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The Restitution Portrait. Introduction: Electrical restitution, relating action potential duration (APD) to diastolic interval (DI), was believed to determine the stability of heart rhythm. However, recent studies demonstrate that stability also depends on long-term APD changes caused by memory. This study presents a new method for investigation of rate- and memory-dependent aspects of restitution and for assessment of mapping models of APD. Methods and Results: Bullfrog ventricular myocardium was paced with a 'perturbed downsweep protocol.' Starting from a basic cycle length (BCL) of 1,000 ms, the tissue was paced until steady state was achieved, followed by single beats of longer and shorter cycle lengths. BCL was decreased by 50 to 100 ms and the process repeated. All APDs were plotted as a function of the preceding DI, which allowed simultaneous observation of dynamic, S1-S2, and two constant-BCL restitution curves in a 'restitution portrait.' Responses were classified as 1:1 (stimulus:response), transient 2:2, or persistent 2:2 (alternans) and were related to the slopes of the restitution curves. None of these slopes approached unity for the persistent 2:2 response, demonstrating that the traditional restitution condition does not predict alternans. The restitution portrait was used to evaluate three mapping models of APD. The models with no memory and with one-beat memory did not produce restitution portraits similar to the experimental one. A model with two-beat memory produced a qualitatively similar portrait. Conclusion: The restitution portrait allows a more comprehensive assessment of cardiac dynamics than methods used to date. Further study of models with memory may result in a clinical criterion for electrical instability. (J Cardiovasc Electrophysiol, Vol. 15, pp. 1-12, June 2004) [ABSTRACT FROM AUTHOR]

Oncolytic (cancer-killing) virus treatment is a promising new therapy for cancer, with many viruses currently being tested for their ability to eradicate tumors. One of the major stumbling blocks to the development of this treatment modality has been preventing spread of the virus to non-cancerous cells. Our recent ability to manipulate RNA and DNA now allows for the possibility of creating designer viruses specifically targeted to cancer cells, thereby significantly reducing unwanted side effects in patients. In this study, we use a partial differential equation model to determine the characteristics of a virus needed to contain spread of an oncolytic virus within a spherical tumor and prevent it from spreading to non-cancerous cells outside the tumor. We find that oncolytic viruses that have different infection rates or different cell death rates in cancer and non-cancerous cells can be made to stay within the tumor. We find that there is a minimum difference in infection rates or cell death rates that will contain the virus and that this threshold value depends on the growth rate of the cancer. Identification of these types of thresholds can help researchers develop safer strains of oncolytic viruses allowing further development of this promising treatment., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier Ltd. All rights reserved.)

SARS-CoV-2 caused a global pandemic and is now an endemic virus that will require continued antiviral and vaccine development. A possible new treatment modality was recently suggested that would use vesicular stomatitis virus (VSV) modified to express the ACE2 receptor. Since the modified VSV expresses the cell surface receptor that is used by the SARS-CoV-2 spike protein, the thought is that SARS-CoV-2 virions would bind to the modified VSV and thus be neutralized. Additionally, since SARS-CoV-2 infected cells also express the spike protein, the modified VSV could potentially infect these cells, allowing for its own replication, but also potentially interfering with replication of SARS-CoV-2. This idea has not yet been tested experimentally, but we can investigate the feasibility of this possible treatment theoretically. In this manuscript, we develop a mathematical model of this suggested treatment and explore conditions under which it might be effective. We find that treatment with modified VSV does little to change the SARS-CoV-2 time course except when the treatment is applied at the onset of the SARS-CoV-2 infection at very high doses. In this case, VSV reduces the peak SARS-CoV-2 viral load, but lengthens the duration of the SARS-CoV-2 infection. Thus, we find that modified VSV treatment is unlikely to be effective largely because it does not prevent infection of cells by SARS-CoV-2., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024. Published by Elsevier Ltd.)

Viral coinfections are responsible for a significant portion of cases of patients hospitalized with influenza-like illness. As our awareness of viral coinfections has increased, researchers have started to experimentally examine some of the virus-virus interactions underlying these infections. One mechanism of interaction between viruses is through the innate immune response. This seems to occur primarily through the interferon response, which generates an antiviral state in nearby uninfected cells, a phenomenon know as the bystander effect. Here, we develop a mathematical model of two viruses interacting through the bystander effect. We find that when the rate of removal of cells to the protected state is high, growth of the first virus is suppressed, while the second virus enjoys sole access to the protected cells, enhancing its growth. Conversely, growth of the second virus can be fully suppressed if its ability to infect the protected cells is limited., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier Ltd. All rights reserved.)

SARS-CoV-2 has the ability to form large multi-nucleated cells known as syncytia. Little is known about how syncytia affect the dynamics of the infection or severity of the disease. In this manuscript, we extend a mathematical model of cell-cell fusion assays to estimate both the syncytia formation rate and the average duration of the fusion phase for five strains of SARS-CoV-2. We find that the original Wuhan strain has the slowest rate of syncytia formation (6.4×10 -4 /h), but takes only 4.0 h to complete the fusion process, while the Alpha strain has the fastest rate of syncytia formation (0.36 /h), but takes 7.6 h to complete the fusion process. The Beta strain also has a fairly fast syncytia formation rate (9.7×10 -2 /h), and takes the longest to complete fusion (8.4 h). The D614G strain has a fairly slow syncytia formation rate (2.8×10 -3 /h), but completes fusion in 4.0 h. Finally, the Delta strain is in the middle with a syncytia formation rate of 3.2×10 -2 /h and a fusing time of 6.1 h. We note that for these SARS-CoV-2 strains, there appears to be a tradeoff between the ease of forming syncytia and the speed at which they complete the fusion process., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier Inc. All rights reserved.)

Many viruses have the ability to cause cells to fuse into large multi-nucleated cells, known as syncytia. While the existence of syncytia has long been known and its importance in helping spread viral infection within a host has been understood, few mathematical models have incorporated syncytia formation or examined its role in viral dynamics. This review examines mathematical models that have incorporated virus-mediated cell fusion and the insights they have provided on how syncytia can change the time course of an infection. While the modeling efforts are limited, they show promise in helping us understand the consequences of syncytia formation if future modeling efforts can be coupled with appropriate experimental efforts to help validate the models., (© 2024. The Author(s), under exclusive license to Springer Nature Switzerland AG.)

Influenza virus infection can result in a wide range of clinical outcomes from asymptomatic infection to severe disease and death. While there are undoubtedly many factors that contribute to the severity of disease, one possible contributing factor that needs more investigation is the route of infection. In this study, we use previously published data from cynomolgus macaques infected with A/Vietnam/1203/04 (H5N1) via either aerosol (with and without bronchoalveolar lavages (BAL)) or a combined intrabronchial, oral, and intranasal route. We fit a mathematical model of within host viral kinetics to the data and find that when the macaques are infected via the aerosol route with subsequent BAL, the infecting time is significantly lower than for the other two groups. A lower infecting time indicates that the virus spreads from cell to cell more rapidly for aerosol infection with BAL than for the combined deposition or aerosol deposition alone. This study helps elucidate the mechanism behind different infection outcomes caused by differences in routes of infection., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 Elsevier Inc. All rights reserved.)

New cancer treatment modalities that limit patient discomfort need to be developed. One possible new therapy is the use of oncolytic (cancer-killing) viruses. It is only recently that our ability to manipulate viral genomes has allowed us to consider deliberately infecting cancer patients with viruses. One key consideration is to ensure that the virus exclusively targets cancer cells and does not harm nearby non-cancerous cells. Here, we use a mathematical model of viral infection to determine the characteristics a virus would need to have in order to eradicate a tumor, but leave non-cancerous cells untouched. We conclude that the virus must differ in its ability to infect the two different cell types, with the infection rate of non-cancerous cells needing to be less than one hundredth of the infection rate of cancer cells. Differences in viral production rate or infectious cell death rate alone are not sufficient to protect non-cancerous cells., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 Elsevier Ltd. All rights reserved.)

Oncolytic adenoviruses (OAds) present a promising path for cancer treatment due to their selectivity in infecting and lysing tumor cells and their ability to stimulate the immune response. In this study, we use an ordinary differential equation (ODE) model of tumor growth inhibited by oncolytic virus activity to parameterize previous research on the effect of genetically re-engineered OAds in A549 lung cancer tumors in murine models. We find that the data are best fit by a model that accounts for an immune response, and that the immune response provides a mechanism for elimination of the tumor. We also find that parameter estimates for the most effective OAds share characteristics, most notably a high infection rate and low viral clearance rate, that might be potential reasons for these viruses' efficacy in delaying tumor growth. Further studies observing E1A and P19 recombined viruses in different tumor environments may further illuminate the extent of the effects of these genetic modifications.

Defective viral genomes (DVGs) are viral genomes that contain only a partial viral RNA and so cannot replicate within cells on their own. If a cell containing DVGs is subsequently infected with a complete viral genome, the DVG can then use the missing proteins expressed by the full genome in order to replicate itself. Since the cell is producing defective genomes, it has less resources to produce fully functional virions and thus release of complete virions is often suppressed. Here, we use data from challenge studies of respiratory syncytial virus (RSV) in healthy adults to quantify the effect of DVGs. We use a mathematical model to fit the data, finding that late onset of DVGs and prolonged DVG detection are associated with lower infection rates and higher clearance rates. This result could have implications for the use of DVGs as a therapeutic.

Illness negatively affects all aspects of life and one major cause of illness is viral infections. Some viral infections can last for weeks; others, like influenza (the flu), can resolve quickly. During infections, uninfected cells can replicate in order to replenish the cells that have died due to the virus. Many viral models, especially those for short-lived infections like influenza, tend to ignore cellular regeneration since many think that uncomplicated influenza resolves much faster than cells regenerate. This research accounts for cellular regeneration, using an agent-based framework, and varies the regeneration rate in order to understand how cell regeneration affects viral infection dynamics under assumptions of different modes of transmission. We find that although the general trends in peak viral load, time of viral peak, and chronic viral load as regeneration rate changes are the same for cell-free or cell-to-cell transmission, the changes are more extreme for cell-to-cell transmission due to limited access of infected cells to newly generated cells., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022 Elsevier Ltd. All rights reserved.)

Several viruses have the ability to form large multinucleated cells known as syncytia. Many properties of syncytia and the role they play in the evolution of a viral infection are not well understood. One basic question that has not yet been answered is how quickly syncytia form. We use a novel mathematical model of cell-cell fusion assays and apply it to experimental data from SARS-CoV-2 fusion assays to provide the first estimates of virus-mediated cell fusion rate. We find that for SARS-CoV2, the fusion rate is in the range of 6 × 10 -4 -12×10 -4 /h. We also use our model to compare fusion rates when the protease TMPRSS2 is overexpressed (2-4 times larger fusion rate), when the protease furin is removed (one third the original fusion rate), and when the spike protein is altered (1/10th the original fusion rate). The use of mathematical models allows us to provide additional quantitative information about syncytia formation., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022 Elsevier Inc. All rights reserved.)

Some viruses have the ability to block or suppress growth of other viruses when simultaneously present in the same host. This type of viral interference or viral block has been suggested as a potential interaction between some respiratory viruses including SARS-CoV-2 and other co-circulating respiratory viruses. We explore how one virus' ability to block infection with another within a single host affects spread of the viruses within a susceptible population using a compartmental epidemiological model. We find that population-level effect of viral block is a decrease in the number of people infected with the suppressed virus. This effect is most pronounced when the viruses have similar epidemiological parameters. We use the model to simulate co-circulating epidemics of SARS-CoV-2 and influenza, respiratory syncytial virus (RSV), and rhinovirus, finding that co-circulation of SARS-CoV-2 and RSV causes the most suppression of SARS-CoV-2. Paradoxically, co-circulation of SARS-CoV-2 and influenza or rhinovirus results in almost no change in the SARS-CoV-2 epidemic, but causes a shift in the timing of the influenza and rhinovirus epidemics., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Pinky and Dobrovolny.)

With the advent of rapid multiplex PCR, physicians have been able to test for multiple viral pathogens when a patient presents with influenza-like illness. This has led to the discovery that many respiratory infections are caused by more than one virus. Antiviral treatment of viral coinfections can be complex because treatment of one virus will affect the time course of the other virus. Since effective antivirals are only available for some respiratory viruses, careful consideration needs to be given on the effect treating one virus will have on the dynamics of the other virus, which might not have available antiviral treatment. In this study, we use mathematical models of viral coinfections to assess the effect of antiviral treatment on coinfections. We examine the effect of the mechanism of action, relative growth rates of the viruses, and the assumptions underlying the interaction of the viruses. We find that high antiviral efficacy is needed to suppress both infections. If high doses of both antivirals are not achieved, then we run the risk of lengthening the duration of coinfection or even of allowing a suppressed virus to replicate to higher viral titers.

During the COVID-19 pandemic, mathematical modeling of disease transmission has become a cornerstone of key state decisions. To advance the state-of-the-art host viral modeling to handle future pandemics, many scientists working on related issues assembled to discuss the topics. These discussions exposed the reproducibility crisis that leads to inability to reuse and integrate models. This document summarizes these discussions, presents difficulties, and mentions existing efforts towards future solutions that will allow future model utility and integration. We argue that without addressing these challenges, scientists will have diminished ability to build, disseminate, and implement high-impact multi-scale modeling that is needed to understand the health crises we face.

One of the primary cancer treatment modalities is chemotherapy. Unfortunately, traditional anti-cancer drugs are often not selective and cause damage to healthy cells, leading to serious side effects for patients. For this reason more targeted therapeutics and drug delivery methods are being developed. The effectiveness of new treatments is initially determined via in vitro cell viability assays, which determine the IC 50  of the drug. However, these assays are known to result in estimates of IC 50  that depend on the measurement time, possibly resulting in over- or under-estimation of the IC 50 . Here, we test the possibility of using cell growth curves and fitting of mathematical models to determine the IC 50  as well as the maximum efficacy of a drug ( ε max ). We measured cell growth of MCF-7 and HeLa cells in the presence of different concentrations of doxorubicin and fit the data with a logistic growth model that incorporates the effect of the drug. This method leads to measurement time-independent estimates of IC 50  and ε max , but we find that ε max  is not identifiable. Further refinement of this methodology is needed to produce uniquely identifiable parameter estimates., Competing Interests: Conflict of interestThe authors have no conflicts of interest to declare., (© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021.)

The SARS-CoV-2 virus disproportionately causes serious illness and death in older individuals. In order to have the greatest impact in decreasing the human toll caused by the virus, antiviral treatment should be targeted to older patients. For this, we need a better understanding of the differences in viral dynamics between SARS-CoV-2 infection in younger and older adults. In this study, we use previously published averaged viral titre measurements from the nose and throat of SARS-CoV-2 infection in young and aged cynomolgus macaques to parametrize a viral kinetics model. We find that all viral kinetics parameters differ between young and aged macaques in the nasal passages, but that there are fewer differences in parameter estimates from the throat. We further use our parametrized model to study the antiviral treatment of young and aged animals, finding that early antiviral treatment is more likely to lead to a lengthening of the infection in aged animals, but not in young animals., (© 2021 The Authors.)

Respiratory syncytial virus can cause severe illness and even death, particularly in infants. The increased severity of disease in young children is thought to be due to a lack of previous exposure to the virus as well as the limited immune response in infants. While studies have examined the clinical differences in disease between infants and adults, there has been limited examination of how the viral dynamics differ as infants develop. In this study, we apply a mathematical model to data from cotton rats and ferrets of different ages to assess how viral kinetics parameters change as the animals age. We find no clear trend in the viral decay rate, infecting time, and basic reproduction number as the animals age. We discuss possible reasons for the null result including the limited data, lack of detail of the mathematical model, and the limitations of animal models., (Copyright © 2021 Elsevier B.V. All rights reserved.)

Respiratory syncytial virus (RSV) is a common, contagious infection of the lungs and the respiratory tract. RSV is characterized by syncytia, which are multinuclear cells created by cells that have fused together. We use a mathematical model to study how different assumptions about the viral production and lifespan of syncytia change the resulting infection time course. We find that the effect of syncytia on viral titer is only apparent when the basic reproduction number for infection via syncytia formation is similar to the reproduction number for cell free viral transmission. When syncytia fusion rate is high, we find the presence of syncytia can lead to slowly growing infections if viral production is suppressed in syncytia. Our model provides insight into how the presence of syncytia can affect the time course of a viral infection., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2021 Elsevier Ltd. All rights reserved.)

The SARS coronavirus (SARS-CoV) has the potential to cause serious disease that can spread rapidly around the world. Much of our understanding of SARS-CoV pathogenesis comes from in vitro experiments. Unfortunately, in vitro experiments cannot replicate all the complexity of the in vivo infection. For example, proteases in the respiratory tract cleave the SARS-CoV surface protein to facilitate viral entry, but these proteases are not present in vitro. Unfortunately, proteases might also have an effect on other parts of the replication cycle. Here, we use mathematical modeling to estimate parameters characterizing viral replication for SARS-CoV in the presence of trypsin or elastase, and in the absence of either. In addition to increasing the infection rate, the addition of trypsin and elastase causes lengthening of the eclipse phase duration and the infectious cell lifespan., (Copyright © 2021 Elsevier B.V. All rights reserved.)

Outside the host, viruses will eventually lose their ability to infect cells due to conformational changes that occur to proteins on the viral capsid. In order to undergo a conformational change, these proteins require energy to activate the chemical reaction that leads to the conformational change. In this study, data from the literature is used to calculate the energy required for viral inactivation for a variety of different viruses by means of the Arrhenius equation. We find that some viruses (rhinovirus, poliovirus, human immunodeficiency virus, Alkhumra hemorrhagic fever virus, and hepatitis A virus) have high inactivation energies, indicative of breaking of a chemical double bond. We also find that several viruses (respiratory syncytial virus, poliovirus, and norovirus) have nonlinear Arrhenius plots, suggesting that there is more than a single pathway for inactivation of these viruses.

The novel coronavirus severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has rapidly spread around the world, causing serious illness and death and creating a heavy burden on the healthcare systems of many countries. Since the virus first emerged in late November 2019, its spread has coincided with peak circulation of several seasonal respiratory viruses, yet some studies have noted limited coinfections between SARS-CoV-2 and other viruses. We use a mathematical model of viral coinfection to study SARS-CoV-2 coinfections, finding that SARS-CoV-2 replication is easily suppressed by many common respiratory viruses. According to our model, this suppression is because SARS-CoV-2 has a lower growth rate (1.8/d) than the other viruses examined in this study. The suppression of SARS-CoV-2 by other pathogens could have implications for the timing and severity of a second wave., (© 2020 Wiley Periodicals LLC.)

The world is in the midst of a pandemic caused by a novel coronavirus and is desperately searching for possible treatments. The antiviral remdesivir has shown some effectiveness against SARS-CoV-2 in vitro and in a recent animal study. We use data from a study of remdesivir in rhesus macaques to fit a viral kinetics model in an effort to determine the most appropriate mathematical descripton of the effect of remdesivir. We find statistically significant differences in the viral decay rate and use this to inform a possible mathematical formulation of the effect of remdesivir. Unfortunately, this model formulation suggests that the application of remdesivir will lengthen SARS-CoV-2 infections, putting into question its potential clinical benefit., (Copyright © 2020 Elsevier Inc. All rights reserved.)

SARS-CoV-2 (Severe acute respiratory syndrome coronavirus 2) causes a variety of responses in those who contract the virus, ranging from asymptomatic infections to acute respiratory failure and death. While there are likely multiple mechanisms triggering severe disease, one potential cause of severe disease is the size of the initial inoculum. For other respiratory diseases, larger initial doses lead to more severe outcomes. We investigate whether there is a similar link for SARS-CoV-2 infections using the combination of an agent-based model (ABM) and a partial differential equation model (PDM). We use the model to examine the viral time course for different sizes of initial inocula, generating dose-response curves for peak viral load, time of viral peak, viral growth rate, infection duration, and area under the viral titer curve. We find that large initial inocula lead to short infections, but with higher viral titer peaks; and that smaller initial inocula lower the viral titer peak, but make the infection last longer.

SARS-CoV-2 started causing infections in humans in late 2019 and has spread rapidly around the world. While the number of symptomatically infected and severely ill people is high and has overwhelmed the medical systems of many countries, there is mounting evidence that some of the rapid spread of this virus has been driven by asymptomatic infections. In this study, we use a compartmental mathematical model of a viral epidemic that includes asymptomatic infection to examine the role of asymptomatic individuals in the spread of the infection. We apply the model to epidemics in California, Florida, New York, and Texas, finding that asymptomatic infections far outnumber reported symptomatic infections at the peak of the epidemic in all four states. The model suggests that relaxing of social distancing measures too quickly could lead to a rapid rise in the number of cases, driven in part by asymptomatic infections., Competing Interests: The authors have declared that no competing interests exist.

The analysis of viral kinetics models is mostly achieved by numerical methods. We present an approach via a Magnus expansion that allows us to give an approximate solution to the interferon-dependent viral infection model of influenza which is compared with numerical results. The time of peak viral load is calculated from the approximation and stays within 10% in the studied range of interferon (IFN) efficacy ϵ ∈ [0, 1000]. We utilize our solution to interpret the effect of varying IFN efficacy, suggesting a competition between virions and interferon that can cause an additional peak in the usually exponential increase in the viral load., (Copyright © 2020 Elsevier Ltd. All rights reserved.)

In order to determine correct dosage of chemotherapy drugs, the effect of the drug must be properly quantified. There are two important values that characterize the effect of the drug: εmax is the maximum possible effect of a drug, and IC50 is the drug concentration where the effect diminishes by half. There is currently a problem with the way these values are measured because they are time-dependent measurements. We use mathematical models to determine how the εmax and IC50 values depend on measurement time and model choice. Seven ordinary differential equation models (ODE) are used for the mathematical analysis; the exponential, Mendelsohn, logistic, linear, surface, Bertalanffy, and Gompertz models. We use the models to simulate tumor growth in the presence and absence of treatment with a known IC50 and εmax. Using traditional methods, we then calculate the IC50 and εmax values over fifty days to show the time-dependence of these values for all seven mathematical models. The general trend found is that the measured IC50 value decreases and the measured εmax increases with increasing measurement day for most mathematical models. Unfortunately, the measured values of IC50 and εmax rarely matched the values used to generate the data. Our results show that there is no optimal measurement time since models predict that IC50 estimates become more accurate at later measurement times while εmax is more accurate at early measurement times., Competing Interests: The authors have declared that no competing interests exist.

Respiratory syncytial virus can lead to serious lower respiratory infection (LRI), particularly in children and the elderly. LRI can cause longer infections, lingering respiratory problems, and higher incidence of hospitalization. In this paper, we use a simplified ordinary differential equation model of viral dynamics to study the role of transport mechanisms in the occurrence of LRI. Our model uses two compartments to simulate the upper respiratory tract and the lower respiratory tract (LRT) and assumes two distinct types of viral transfer between the two compartments: diffusion and advection. We find that a range of diffusion and advection values lead to long-lasting infections in the LRT, elucidating a possible mechanism for the severe LRI infections observed in humans.

Background: Respiratory viral infections are a leading cause of mortality worldwide. As many as 40% of patients hospitalized with influenza-like illness are reported to be infected with more than one type of virus. However, it is not clear whether these infections are more severe than single viral infections. Mathematical models can be used to help us understand the dynamics of respiratory viral coinfections and their impact on the severity of the illness. Most models of viral infections use ordinary differential equations (ODE) that reproduce the average behavior of the infection, however, they might be inaccurate in predicting certain events because of the stochastic nature of viral replication cycle. Stochastic simulations of single virus infections have shown that there is an extinction probability that depends on the size of the initial viral inoculum and parameters that describe virus-cell interactions. Thus the coinfection dynamics predicted by the ODE might be difficult to observe in reality., Results: In this work, a continuous-time Markov chain (CTMC) model is formulated to investigate probabilistic outcomes of coinfections. This CTMC model is based on our previous coinfection model, expressed in terms of a system of ordinary differential equations. Using the Gillespie method for stochastic simulation, we examine whether stochastic effects early in the infection can alter which virus dominates the infection., Conclusions: We derive extinction probabilities for each virus individually as well as for the infection as a whole. We find that unlike the prediction of the ODE model, for similar initial growth rates stochasticity allows for a slower growing virus to out-compete a faster growing virus.

Molecular diagnostic techniques have revealed that approximately 43% of the patients hospitalized with influenza-like illness are infected by more than one viral pathogen, sometimes leading to long-lasting infections. It is not clear how the heterologous viruses interact within the respiratory tract of the infected host to lengthen the duration of what are usually short, self-limiting infections. We develop a mathematical model which allows for single cells to be infected simultaneously with two different respiratory viruses (superinfection) to investigate the possibility of chronic coinfections. We find that a model with superinfection and cell regeneration has a stable chronic coinfection fixed point, while superinfection without cell regeneration produces only acute infections. This analysis suggests that both superinfection and cell regeneration are required to sustain chronic coinfection via this mechanism since coinfection is maintained by superinfected cells that allow slow-growing infections a chance to infect cells and continue replicating. This model provides a possible mechanism for chronic coinfection independent of any viral interactions via the immune response., (Copyright © 2019 Elsevier Ltd. All rights reserved.)

Respiratory syncytial virus (RSV) is a respiratory infection that can cause serious illness, particularly in infants. In this study, we test four different model implementations for the effect of a fusion inhibitor, including one model that combines different drug effects, by fitting the models to data from a study of TMC353121 in African green monkeys. We use mathematical modeling to estimate the drug efficacy parameters, ε max , the maximum efficacy of the drug, and EC 50 , the drug concentration needed to achieve half the maximum effect. We find that if TMC353121 is having multiple effects on viral kinetics, more detailed data, using different treatment delays, is needed to detect this effect., (Copyright © 2018 Elsevier Ltd. All rights reserved.)

Combination therapy for influenza can have several benefits, from reducing the emergence of drug resistant virus strains to decreasing the cost of antivirals. However, there are currently only two classes of antivirals approved for use against influenza, limiting the possible combinations that can be considered for treatment. However, new antivirals are being developed that target different parts of the viral replication cycle, and their potential for use in combination therapy should be considered. The role of antiviral mechanism of action in the effectiveness of combination therapy has not yet been systematically investigated to determine whether certain antiviral mechanisms of action pair well in combination. Here, we use a mathematical model of influenza to model combination treatment with antivirals having different mechanisms of action to measure peak viral load, infection duration, and synergy of different drug combinations. We find that antivirals that lower the infection rate and antivirals that increase the duration of the eclipse phase perform poorly in combination with other antivirals.

Experimental results in vitro and in animal models are used to guide researchers in testing vaccines or treatment in humans. However, viral kinetics are different in vitro, in animals, and in humans, so it is sometimes difficult to translate results from one system to another. In this study, we use a mathematical model to fit experimental data from multiple cycle respiratory syncytial virus (RSV) infections in vitro, in african green monkey (AGM), and in humans in order to quantitatively compare viral kinetics in the different systems. We find that there are differences in viral clearance rate, productively infectious cell lifespan, and eclipse phase duration between in vitro and in vivo systems and among different in vivo systems. We show that these differences in viral kinetics lead to different estimates of drug effectiveness of fusion inhibitors in vitro and in AGM than in humans., (Copyright © 2018 Elsevier Inc. All rights reserved.)

Severe, long-lasting influenza infections are often caused by new strains of the virus. The long duration of these infections leads to an increased opportunity for the emergence of drug resistant mutants. This is particularly problematic since for new strains there is often no vaccine, so drug treatment is the first line of defense. One strategy for trying to minimize drug resistance is to apply drugs periodically. During treatment phases the wild-type virus decreases, but resistant virus might increase; when there is no treatment, wild-type virus will hopefully out-compete the resistant virus, driving down the number of resistant virus. A stochastic model of severe influenza is combined with a model of drug resistance to simulate long-lasting infections and intermittent treatment with two types of antivirals: neuraminidase inhibitors, which block release of virions; and adamantanes, which block replication of virions. Each drug's ability to reduce emergence of drug resistant mutants is investigated. We find that cell regeneration is required for successful implementation of intermittent treatment and that the optimal cycling parameters change with regeneration rate., (Copyright © 2018 Elsevier Ltd. All rights reserved.)

Influenza and respiratory syncytial virus (RSV) cause acute infections of the respiratory tract. Since the viruses both cause illnesses with similar symptoms, researchers often try to apply knowledge gleaned from study of one virus to the other virus. This can be an effective and efficient strategy for understanding viral dynamics or developing treatment strategies, but only if we have a full understanding of the similarities and differences between the two viruses. This study used mathematical modeling to quantitatively compare the viral kinetics of in vitro RSV and influenza virus infections. Specifically, we determined the viral kinetics parameters for RSV A2 and three strains of influenza virus, A/WSN/33 (H1N1), A/Puerto Rico/8/1934 (H1N1), and pandemic H1N1 influenza virus. We found that RSV viral titer increases at a slower rate and reaches its peak value later than influenza virus. Our analysis indicated that the slower increase of RSV viral titer is caused by slower spreading of the virus from one cell to another. These results provide estimates of dynamical differences between influenza virus and RSV and help provide insight into the virus-host interactions that cause observed differences in the time courses of the two illnesses in patients.

Globally, rotavirus is the most common cause of diarrhea in children younger than 5 years of age, however, a quantitative understanding of the infection dynamics is still lacking. In this paper, we present the first study to extract viral kinetic parameters for in vitro rotavirus infections in the REH cell tumor line. We use a mathematical model of viral kinetics to extract parameter values by fitting the model to data from rotavirus infection of REH cells. While accurate results for some of the parameters of the mathematical model were not achievable due to its global non-identifiability, we are able to quantify approximately the time course of the infection for the first time. We also find that the basic reproductive number of rotavirus, which gives the number of secondary infections from a single infected cell, is much greater than one. Quantifying the kinetics of rotavirus leads not only to a better understanding of the infection process, but also provides a method for quantitative comparison of kinetics of different strains or for quantifying the effectiveness of antiviral treatment., (Copyright © 2017 Elsevier B.V. All rights reserved.)

The emergence of influenza drug resistance has become of particular interest as current planning for an influenza pandemic involves using massive amounts of antiviral drugs. We use semi-stochastic simulations to examine the emergence of drug resistant mutants during the course of a single infection within a patient in the presence and absence of antiviral therapy. We specifically examine three factors and their effect on the emergence of drug-resistant mutants: antiviral mechanism, the immune response, and surface proteins. We find that adamantanes, because they act at the start of the replication cycle to prevent infection, are less likely to produce drug-resistant mutants than NAIs, which act at the end of the replication cycle. A mismatch between surface proteins and internal RNA results in drug-resistant mutants being less likely to emerge, and emerging later in the infection because the mismatch gives antivirals a second chance to prevent propagation of the mutation. The immune response subdues slow growing infections, further reducing the probability that a drug resistant mutant will emerge and yield a drug-resistant infection. These findings improve our understanding of the factors that contribute to the emergence of drug resistance during the course of a single influenza infection.

Many mathematical models of respiratory viral infections do not include regeneration of cells within the respiratory tract, arguing that the infection is resolved before there is significant cellular regeneration. However, recent studies have found that ∼40% of patients hospitalized with influenza-like illness are infected with at least two different viruses, which could potentially lead to longer-lasting infections. In these longer infections, cell regeneration might affect the infection dynamics, in particular, allowing for the possibility of chronic coinfections. Several mathematical models have been used to describe cell regeneration in infection models, though the effect of model choice on the predicted time course of viral coinfections is not clear. We investigate four mathematical models incorporating different mechanisms of cell regeneration during respiratory viral coinfection to determine the effect of cell regeneration on infection dynamics. We perform linear stability analysis for each of the models and find the steady states analytically. The analysis suggests that chronic illness is possible but only with one viral species; chronic coexistence of two different viral species is not possible with the regeneration models considered here.

Antiviral therapy is a first line of defence against new influenza strains. Current pandemic preparations involve stock- piling oseltamivir, an oral neuraminidase inhibitor (NAI), so rapidly determining the effectiveness of NAIs against new viral strains is vital for deciding how to use the stockpile. Previous studies have shown that it is possible to extract the drug efficacy of antivirals from the viral decay rate of chronic infections. In the present work, we use a nonlinear mathematical model representing the course of an influenza infection to explore the possibility of extracting NAI drug efficacy using only the observed viral titer decay rates seen in patients. We first show that the effect of a time-varying antiviral concentration can be accurately approximated by a constant efficacy. We derive a relationship relating the true treatment dose and time elapsed between doses to the constant drug dose required to approximate the time- varying dose. Unfortunately, even with the simplification of a constant drug efficacy, we show that the viral decay rate depends not just on drug efficacy, but also on several viral infection parameters, such as infection and production rate, so that it is not possible to extract drug efficacy from viral decay rate alone., Competing Interests: H.M.D. is currently receiving a grant from Janssen R&D, and C.A.A.B. has previously received a grant from AstraZeneca R&D.

Studies have shown that simultaneous infection of the respiratory tract with at least two viruses is common in hospitalized patients, although it is not clear whether these infections are more or less severe than single virus infections. We use a mathematical model to study the dynamics of viral coinfection of the respiratory tract in an effort to understand the kinetics of these infections. Specifically, we use our model to investigate coinfections of influenza, respiratory syncytial virus, rhinovirus, parainfluenza virus, and human metapneumovirus. Our study shows that during coinfections, one virus can block another simply by being the first to infect the available host cells; there is no need for viral interference through immune response interactions. We use the model to calculate the duration of detectable coinfection and examine how it varies as initial viral dose and time of infection are varied. We find that rhinovirus, the fastest-growing virus, reduces replication of the remaining viruses during a coinfection, while parainfluenza virus, the slowest-growing virus is suppressed in the presence of other viruses.

Viral titer data collected in vitro or in vivo is often analyzed by extracting viral titer characteristics such as peak viral titer, time of viral peak and area under the curve (AUC). Researchers compare these characteristics in the absence and presence of various concentrations of antivirals in an attempt to quantify the effect of antivirals. Often these characteristics are estimated using only measured data points, although fitting of simple mathematical models to estimate these parameters is becoming more prevalent. In this article, our aim is to compare the estimates of different viral titer characteristics using three different approaches. The first approach is the traditional method that uses estimates based on experimentally measured data. The second approach relies on the use of a linear model to fit the viral titer data. The third approach uses an exponential model for the fitting process and the parameters of interest are extracted from there. The mathematical models are tested using in vivo and in vitro influenza infection data. Estimates of viral titer characteristics using either of the two fitting approaches were similar, but differed from estimates using the traditional method., (Copyright © 2016 Elsevier B.V. All rights reserved.)

Background: While mathematical models are often used to predict progression of cancer and treatment outcomes, there is still uncertainty over how to best model tumor growth. Seven ordinary differential equation (ODE) models of tumor growth (exponential, Mendelsohn, logistic, linear, surface, Gompertz, and Bertalanffy) have been proposed, but there is no clear guidance on how to choose the most appropriate model for a particular cancer., Methods: We examined all seven of the previously proposed ODE models in the presence and absence of chemotherapy. We derived equations for the maximum tumor size, doubling time, and the minimum amount of chemotherapy needed to suppress the tumor and used a sample data set to compare how these quantities differ based on choice of growth model., Results: We find that there is a 12-fold difference in predicting doubling times and a 6-fold difference in the predicted amount of chemotherapy needed for suppression depending on which growth model was used., Conclusion: Our results highlight the need for careful consideration of model assumptions when developing mathematical models for use in cancer treatment planning.

Antivirals are the first line of defence against influenza, so drug efficacy should be re-evaluated for each new strain. However, due to the time and expense involved in assessing the efficacy of drug treatments both in vitro and in vivo, treatment regimens are largely not re-evaluated even when strains are found to be resistant to antivirals. Mathematical models of the infection process can help in this assessment, but for accurate model predictions, we need to measure model parameters characterizing the efficacy of antivirals. We use computer simulations to explore whether in vitro experiments can be used to extract drug efficacy parameters for use in viral kinetics models. We find that the efficacy of neuraminidase inhibitors can be determined by measuring viral load during a single cycle assay, while the efficacy of adamantanes can be determined by measuring infected cells during the preparation stage for the single cycle assay.

Respiratory syncytial virus (RSV) is the most common cause of bronchiolitis and pneumonia in children younger than 1 year of age in the United States. Moreover, RSV is being recognized more often as a significant cause of respiratory illness in older adults. Although RSV has been studied both clinically and in vitro, a quantitative understanding of the infection dynamics is still lacking. In this paper, we study the effect of uncertainty in the main parameters of a viral kinetics model of RSV. We first characterize the RSV replication cycle and extract parameter values by fitting the mathematical model to in vivo data from eight human subjects. We then use Monte Carlo numerical simulations to determine how uncertainty in the parameter values will affect model predictions. We find that uncertainty in the infection rate, eclipse phase duration, and infectious lifespan most affect the predicted dynamics of RSV. This study provides the first estimate of in vivo RSV infection parameters, helping to quantify RSV dynamics. Our assessment of the effect of uncertainty will help guide future experimental design to obtain more precise parameter values.

The role of the host immune response in determining the severity and duration of an influenza infection is still unclear. In order to identify severity factors and more accurately predict the course of an influenza infection within a human host, an understanding of the impact of host factors on the infection process is required. Despite the lack of sufficiently diverse experimental data describing the time course of the various immune response components, published mathematical models were constructed from limited human or animal data using various strategies and simplifying assumptions. To assess the validity of these models, we assemble previously published experimental data of the dynamics and role of cytotoxic T lymphocytes, antibodies, and interferon and determined qualitative key features of their effect that should be captured by mathematical models. We test these existing models by confronting them with experimental data and find that no single model agrees completely with the variety of influenza viral kinetics responses observed experimentally when various immune response components are suppressed. Our analysis highlights the strong and weak points of each mathematical model and highlights areas where additional experimental data could elucidate specific mechanisms, constrain model design, and complete our understanding of the immune response to influenza.

Treatment of seasonal influenza viral infections using antivirals such as neuraminidase inhibitors (NAIs) has been proven effective if administered within 48h post-infection. However, there is growing evidence that antiviral treatment of infections with avian-derived strains even as late as 6 days post-infection (dpi) can significantly reduce infection severity and duration. Using a mathematical model of in-host influenza viral infections which can capture the kinetics of both a short-lived, typical, seasonal infection and a severe infection exhibiting sustained viral titer, we explore differences in the effects of NAI treatment on both types of influenza viral infections. Comparison of our model's behavior against experimental data from patients naturally infected with avian strains yields estimates for the times at which patients were infected that are consistent with those reported by the patients, and estimates of drug efficacies that are lower for patients who died than for those who recovered. In addition, our model suggests that the sustained, high, viral titers often seen in more severe influenza virus infections are the reason why antiviral treatment delayed by as much as 6 dpi will still lead to reduced viral titers and shortened illness. We conclude that NAIs may be an effective and beneficial treatment strategy against more severe strains of influenza virus characterized by high, sustained, viral titers. We believe that our mathematical model will be an effective tool in guiding treatment of severe influenza viral infections with antivirals., (Copyright © 2010 Elsevier Ltd. All rights reserved.)

Several mechanisms have been proposed to account for the marked increase in severity of human infections with avian compared to human influenza strains, including increased cytokine expression, poor immune response, and differences in target cell receptor affinity. Here, the potential effect of target cell tropism on disease severity is studied using a mathematical model for in-host influenza viral infection in a cell population consisting of two different cell types. The two cell types differ only in their susceptibility to infection and rate of virus production. We show the existence of a parameter regime which is characterized by high viral loads sustained long after the onset of infection. This finding suggests that differences in cell tropism between influenza strains could be sufficient to cause significant differences in viral titer profiles, similar to those observed in infections with certain strains of influenza A virus. The two target cell mathematical model offers good agreement with experimental data from severe influenza infections, as does the usual, single target cell model albeit with biologically unrealistic parameters. Both models predict that while neuraminidase inhibitors and adamantanes are only effective when administered early to treat an uncomplicated seasonal infection, they can be effective against more severe influenza infections even when administered late.

Traditionally, it was believed that cardiac rhythm stability was governed by the slope of the restitution curve (RC), which relates the duration of an action potential to the preceding diastolic interval. However, a single RC does not exist; rate-dependence leads to multiple distinct RCs. We measure spatial differences in the steady-state action potential duration (APD), as well as in three different RCs: the S1-S2 (SRC), constant-basic-cycle-length (BRC), and dynamic (DRC), and correlate these differences with the tissue's propensity to develop alternans. The results show that spatial differences in APD, SRC slope, and DRC slope are correlated with the tissue's propensity to exhibit alternans. These results may lead to a new diagnostic approach to identifying patients with vulnerability to arrhythmias, which will involve pacing at slow rates and analyzing spatial differences in restitution properties.

A panoramic cardiac imaging system consisting of three high-speed CCD cameras has been developed to image the surface electrophysiology of a rabbit heart via fluorescence imaging using a voltage-sensitive fluorescent dye. A robust, unique mechanical system was designed to accommodate the three cameras and to adapt to the requirements of future experiments. A unified computer interface was created for this application - a single workstation controls all three CCD cameras, illumination, stimulation, and a stepping motor that rotates the heart. The geometric reconstruction algorithms were adapted from a previous cardiac imaging system. We demonstrate the system by imaging a polymorphic cardiac tachycardia.