Relationship between the inclusion/exclusion criteria and sample size in randomized controlled trials for SARS-CoV-2 entry inhibitors

The coronavirus disease 2019 (COVID-19) pandemic that has been ongoing since 2019 is still ongoing and how to control it is one of the international issues to be addressed. Antiviral drugs that reduce the viral load in terms of reducing the risk of secondary infection are important. For the general control of emerging infectious diseases, establishing an efficient method to evaluate candidate therapeutic agents will lead to a rapid response. We evaluated clinical trial designs for viral entry inhibitors that have the potential to be effective pre-exposure prophylactic drugs in addition to reducing viral load after infection. We used a previously developed simulation of clinical trials based on a mathematical model of within-host viral infection dynamics to evaluate sample sizes in clinical trials of viral entry inhibitors against COVID-19. We assumed four measures as outcomes, namely change in log10-transformed viral load from symptom onset, PCR positive ratio, log10-transformed viral load, and cumulative viral load, and then sample sizes were calculated for drugs with 99 % and 95 % antiviral efficacy. Consistent with previous results, we found that sample sizes could be dramatically reduced for all outcomes used in an analysis by adopting inclusion/exclusion criteria such that only patients in the early post-infection period would be included in a clinical trial. A comparison of sample sizes across outcomes demonstrated an optimal measurement schedule associated with the nature of the outcome measured for the evaluation of drug efficacy. In particular, the sample sizes calculated from the change in viral load and from viral load tended to be small when measurements were taken at earlier time points after treatment initiation. For the cumulative viral load, the sample size was lower than that from the other outcomes when the stricter inclusion/exclusion criteria to include patients whose time since onset is earlier than 2 days was used. We concluded that the design of efficient clinical trials should consider the inclusion/exclusion criteria and measurement schedules, as well as outcome selection based on sample size, personnel and budget needed to conduct the trial, and the importance of the outcome regarding the medical and societal requirements. This study provides insights into clinical trial design for a variety of situations, especially addressing infectious disease prevalence and feasible trial sizes. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

SARS-coronavirus-2 infections: biological instabilities characterized by order parameters

A four-variable virus dynamics TIIV model was considered that involves infected cells in an eclipse phase. The state space description of the model was transferred into an amplitude space description which is the appropriate general, nonlinear physics framework to describe instabilities. In this context, the unstable eigenvector or order parameter of the model was determined. Subsequently, a model-based analysis of viral load data from eight symptomatic COVID-19 patients was conducted. For all patients, it was found that the initial SARS-CoV-2 infection evolved along the respective patient-specific order parameter, as expected by theoretical considerations. The order parameter amplitude that described the initial virus multiplication showed doubling times between 30 minutes and 3 hours. Peak viral loads of patients were linearly related to the amplitudes of the patient order parameters. Finally, it was found that the patient order parameters determined qualitatively and quantitatively the relationships between the increases in virus-producing infected cells and infected cells in the eclipse phase. Overall, the study echoes the 40 years old suggestion by Mackey and Glass to consider diseases as instabilities.

Modeling the dynamics of Usutu virus infection in birds

Usutu virus is an emerging zoonotic flavivirus causing high avian mortality rates and occasional severe neurological disorders in humans. Several virus strains are co-circulating and the differences in their characteristics and avian pathogenesis levels are still unknown. In this study, we use within-host mathematical models to characterize the mechanisms responsible for virus expansion and clearance in juvenile chickens challenged with four Usutu virus strains. We find heterogeneity between the virus strains, with the time between cell infection and viral production varying between 16 h and 23 h, the infected cell lifespan varying between 48 min and 9.5 h, and the basic reproductive number R₀ varying between 12.05 and 19.49. The strains with high basic reproductive number have short infected cell lifespan, indicative of immune responses. The virus strains with low basic reproductive number have lower viral peaks and longer lasting viremia, due to lower infection rates and high infected cell lifespan. We discuss how the host and virus heterogeneities may differently impact the public health threat presented by these virus strains.

Quantifying antiviral effects against simian/human immunodeficiency virus induced by host immune response

Chimeric simian and human immunodeficiency viruses (SHIVs) are appropriate animal models for the human immunodeficiency virus (HIV) because HIV has quite a narrow host range. Additionally, SHIVs that encode the HIV-1 Env protein and are infectious to macaques have many strains that show different pathogenesis, such as the highly pathogenic SHIV-KS661 and the less pathogenic SHIV-#64. Therefore, we used SHIVs to understand different aspects of AIDS pathogenesis. In a previous study, we established a mathematical model of in vivo early SHIV infection dynamics, which revealed the expected uninfected and infected dynamics in Rhesus macaques. In concrete, the number of uninfected CD4⁺ T cells in SHIV-KS661-infected Rhesus macaques decreased more significantly and rapidly than that of SHIV-#64 Rhesus macaques, and these Rhesus macaques did not any induce host immune response. In contrast, the number of uninfected CD4⁺ T cells in SHIV-#64-infected Rhesus macaques is maintained, and host immune response developed. Although we considered that the peak viral load might determine whether systemic CD4⁺ T cell depletion occurs or host immune responses develop, we could not investigate this because our model quantified only SHIV infection prior to the development of the pathogenicity or host immune responses. Therefore, we developed a new mathematical model to investigate why SHIV-#64 and SHIV-KS661 showed different long-term viral dynamics. We fitted our new model considering antibody responses to our experimental datasets that included antibody titers, CD4⁺ T cells, and viral load data. We performed a maximum likelihood estimation using a non-linear mixed effect model. From the results, we derived the basic reproduction numbers of SHIV-#64 and SHIV-KS661 from intravenous infection (IV) and SHIV-KS661 from intrarectal infection (IR), as well as the antiviral effects of antibodies against SHIV-#64(IV) and SHIV-KS661(IR). We found significant differences between the basic reproduction number of SHIV-#64(IV) or -KS661(IR) and that of SHIV-KS661(IV). We found no clear difference between the antiviral effects of SHIV-#64(IV) and SHIV-KS661(IR), and revealed that an antiviral effect more than 90% of that of maximum antibody responses was induced from initial antibody responses (i.e., antibody response just after its inducement). In conclusion, we found that the basic reproduction number, rather than SHIV strains determines whether systemic CD4⁺ T cell depletion develops, and the subsequent antibody responses occurs.

Dynamics and predisposition of respiratory viral co-infections in children and adults

OBJECTIVES

The epidemiology of respiratory co-infection pairings is poorly understood. Here we assess the dynamics of respiratory viral co-infections in children and adults and determine predisposition for or against specific viral pairings.

METHODS

Over five respiratory seasons from 30 November 2013 through 6 June 2018, the mono-infection and co-infection prevalence of 13 viral pathogens was tabulated at The Cleveland Clinic. Employing a model to proportionally distribute viral pairs using individual virus co-infection rate with prevalence patterns of concurrent co-circulating viruses, we compared predicted occurrence with observed occurrence of 132 viral pairing permutations using binomial analysis.

RESULTS

Of 30 535 respiratory samples, 9843 (32.2%) were positive for at least one virus and 1018 (10.8%) of these were co-infected. Co-infected samples predominantly originated from children. Co-infection rate in paediatric population was 35.0% (2068/5906), compared with only 5.8% (270/4591) in adults. Adenovirus C (ADVC) had the highest co-infection rate (426/623, 68.3%) while influenza virus B had the lowest (55/546, 10.0%). ADVC-rhinovirus (HRV), respiratory syncytial virus A (RSVA)-HRV and RSVB-HRV pairings occurred at significantly higher frequencies than predicted by the proportional distribution model (p < 0.05). Additionally, several viral pairings had fewer co-infections than predicted by our model: notably metapneumovirus (hMPV)-parainfluenza virus 3, hMPV-RSVA and RSVA-RSVB.

CONCLUSIONS

This is one of the largest studies on respiratory viral co-infections in children and adults. Co-infections are substantially more common in children, especially under 5 years of age, and the most frequent pairings occurred at a higher frequency than would be expected by random. Specific pairings occur at altered rates compared with those predicted by proportional distribution, suggesting either direct or indirect interactions result between specific viral pathogens.

A within-host mathematical model of H9N2 avian influenza infection and type-I interferon response pathways in chickens

Chickens infected with avian influenza virus (AIV) transmit the virus via respiratory and cloacal shedding. While previous mathematical models have shown that the innate immune response is necessary for the early suppression of virus production in infected respiratory cells, the different pathways by which the innate immune response can affect cloacal viral shedding have not been studied in chickens. The present study aims to evaluate the sensitivity of H9N2 low pathogenic AIV shedding in chicken gastrointestinal cells to different type-I interferon (IFN) response pathways, and to determine the impact of a cellular eclipse phase (latent period) on the time to peak virus shedding using a mathematical model describing within host viral kinetics. Our model results demonstrate that a mechanistic model that incorporates 1) the intracellular antiviral effects of type-I IFN on virus production, 2) destruction of infected cells by type-I IFN activated Natural Killer cells, and 3) an eclipse phase is most consistent with experimental cloacal virus shedding data. These results provide a potential mechanistic explanation for the delay to peak cloacal virus shedding observed in experimental studies conducted in chickens, as well as an improved understanding of the primary type-I IFN pathways involved in the control of cloacal virus shedding, which may lead to the development of more targeted vaccine candidates.

Quantifying the antiviral effect of APOBEC3 on HIV-1 infection in humanized mouse model

APOBEC3 proteins inhibit human immunodeficiency virus (HIV)-1 infection by independently impairing viral reverse transcription and inducing G-to-A mutations in viral DNA. An HIV-1-encoded protein, viral infectivity factor (Vif), can counteract these antiviral activities of APOBEC3 proteins. Although previous studies using in vitro cell culture systems have revealed the molecular mechanisms of the antiviral action of APOBEC3 proteins and their antagonism by Vif, it remains unclear how APOBEC3 proteins affect the kinetics of HIV-1 replication in vivo. Here we quantified the time-series of viral load datasets from humanized mice infected with HIV-1 variants in the presence of APOBEC3F, APOBEC3G, or both APOBEC3F/G using a simple mathematical model that accounted for inter-individual variability. Through experimental and mathematical investigation, we formulated and calculated the total antiviral activity of APOBEC3F and APOBEC3G based on the estimated initial growth rates of viral loads in vivo. Interestingly, we quantitatively demonstrated that compared with APOBEC3G, the antiviral activity of APOBEC3F was widely distributed but skewed toward lower activity, although their mean values were similar. We concluded that APOBEC3G markedly and robustly restricted the initial stages of viral growth in vivo. This is the first report to quantitatively elucidate how APOBEC3F and APOBEC3G differ in their anti-HIV-1 modes in vivo.

Revealing uninfected and infected target cell dynamics from peripheral blood data in highly and less pathogenic simian/human immunodeficiency virus infected Rhesus macaque

Since chimeric simian and human immunodeficiency viruses (SHIVs) used here, that is, SHIV-#64 and -KS661 utilize both CCR5 and CXCR4 chemokine receptors, they have broad target cell properties. A highly pathogenic SHIV strain, SHIV-KS661, causes an infection that systemically depletes the CD4⁺ T cells of Rhesus macaques, while a less pathogenic strain, SHIV-#64, does not cause severe symptoms in the macaques. In our previous studies, we established in vitro quantification system for virus infection dynamics, and concluded that SHIV-KS661 effectively produces infectious virions compared with SHIV-#64 in the HSC-F cell culture. However, in vivo dynamics of SHIV infection have not been well understood. To quantify SHIV-#64 and -KS661 infection dynamics in Rhesus macaques, we developed a novel approach and analyzed total CD4⁺ T cells and viral load in peripheral blood, and reproduced the expected dynamics for the uninfected and infected CD4⁺ T cells in silico. Using our previous cell culture experimental datasets, we revealed that an infection rate constant is different between SHIV-#64 and -KS661, but the viral production rate and the death rate are similar for the both strains. Thus, here, we assumed these relations in our in vivo data and carried out the data fitting. We performed Bayesian estimation for the whole dataset using MCMC sampling, and simultaneously fitted our novel model to total CD4⁺ T cells and viral load of SHIV-#64 and -KS661 infection. Our analyses explained that the Malthusian parameter (i.e., fitness of virus infection) and the basic reproduction number (i.e., potential of virus infection) for SHIV-KS661 are significantly higher than those of SHIV-#64. In addition, we demonstrated that the number of uninfected CD4⁺ T cells in SHIV-KS661 infected Rhesus macaques decreases to the significantly lower value than that before the inoculation several days earlier compared with SHIV-#64 infection. Taken together, the differences between SHIV-#64 and -KS661 infection before the peak viral load might determine the subsequent destiny, that is, whether the systemic CD4⁺ T cell depletion occurs or the host immune response develop.

Stochastic Dynamics of the Latently Infected Cell Reservoir During HIV Infection

The presence of cells latently infected with HIV is currently considered to be a major barrier to viral eradication within a patient. Here, we consider birth-death-immigration models for the latent cell population in a single patient, and present analytical results for the size of this population in the absence of treatment. We provide results both at steady state (viral set point), and during the non-equilibrium setting of early infection. We obtain semi-analytic results showing how latency-reversing drugs might be expected to affect the size of the latent pool over time. We also analyze the probability of rare mutant viral strains joining the latent cell population, allowing for steady-state and dynamic viral populations within the host.

Size-dependent Catalysis of Chlorovirus Population Growth by A Messy Feeding Predator

Many chloroviruses replicate in endosymbiotic zoochlorellae that are protected from infection by their symbiotic host. To reach the high virus concentrations that often occur in natural systems, a mechanism is needed to release zoochlorellae from their hosts. We demonstrate that the ciliate predator Didinium nasutum foraging on zoochlorellae-bearing Paramecium bursaria can release live zoochlorellae from the ruptured prey cell that can then be infected by chloroviruses. The catalysis process is very effective, yielding roughly 95% of the theoretical infectious virus yield as determined by sonication of P. bursaria. Chlorovirus activation is more effective with smaller Didinia, as larger Didinia typically consume entire P. bursaria cells without rupturing them, precluding the release of zoochlorellae. We also show that the timing of Chlorovirus growth is tightly linked to the predator-prey cycle between Didinium and Paramecium, with the most rapid increase in chloroviruses temporally linked to the peak foraging rate of Didinium, supporting the idea that predator-prey cycles can drive cycles of Chlorovirus abundance.

A PDE multiscale model of hepatitis C virus infection can be transformed to a system of ODEs

Direct-acting antivirals (DAAs) treat hepatitis C virus (HCV) by targeting its intracellular viral replication. DAAs are effective and deliver high clinical performance against HCV infection, but optimization of the DAA treatment regimen is ongoing. Different classes of DAAs are currently under development, and HCV treatments that combine two or three DAAs with different action mechanisms are being improved. To accurately quantify the antiviral effect of these DAA treatments and optimize multi-drug combinations, we must describe the intracellular viral replication processes corresponding to the action mechanisms by multiscale mathematical models. Previous multiscale models of HCV treatment have been formulated by partial differential equations (PDEs). However, estimating the parameters from clinical datasets requires comprehensive numerical PDE computations that are time consuming and often converge poorly. Here, we propose a user-friendly approach that transforms a standard PDE multiscale model of HCV infection (Guedj J et al., Proc. Natl. Acad. Sci. USA 2013; 110(10):3991-6) to mathematically identical ordinary differential equations (ODEs) without any assumptions. We also confirm consistency between the numerical solutions of our transformed ODE model and the original PDE model. This relationship between a detailed structured model and a simple model is called ``model aggregation problem'' and a fundamental important in theoretical biology. In particular, as the parameters of ODEs can be estimated by already established methods, our transformed ODE model and its modified version avoid the time-consuming computations and are broadly available for further data analysis.

Dynamics of virus and immune response in multi-epitope network

The host immune response can often efficiently suppress a virus infection, which may lead to selection for immune-resistant viral variants within the host. For example, during HIV infection, an array of CTL immune response populations recognize specific epitopes (viral proteins) presented on the surface of infected cells to effectively mediate their killing. However HIV can rapidly evolve resistance to CTL attack at different epitopes, inducing a dynamic network of interacting viral and immune response variants. We consider models for the network of virus and immune response populations, consisting of Lotka-Volterra-like systems of ordinary differential equations. Stability of feasible equilibria and corresponding uniform persistence of distinct variants are characterized via a Lyapunov function. We specialize the model to a "binary sequence" setting, where for n epitopes there can be [Formula: see text] distinct viral variants mapped on a hypercube graph. The dynamics in several cases are analyzed and sharp polychotomies are derived characterizing persistent variants. In particular, we prove that if the viral fitness costs for gaining resistance to each epitope are equal, then the system of [Formula: see text] virus strains converges to a "perfectly nested network" with less than or equal to [Formula: see text] persistent virus strains. Overall, our results suggest that immunodominance, i.e. relative strength of immune response to an epitope, is the most important factor determining the persistent network structure.

Dynamics of lentiviral infection in vivo in the absence of adaptive immune responses

Understanding the dynamics of acute viral infection is crucial for developing strategies to prevent and control infection. In this study, lentiviral dynamics in a host without adaptive immunity were examined in order to determine kinetic parameters of infection and quantify the effect of neutralizing antibodies in preventing infection, using mathematical modeling of data from equine infectious anemia virus (EIAV) infection of horses with severe combined immunodeficiency (SCID). Estimated parameters were used to calculate the basic reproductive number and virus doubling time and found that the rate that antibodies neutralized virus was ~18 times greater than the virus clearance rate. These results establish EIAV replication kinetics in SCID horses and the minimal efficacy of antibodies that blocked infection. Furthermore, they indicate that EIAV is at most mildly cytopathic. This study advances our understanding of EIAV infection and may have important implications for the control of other viral infections, including HIV.

A highly pathogenic simian/human immunodeficiency virus effectively produces infectious virions compared with a less pathogenic virus in cell culture

BACKGROUND

The host range of human immunodeficiency virus (HIV) is quite narrow. Therefore, analyzing HIV-1 pathogenesis in vivo has been limited owing to lack of appropriate animal model systems. To overcome this, chimeric simian and human immunodeficiency viruses (SHIVs) that encode HIV-1 Env and are infectious to macaques have been developed and used to investigate the pathogenicity of HIV-1 in vivo. So far, we have many SHIV strains that show different pathogenesis in macaque experiments. However, dynamic aspects of SHIV infection have not been well understood. To fully understand the dynamic properties of SHIVs, we focused on two representative strains-the highly pathogenic SHIV, SHIV-KS661, and the less pathogenic SHIV, SHIV-#64-and measured the time-course of experimental data in cell culture.

METHODS

We infected HSC-F with SHIV-KS661 and -#64 and measured the concentration of Nef-negative (target) and Nef-positive (infected) HSC-F cells, the total viral load, and the infectious viral load daily for 9 days. The experiments were repeated at two different multiplicities of infection, and a previously developed mathematical model incorporating the infectious and non-infectious viruses was fitted to the full dataset of each strain simultaneously to characterize the infection dynamics of these two strains.

RESULTS AND CONCLUSIONS

We quantified virological indices including virus burst sizes and basic reproduction number of both SHIV-KS661 and -#64. Comparing the burst size of total and infectious viruses (viral RNA copies and TCID₅₀, respectively), we found that there was a statistically significant difference between the infectious virus burst size of SHIV-KS661 and -#64, while there was no significant difference between the total virus burst size. Furthermore, our analyses showed that the fraction of infectious virus among the produced SHIV-KS661 viruses, which is defined as the infectious viral load (TCID₅₀/ml) divided by the total viral load (RNA copies/ml), is more than 10-fold higher than that of SHIV-#64 during overall infection (i.e., for 9 days). Taken together, we conclude that the highly pathogenic SHIV produces infectious virions more effectively than the less pathogenic SHIV in cell culture.

Global properties of nested network model with application to multi-epitope HIV/CTL dynamics

Mathematical modeling and analysis can provide insight on the dynamics of ecosystems which maintain biodiversity in the face of competitive and prey-predator interactions. Of primary interests are the underlying structure and features which stabilize diverse ecological networks. Recently Korytowski and Smith (Theor Ecol 8(1):111-120, 2015) proved that a perfectly nested infection network, along with appropriate life history trade-offs, leads to coexistence and persistence of bacteria-phage communities in a chemostat model. In this article, we generalize their model in order to apply it to the within-host dynamics virus and immune response, in particular HIV and CTL (Cytotoxic T Lymphocyte) cells. Our model can describe sequential viral escape from dominant immune responses and rise in subdominant immune responses, consistent with observed patterns of HIV/CTL evolution. We find a Lyapunov function for the system which leads to rigorous characterization of persistent viral and immune variants, along with informing upon equilibria stability and global dynamics. Results are interpreted in the context of within-host HIV/CTL evolution and numerical simulations are provided.

Modelling Ebola virus dynamics: Implications for therapy

Ebola virus (EBOV) causes a severe, often fatal Ebola virus disease (EVD), for which no approved antivirals exist. Recently, some promising anti-EBOV drugs, which are experimentally potent in animal models, have been developed. However, because the quantitative dynamics of EBOV replication in humans is uncertain, it remains unclear how much antiviral suppression of viral replication affects EVD outcome in patients. Here, we developed a novel mathematical model to quantitatively analyse human viral load data obtained during the 2000/01 Uganda EBOV outbreak and evaluated the effects of different antivirals. We found that nucleoside analogue- and siRNA-based therapies are effective if a therapy with a >50% inhibition rate is initiated within a few days post-symptom-onset. In contrast, antibody-based therapy requires not only a higher inhibition rate but also an earlier administration, especially for otherwise fatal cases. Our results demonstrate that an appropriate choice of EBOV-specific drugs is required for effective EVD treatment.

Compartmentalized dynamics of cytomegalovirus replication in treated congenital infection

BACKGROUND

Cytomegalovirus (CMV) is the most prevalent congenital infection in developed countries. A significant number of infected infants develop long-term neurodevelopmental and hearing impairment irrespective of whether disease is detectable at birth. Studies of viral load and replication dynamics have informed the treatment of CMV in adult populations but no similar data exist in neonates.

OBJECTIVES

To study CMV virus kinetics in different body fluids of babies treated for congenital infection.

STUDY DESIGN

CMV virus load was sequentially analyzed in blood, urine and saliva in 17 babies treated for symptomatic congenital CMV infection.

RESULTS

Virus was detectable in the urine and saliva of all babies at baseline but in only 15/17 in blood. At the end of 6 weeks of antiviral treatment CMV remained detectable in 9/14 blood samples, 9/12 urine samples and 4/7 salivary swabs. Median half-life (T1/2) of virus decline in blood was 2.4 days (IQR 1.9-3.3) and basic reproductive number (Ro) was 2.3. Although T1/2 values were similar in urine and saliva to those observed in blood, virus dynamics differed both during and after treatment.

CONCLUSIONS

T1/2 and Ro in blood in this group of neonates were similar to values derived from studies of immunocompromised adults. The persistent viremia observed in treated neonates cannot therefore be adequately explained by the virus dynamics early in treatment. The different dynamics exhibited in blood and urine suggests that studying changes in distinct body compartments may assist in further understanding long-term manifestations of disease.

Quantifying the effect of Vpu on the promotion of HIV-1 replication in the humanized mouse model

BACKGROUND

Tetherin is an intrinsic anti-viral factor impairing the release of nascent HIV-1 particles from infected cells. Vpu, an HIV-1 accessory protein, antagonizes the anti-viral action of tetherin. Although previous studies using in vitro cell culture systems have revealed the molecular mechanisms of the anti-viral action of tetherin and the antagonizing action of Vpu against tetherin, it still remains unclear how Vpu affects the kinetics of HIV-1 replication in vivo.

RESULTS

To quantitatively assess the role of Vpu in viral replication in vivo, we analyzed time courses of experimental data with viral load and target cell levels in the peripheral blood of humanized mice infected with wild-type and vpu-deficient HIV-1. Our recently developed mathematical model describes the acute phase of this infection reasonably, and allowed us to estimate several parameters characterizing HIV-1 infection in mice. Using a technique of Bayesian parameter estimation, we estimate distributions of the basic reproduction number of wild-type and vpu-deficient HIV-1. This reveals that Vpu markedly increases the rate of viral replication in vivo.

CONCLUSIONS

Combining experiments with mathematical modeling, we provide an estimate for the contribution of Vpu to viral replication in humanized mice.

Markov process models of the dynamics of HIV reservoirs

While latently infected CD4+ T cells are extremely sparse, they are a reality that prevents HIV from being cured, and their dynamics are largely unknown. We begin with a two-state Markov process that models the outcomes of regular but infrequent blood tests for latently infected cells in an HIV positive patient under drug therapy. We then model the hidden dynamics of a latently infected CD4+ T cell in an HIV positive patient and show there is a limiting distribution, which indicates in which compartments the HIV typically can be found. Our model shows that the limiting distribution of latently infected cells reveals the presence of latency in every compartment with positive probability, supported by clinical data. We also show that the hidden Markov model determines the outcome of blood tests and analyze its connection to the blood test model.

Front propagation speeds of T7 virus mutants

We propose a new reaction-diffusion model with an eclipse time to study the spread of viruses on bacterial populations. This new model is both biologically and physically sound, unlike previous ones. We determine important parameter values from experimental data, such as the one-step growth. We verify the proposed model by comparing theoretical and experimental data of the front propagation speed for several T7 virus strains.

Modeling multiple infection of cells by viruses: Challenges and insights

The multiple infection of cells with several copies of a given virus has been demonstrated in experimental systems, and has been subject to previous mathematical modeling approaches. Such models, especially those based on ordinary differential equations, can be characterized by difficulties and pitfalls. One such difficulty arises from what we refer to as multiple infection cascades. That is, such models subdivide the infected cell population into sub-populations that are carry i viruses, and each sub-population can in principle always be further infected to contain i + 1 viruses. In order to study the model with numerical simulations, the infection cascade needs to be cut artificially, and this can influence the results. This is shown here in the context of the simplest setting that involves a single, homogeneous virus population. If the viral replication rate is sufficiently fast, then most infected cells will accumulate in the last member of the infection cascade, leading to incorrect numerical results. This can be observed even with relatively long infection cascades, and in this case computational costs associated with a sufficiently long infection cascade can render this approach impractical. We subsequently examine a more complex scenario where two virus types/strains with different fitness are allowed to compete. Again, we find that the length of the infection cascade can have a crucial influence on the results. Competitive exclusion can be observed for shorter infection cascades, while coexistence can be observed for longer infection cascades. More subtly, the length of the infection cascade can influence the equilibrium level of the populations in numerical simulations. Studying the model in a parameter regime where an increase in the infection cascade length does not influence the results, we examine the effect of multiple infection on the outcome of competition. We find that multiple infection can promote coexistence of virus types if there is a degree of intracellular niche separation. If this is not the case, the only outcome is competitive exclusion, similar to equivalent models that do not take into account multiple infection of cells. We further find that multiple infection has a reduced ability to allow coexistence if virus spread is spatially restricted compared to a well-mixed system. These results provide important insights when analyzing and interpreting multiple infection models.

Contribution of HIV-1 genomes that do not integrate to the basic reproductive ratio of the virus

Recent experimental data indicate that HIV-1 DNA that fails to integrate (from now on called uDNA) can by itself successfully produce infectious offspring virions in resting T cells that become activated after infection. This scenario is likely important at the initial stages of the infection. We use mathematical models to calculate the relative contribution of unintegrated and integrated viral DNA to the basic reproductive ratio of the virus, R0, and the models are parameterized with preliminary data. This is done in the context of both free virus spread and transmission of the virus through virological synapses. For free virus transmission, we find that under preliminary parameter estimates, uDNA might contribute about 20% to the total R0. This requires that a single copy of uDNA can successfully replicate. If the presence of more than one uDNA copy is required for replication, uDNA does not contribute to R0. For synaptic transmission, uDNA can contribute to R0 regardless of the number of uDNA copies required for replication. The larger the number of viruses that are successfully transmitted per synapse, however, the lower the contribution of uDNA to R0 because this increases the chances that at least one virus integrates. Using available parameter values, uDNA can maximally contribute 20% to R0 in this case. We argue that the contribution of uDNA to virus reproduction might also be important for continued low level replication of HIV-1 in the presence of integrase inhibitor therapy. Assuming a 20% contribution of uDNA to the overall R0, our calculations suggest that R0=1.6 in the absence of virus integration. While these are rough estimates based on preliminary data that are currently available, this analysis provides a framework for future experimental work which should directly measure key parameters.

Tissue architecture, feedback regulation, and resilience to viral infection

Tissue homeostasis is one of the central requirements for the existence of multicellular organisms, and is maintained by complex feedback regulatory processes. Homeostasis can be disturbed by diseases such as viruses and tumors. Here, we use mathematical models to investigate how tissue architecture influences the ability to maintain tissue homeostasis during viral infections. In particular, two different tissue designs are considered. In the first scenario, stem cells secrete negative feedback factors that influence the balance between stem cell self-renewal and differentiation. In the second scenario, those feedback factors are not produced by stem cells but by differentiated cells. The model shows a tradeoff. If feedback factors are produced by stem cells, then a viral infection will lead to a significant reduction in the number of differentiated cells leading to tissue pathology, but the number of stem cells is not affected at equilibrium. In contrast, if the feedback factors are produced by differentiated cells, a viral infection never reduces the number of tissue cells at equilibrium because the feedback mechanism compensates for virus-induced cells death. The number of stem cells, however, becomes elevated, which could increase the chance of these stem cells to accumulate mutations that can drive cancer. Interestingly, if the virus interferes with feedback factor production by cells, uncontrolled growth can occur in the presence of the virus even in the absence of genetic lesions in cells. Hence, the optimal design would be to produce feedback factors by both stem and differentiated cells in quantities that strike a balance between protecting against tissue destruction and stem cell elevation during infection.