlights how infectious diseases can be better understood by connecting scientists from medicine and molecular biology with those in computer science and applied mathematics.

Modelling the impact of antibody-dependent enhancement on disease severity of Zika virus and dengue virus sequential and co-infection

Human infections with viruses of the genus Flavivirus, including dengue virus (DENV) and Zika virus (ZIKV), are of increasing global importance. Owing to antibody-dependent enhancement (ADE), secondary infection with one Flavivirus following primary infection with another Flavivirus can result in a significantly larger peak viral load with a much higher risk of severe disease. Although several mathematical models have been developed to quantify the virus dynamics in the primary and secondary infections of DENV, little progress has been made regarding secondary infection of DENV after a primary infection of ZIKV, or DENV-ZIKV co-infection. Here, we address this critical gap by developing compartmental models of virus dynamics. We first fitted the models to published data on dengue viral loads of the primary and secondary infections with the observation that the primary infection reaches its peak much more gradually than the secondary infection. We then quantitatively show that ADE is the key factor determining a sharp increase/decrease of viral load near the peak time in the secondary infection. In comparison, our simulations of DENV and ZIKV co-infection (simultaneous rather than sequential) show that ADE has very limited influence on the peak DENV viral load. This indicates pre-existing immunity to ZIKV is the determinant of a high level of ADE effect. Our numerical simulations show that (i) in the absence of ADE effect, a subsequent co-infection is beneficial to the second virus; and (ii) if ADE is feasible, then a subsequent co-infection can induce greater damage to the host with a higher peak viral load and a much earlier peak time for the second virus, and for the second peak for the first virus.

Varying Inoculum Dose to Assess the Roles of the Immune Response and Target Cell Depletion by the Pathogen in Control of Acute Viral Infections

It is difficult to determine whether an immune response or target cell depletion by the infectious agent is most responsible for the control of acute primary infection. Both mechanisms can explain the basic dynamics of an acute infection-exponential growth of the pathogen followed by control and clearance-and can also be represented by many different differential equation models. Consequently, traditional model comparison techniques using time series data can be ambiguous or inconclusive. We propose that varying the inoculum dose and measuring the subsequent infectious load can rule out target cell depletion by the pathogen as the main control mechanism. Infectious load can be any measure that is proportional to the number of infected cells, such as viraemia. We show that a twofold or greater change in infectious load is unlikely when target cell depletion controls infection, regardless of the model details. Analyzing previously published data from mice infected with influenza, we find the proportion of lung epithelial cells infected was 21-fold greater (95% confidence interval 14-32) in the highest dose group than in the lowest. This provides evidence in favor of an alternative to target cell depletion, such as innate immunity, in controlling influenza infections in this experimental system. Data from other experimental animal models of acute primary infection have a similar pattern.

Model Averaging in Viral Dynamic Models

The paucity of experimental data makes both inference and prediction particularly challenging in viral dynamic models. In the presence of several candidate models, a common strategy is model selection (MS), in which models are fitted to the data but only results obtained with the "best model" are presented. However, this approach ignores model uncertainty, which may lead to inaccurate predictions. When several models provide a good fit to the data, another approach is model averaging (MA) that weights the predictions of each model according to its consistency to the data. Here, we evaluated by simulations in a nonlinear mixed-effect model framework the performances of MS and MA in two realistic cases of acute viral infection, i.e., (1) inference in the presence of poorly identifiable parameters, namely, initial viral inoculum and eclipse phase duration, (2) uncertainty on the mechanisms of action of the immune response. MS was associated in some scenarios with a large rate of false selection. This led to a coverage rate lower than the nominal coverage rate of 0.95 in the majority of cases and below 0.50 in some scenarios. In contrast, MA provided better estimation of parameter uncertainty, with coverage rates ranging from 0.72 to 0.98 and mostly comprised within the nominal coverage rate. Finally, MA provided similar predictions than those obtained with MS. In conclusion, parameter estimates obtained with MS should be taken with caution, especially when several models well describe the data. In this situation, MA has better performances and could be performed to account for model uncertainty.

A personalized computational model of edema formation in myocarditis based on long-axis biventricular MRI images

Background

Myocarditis is defined as the inflammation of the myocardium, i.e. the cardiac muscle. Among the reasons that lead to this disease, we may include infections caused by a virus, bacteria, protozoa, fungus, and others. One of the signs of the inflammation is the formation of edema, which may be a consequence of the interaction between interstitial fluid dynamics and immune response. This complex physiological process was mathematically modeled using a nonlinear system of partial differential equations (PDE) based on porous media approach. By combing a model based on Biot’s poroelasticity theory with a model for the immune response we developed a new hydro-mechanical model for inflammatory edema. To verify this new computational model, T2 parametric mapping obtained by Magnetic Resonance (MR) imaging was used to identify the region of edema in a patient diagnosed with unspecific myocarditis.

Results

A patient-specific geometrical model was created using MRI images from the patient with myocarditis. With this model, edema formation was simulated using the proposed hydro-mechanical mathematical model in a two-dimensional domain. The computer simulations allowed us to correlate spatiotemporal dynamics of representative cells of the immune systems, such as leucocytes and the pathogen, with fluid accumulation and cardiac tissue deformation.

Conclusions

This study demonstrates that the proposed mathematical model is a very promising tool to better understand edema formation in myocarditis. Simulations obtained from a patient-specific model reproduced important aspects related to the formation of cardiac edema, its area, position, and shape, and how these features are related to immune response.

Within-host modeling of blood-stage malaria

Malaria infection continues to be a major health problem worldwide and drug resistance in the major human parasite species, Plasmodium falciparum, is increasing in South East Asia. Control measures including novel drugs and vaccines are in development, and contributions to the rational design and optimal usage of these interventions are urgently needed. Infection involves the complex interaction of parasite dynamics, host immunity, and drug effects. The long life cycle (48 hours in the common human species) and synchronized replication cycle of the parasite population present significant challenges to modeling the dynamics of Plasmodium infection. Coupled with these, variation in immune recognition and drug action at different life cycle stages leads to further complexity. We review the development and progress of "within-host" models of Plasmodium infection, and how these have been applied to understanding and interpreting human infection and animal models of infection.

Antiviral interferon response at single-cell resolution

Experimental studies of the innate immune response of mammalian cells to viruses reveal pervasive heterogeneity at the level of single cells. Interferons are induced only in a fraction of virus-infected cells; subsequently a fraction of cells exposed to interferons upregulate interferon-stimulated genes. Nevertheless, quantitative experiments and linked mathematical models show that the interferon response can be effective in curbing viral spread through two distinct mechanisms. First, paracrine interferon signals from scattered source cells can protect many uninfected cells, and the self-amplification of interferon production might serve to calibrate response amplitude to strength of viral infection. Second, models of the tug-of-war between viral replication and the innate interferon response imply a pivotal role of interferon action on already infected cells in curbing viral spread, through effectively lowering virus replication rate. This finding is in line with the observation that several pathogenic viruses selectively abrogate interferon action on infected cells. Thus, interferons may delay viral spread in acute infections by acting as sentinels, warning uninfected cells of imminent danger, or as negative feedback regulators of virus replication in infected cells. The timing of the interferon response relative to the onset of viral replication is critical for its effectiveness in curbing viral spread.

Validated Models of Immune Response to Virus Infection

Viruses are a main cause of disease worldwide and many are without effective therapeutics or vaccines. A lack of understanding about how host responses work to control viral spread is one factor limiting effective management. How different immune components regulate infection dynamics is beginning to be better understood with the help of mathematical models. These models have been key in discriminating between hypotheses and in identifying rates of virus growth and clearance, dynamical control by different host factors and antivirals, and synergistic interactions during multi-pathogen infections. A recent focus in evaluating model predictions in the laboratory and clinic has illuminate the accuracy of models for a variety of viruses and highlighted the critical nature of theoretical approaches in virology. Here, I discuss recent model-driven exploration of host-pathogen interactions that have illustrated the importance of model validation in establishing the model's predictive capability and in defining new biology.