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Recent studies have demonstrated the superiority of cell-to-cell transmission over cell-free virus infection, and highlighted the role of inflammatory cytokines in enhancing viral infection. To investigate their impacts on viral infection dynamics, we have proposed an HIV infection model incorporating general incidence rates, these infection modes, and two time delays. We derived the basic reproduction number and showed that it governs the existence and local stability of steady states. Through the construction of appropriate Lyapunov functionals and application of the LaSalle invariance principle, we established the global asymptotic stability of both the infection-free and infected steady states.

Understanding population migration is essential for controlling highly infectious diseases. This paper studies the global dynamics of an infectious disease epidemic model incorporating population migration and a stochastic transmission rate. Our findings demonstrate that in deterministic and stochastic environments, the models exhibit global Lyapunov stability near the disease-free equilibrium point, determined by a threshold parameter. Furthermore, we analyze the effect of migration on infectious diseases. We discover that the number of infections and the peak value of the infection curve increase with a higher level of population migration. These results are supported by numerical illustrations that hold epidemiological relevance. Additionally, the disease-free equilibrium of the associated time delay model is linearly asymptotically stable, and the endemic equilibrium exhibits more bifurcation for larger time delay values.

ABSTRACTLive poultry markets (LPMs) are regarded as hubs for avian influenza virus (AIV) transmission in poultry and are a major risk factor in human AIV infections. We performed an AIV surveillance study at a wholesale LPM, where different poultry species were sold in separate stalls, and nine retail LPMs, which received poultry from the wholesale LPM but where different poultry species were sold in one stall, in Guangdong province from 2017 to 2019. A higher AIV isolation rate was observed at the retail LPMs than the wholesale LPM. H9N2 was the dominant AIV subtype and was mainly present in chickens and quails. The genetic diversity of H9N2 viruses was greater at the retail LPMs, where a complex system of two-way transmission between different poultry species had formed. The isolated H9N2 viruses could be classed into four genotypes: G57 and the three novel genotypes, NG164, NG165, and NG166. The H9N2 AIVs isolated from chickens and quails at the wholesale LPM only belonged to the G57 and NG164 genotypes, respectively. However, the G57, NG164, and NG165 genotypes were identified in both chickens and quails at the retail LPMs. We found that the replication and transmission of the NG165 genotype were more adaptive to both poultry and mammalian models than those of its precursor genotype, NG164. Our findings revealed that mixed poultry selling at retail LPMs has increased the genetic diversity of AIVs, which might facilitate the emergence of novel viruses that threaten public health.

In this paper, an insect-parasite-host model with logistic growth of triatomine bugs is formulated to study the transmission between hosts and vectors of the Chagas disease by using dynamical system approach. We derive the basic reproduction numbers for triatomine bugs and Trypanosoma rangeli as two thresholds. The local and global stability of the vector-free equilibrium, parasite-free equilibrium and parasite-positive equilibrium is investigated through the derived two thresholds. Forward bifurcation, saddle-node bifurcation and Hopf bifurcation are proved analytically and illustrated numerically. We show that the model can lose the stability of the vector-free equilibrium and exhibit a supercritical Hopf bifurcation, indicating the occurrence of a stable limit cycle. We also find it unlikely to have backward bifurcation and Bogdanov-Takens bifurcation of the parasite-positive equilibrium. However, the sustained oscillations of infected vector population suggest that Trypanosoma rangeli will persist in all the populations, posing a significant challenge for the prevention and control of Chagas disease.

Environmentally induced or epigenetic-related beta-cell dysfunction and insulin resistance play a critical role in the progression to diabetes. We developed a mathematical modeling framework capable of studying the progression to diabetes incorporating various diabetogenic factors. Considering the heightened risk of beta-cell defects induced by obesity, we focused on the obesity-diabetes model to further investigate the influence of obesity on beta-cell function and glucose regulation. The model characterizes individualized glucose and insulin dynamics over the span of a lifetime. We then fit the model to the longitudinal data of the Pima Indian population, which captures both the fluctuations and long-term trends of glucose levels. As predicted, controlling or eradicating the obesity-related factor can alleviate, postpone, or even reverse diabetes. Furthermore, our results reveal that distinct abnormalities of beta-cell function and levels of insulin resistance among individuals contribute to different risks of diabetes. This study may encourage precise interventions to prevent diabetes and facilitate individualized patient treatment.

Drug-resistant HIV-1 has caused a growing concern in clinic and public health. Although combination antiretroviral therapy can contribute massively to the suppression of viral loads in patients with HIV-1, it cannot lead to viral eradication. Continuing viral replication during sub-optimal therapy (due to poor adherence or other reasons) may lead to the accumulation of drug resistance mutations, resulting in an increased risk of disease progression. Many studies also suggest that events occurring during the early stage of HIV-1 infection (i.e., the first few hours to days following HIV exposure) may determine whether the infection can be successfully established. However, the numbers of infected cells and viruses during the early stage are extremely low and stochasticity may play a critical role in dictating the fate of infection. In this paper, we use stochastic models to investigate viral infection and the emergence of drug resistance of HIV-1. The stochastic model is formulated by a continuous-time Markov chain (CTMC), which is derived based on an ordinary differential equation model proposed by Kitayimbwa et al. that includes both forward and backward mutations. An analytic estimate of the probability of the clearance of HIV infection of the CTMC model near the infection-free equilibrium is obtained by a multitype branching process approximation. The analytical predictions are validated by numerical simulations. Unlike the deterministic dynamics where the basic reproduction number $ \mathcal{R}_0 $ serves as a sharp threshold parameter (i.e., the disease dies out if $ \mathcal{R}_0 < 1 $ and persists if $ \mathcal{R}_0 > 1 $), the stochastic models indicate that there is always a positive probability for HIV infection to be eradicated in patients. In the presence of antiretroviral therapy, our results show that the chance of clearance of the infection tends to increase although drug resistance is likely to emerge.

Mathematical modeling has provided quantitative information consistent with experimental data, greatly improving our understanding of the progression of type 1 and type 2 diabetes. However, diabetes is a complex metabolic disease and has been found to be involved in crosstalk interactions with diverse endocrine diseases. Mathematical models have also been developed to investigate the quantitative impact of various hormonal disorders on glucose imbalance, advancing the precision treatment for secondary diabetes. Here we review the models established for the study of dysglycemia induced by hormonal disorders, such as excessive glucocorticoids, epinephrine, and growth hormone. To investigate the influence of hyperthyroidism on the glucose regulatory system, we also propose a hyperthyroid-diabetes progression model. Model simulations indicate that timely thyroid treatment can halt the progression of hyperglycemia and prevent beta-cell failure. This highlights the diagnosis of hormonal disorders, together withblood sugar tests, as significant measures for the early diagnosis and treatment of diabetes. The work recapitulates updated biological research on the interactions between the glucose regulatory system and other endocrine axes. Further mathematical modeling of secondary diabetes is desired to promote the quantitative study of the disease and the development of individualized diabetic therapies.

After a major outbreak of the coronavirus disease (COVID-19) starting in late December 2019, there were no new cases reported in mainland China for the first time on March 18, 2020, and no new cases reported in Hong Kong Special Administrative Region on April 20, 2020. However, these places had reported new cases and experienced a second wave since June 11, 2020. Here we develop a stochastic discrete-time epidemic model to evaluate the risk of COVID-19 resurgence by analyzing the data from the beginning of the outbreak to the second wave in these three places. In the model, we use an input parameter to represent a few potential risks that may cause a second wave, including asymptomatic infection, imported cases from other places, and virus from the environment such as frozen food packages. The effect of physical distancing restrictions imposed at different stages of the outbreak is also included in the model. Model simulations show that the magnitude of the input and the time between the initial entry and subsequent case confirmation significantly affect the probability of the second wave occurrence. Although the susceptible population size does not change the probability of resurgence, it can influence the severity of the outbreak when a second wave occurs. Therefore, to prevent the occurrence of a future wave, timely screening and detection are needed to identify infected cases in the early stage of infection. When infected cases appear, various measures such as contact tracing and quarantine should be followed to reduce the size of susceptible population in order to mitigate the COVID-19 outbreak.

Abstract In 2017, 46,157 and 3,127 new oropharyngeal cancer (OPC) cases were reported in the U.S. and Texas, respectively. About 70% of OPC were attributed to human papillomavirus (HPV). However, only 51% of U.S. and 43.5% of Texas adolescents have completed the HPV vaccine series. Therefore, modeling the demographic dynamics and transmission of HPV and OPC progression is needed for accurate estimation of the economic and epidemiological impacts of HPV vaccine in a geographic area. An age-structured population dynamic model was developed for the U.S. state of Texas. With Texas-specific model parameters calibrated, this model described the dynamics of HPV-associated OPC in Texas. Parameters for the Year 2010 were used as the initial values, and the prediction for Year 2012 was compared with the real age-specific incidence rates in 23 age groups for model validation. The validated model was applied to predict 100-year age-adjusted incidence rates. The public health benefits of HPV vaccine uptake were evaluated by computer simulation. Compared with current vaccination program, increasing vaccine uptake rates by 50% would decrease the cumulative cases by 4403, within 100 years. The incremental cost-effectiveness ratio of this strategy was $94,518 per quality-adjusted life year (QALY) gained. Increasing the vaccine uptake rate by 50% can: (i) reduce the incidence rates of OPC among both males and females; (ii) improve the quality-adjusted life years for both males and females; (iii) be cost-effective and has the potential to provide tremendous public health benefits in Texas.

The novel Coronavirus (COVID-19) is spreading and has caused a large-scale infection in China since December 2019. This has led to a significant impact on the lives and economy in China and other countries. Here we develop a discrete-time stochastic epidemic model with binomial distributions to study the transmission of the disease. Model parameters are estimated on the basis of fitting to newly reported data from January 11 to February 13, 2020 in China. The estimates of the contact rate and the effective reproductive number support the efficiency of the control measures that have been implemented so far. Simulations show the newly confirmed cases will continue to decline and the total confirmed cases will reach the peak around the end of February of 2020 under the current control measures. The impact of the timing of returning to work is also evaluated on the disease transmission given different strength of protection and control measures.

Vector-borne infectious diseases may involve both horizontal transmission between hosts and transmission from infected vectors to susceptible hosts. In this paper, we incorporate these two transmission modes into a vector-borne disease model that includes general nonlinear incidence rates and the age of infection for both hosts and vectors. We show the existence, uniqueness, nonnegativity, and boundedness of solutions for the model. We study the existence and local stability of steady states, which is shown to be determined by the basic reproduction number. By showing the existence of a global compact attractor and uniform persistence of the system, we establish the threshold dynamics using the Fluctuation Lemma and the approach of Lyapunov functionals. When the basic reproduction number is less than one, the disease-free steady state is globally asymptotically stable and otherwise the disease will be established when there is initial infection force for the hosts. We also study a model with the standard incidence rate and discuss the effect of different incidence rates on the disease dynamics.

Hubei province in China has completed cycle of quarantine-resumption in 23rd Janauary and 8th April 2020, providing a unique opportunity as for now to assess its intervention impact and the pattern of SARS-COV-2 transmission during the quarantine period. In this study, we evaluate the impact of the metropolitan-wide quarantine on the trend and transmission route of the COVID-19 epidemic in Hubei, China. The intervention reduces more than 70% of new infections in both households and the public space, as well as the deaths caused by COVID-19 pneumonia. Household transmission is the dominant route of disease spread regardless of quarantine. This will provide important evidence and scientific insights to other worldwide countries that are currently under quarantine.

Although a number of cost-e ective strategies have been proposed for the chemotherapy of HIV infection, the termination level of viral load and latent reservoir is barely considered. However, the viral load at the termination time is an important biomarker because suppressing viral load to below the detection limit is a major objective of current antiretroviral therapy. The pool size of latently infected cells at the termination time may also play a critical role in predicting a rapid viral rebound to the pretreatment level or post-treatment control. In this work, we formulate an optimal control problem by incorporating the termination level in terms of viral load, latently and productively infected T cells into an existing HIV model. The necessary condition for this optimal system is derived using the Pontryagin's maximum principle. Numerical analysis is carried out using Runge-Kutta 4 method for the forward-backward sweep. Our results suggest that introducing the termination viral load into the control provides a better strategy in HIV chemotherapy.

OBJECTIVES/GOALS: Evaluate the migration and immune suppressive functions of CCR2+/CX3CR1+ myeloid-derived suppressor cells (MDSCs). Integrate experimental data and biologically relevant mathematical models of infiltrating MDSCs in the context of glioblastoma (GBM). METHODS/STUDY POPULATION: CCR2+/CX3CR1+ cells were enriched from bone marrow obtained from CCR2(+/RFP)/CX3CR1(+/GFP) glioma-bearing mice to evaluate their immune-suppressive phenotype and ability to migrate to CCL2 and CCL7. Fluorescent imaging and quantification were performed on a range of tumor sizes to acquire vasculature, tumor, T cell, and MDSC densities. A system of ordinary differential equations was constructed to represent the temporal dynamics of glioma cells, T cells, and MDSCs within the tumor microenvironment. The Approximate Bayesian Computation method was used to determine probability distributions of important parameters, such as the suppression rate of T cells by MDSCs. RESULTS/ANTICIPATED RESULTS: CCR2+/CX3CR1+ M-MDSCs isolated from the bone marrow of tumor-bearing mice suppress CD8+ T cell proliferation and IFNγ production. CCR2+/CX3CR1+ cells migrate to recombinant and KR158B glioma sourced CCL2 and CCL7. Parameter values determined by the Approximate Bayesian Computation method agreed with parameter values from experimental data. This result further validated the structure and results of the mathematical model when performing computer simulations; thus, we can predict CCR2+/CX3CR1+ M-MDSC infiltration over time. DISCUSSION/SIGNIFICANCE: The immune-suppressive microenvironment in GBM contributes to poor outcomes despite standard of care. This study integrates biological and mathematical models to better understand infiltrating immune-suppressive cells, namely CCR2+/CX3CR1+ M-MDSCs. Future directions include modeling immunotherapies.

The sudden onset of the coronavirus (SARS-CoV-2) pandemic has resulted in tremendous loss of human life and economy in more than 210 countries and territories around the world. While self-protections such as wearing masks, sheltering in place, and quarantine policies and strategies are necessary for containing virus transmission, tens of millions of people in the U.S. have lost their jobs due to the shutdown of businesses. Therefore, how to reopen the economy safely while the virus is still circulating in population has become a problem of significant concern and importance to elected leaders and business executives. In this study, mathematical modeling is employed to quantify the profit generation and the infection risk simultaneously from a business entity's perspective. Specifically, an ordinary differential equation model was developed to characterize disease transmission and infection risk. An algebraic equation is proposed to determine the net profit that a business entity can generate after reopening and take into account the costs associated of several protection/quarantine guidelines. All model parameters were calibrated based on various data and information sources. Sensitivity analyses and case studies were performed to illustrate the use of the model in practice. The results show that with a combination of necessary infection protection measures implemented, a business entity may stand a good opportunity to generate a positive net profit while successfully controlling the within-business infection prevalence under that in the general population. The use of personal protective equipment (PPE) is also found of significant importance, especially at the early stage of business reopening.

In addition to direct virus infection of target cells, HIV can also be transferred from infected to uninfected cells (cell-to-cell transmission). These two routes might facilitate viral production and the establishment of the latent virus pool, which is considered as a major obstacle to HIV cure. We studied an HIV infection model including the two infection routes and the time since latent infection. The basic reproductive ratio R0 was derived. The existence, positivity, and boundedness of the solution are proved. We investigated the existence of steady states and their stability, which were shown to depend on R0. We established the global asymptotic dynamical behavior by proving the existence of the global compact attractor and uniform persistence of the system and by applying the method of Lyapunov functionals. In the end, we formulated and solved the optimal control problem for the age-structured model. The necessary condition for minimization of the viral level and the cost of drug treatment was obtained, and numerical simulations of various optimal control strategies were performed.

Abstract Background Poor adherence to either antiretroviral treatment (ART) or pre-exposure prophylaxis (PrEP) can promote drug resistance, though this risk is thought to be considerably higher for ART. In the population of men who have sex with men (MSM) in San Francisco, PrEP coverage reached 9.6% in 2014 and has continued to rise. Given the risk of drug resistance and high cost of second-line drugs, the costs and benefits of initiating ART earlier while expanding PrEP coverage remain unclear. Methods We develop an infection–age-structured mathematical model and fit this model to the annual incidence of AIDS cases and deaths directly, and to resistance and demographic data indirectly. We investigate the impact of six various intervention scenarios (low, medium, or high PrEP coverage, with or without earlier ART) over the next 20 years. Results Low (medium, high) PrEP coverage with earlier ART could prevent 22% (42%, 57%) of a projected 44,508 total new infections and 8% (26%, 41%) of a projected 18,426 new drug-resistant infections, and result in a gain of 43,649 (74,048, 103,270) QALYs over 20 years compared to the status quo, at a cost of $4745 ($78,811, $115,320) per QALY gained, respectively. Conclusions High PrEP coverage with earlier ART is expected to provide the greatest benefit but also entail the highest costs among the strategies considered. This strategy is cost-effective for the San Francisco MSM population, even considering the acquisition and transmission of ART-mediated drug resistance. However, without a substantial increase to San Francisco’s annual HIV budget, the most advisable strategy may be initiating ART earlier, while maintaining current strategies of PrEP enrollment.

HIV can infect cells via virus-to-cell infection or cell-to-cell viral transmission. These two infection modes may occur in a synergistic way and facilitate viral spread within an infected individual. In this paper, we developed an HIV latent infection model including both modes of transmission and time delays between viral entry and integration or viral production. We analysed the model by defining the basic reproductive number, showing the existence, positivity and boundedness of the solution, and proving the local and global stability of the infection-free and infected steady states. Numerical simulations have been performed to illustrate the theoretical results and evaluate the effects of time delays and fractions of infection leading to latency on the virus dynamics. The estimates of the relative contributions to the HIV latent reservoir and the virus population from the two modes of transmission have also been provided.

HIV latency remains a major obstacle to viral elimination. The activation rate of latently infected cells may depend on the age of latent infection. In this paper, we develop a model of HIV infection including age-structured latently infected cells. We mathematically analyse the model and use numerical simulations with different activation functions to show that the model can explain the persistence of low-level viremia and the latent reservoir stability in patients on therapy. Sensitivity tests suggest that the model is robust to the changes of most parameters but is sensitive to the relative magnitude of the net generation rate and the long-term activation rate of latently infected cells. To reduce the sensitivity, we extend the model to include homeostatic proliferation of latently infected cells. The new model is robust in reproducing the long-term dynamics of the virus and latently infected cells observed in patients receiving prolonged combination therapy.

Time delays can affect the dynamics of HIV infection predicted by mathematical models. In this paper, we studied two mathematical models each with two time delays. In the first model with HIV latency, one delay is the time between viral entry into a cell and the establishment of HIV latency, and the other delay is the time between cell infection and viral production. We defined the basic reproductive number and showed the local and global stability of the steady states. Numerical simulations were performed to evaluate the influence of time delays on the dynamics. In the second model with HIV immune response, one delay is the time between cell infection and viral production, and the other delay is the time needed for the adaptive immune response to emerge to control viral replication. With two positive delays, we obtained the stability crossing curves for the model, which were shown to be a series of open-ended curves.

ABSTRACT IMPACT: Predicting therapeutic responses in GBM. OBJECTIVES/GOALS: The goal of this team approach is to integrate mathematical models of glioblastoma (GBM) infiltrating myeloid cells that contribute to the immunosuppressive phenotype in glioma with experimental data to predict therapeutic responses to combined chemokine receptor and immune checkpoint blockade. METHODS/STUDY POPULATION: Orthotopic murine KR158-luc gliomas were established in fluorescent reporter CCR2WT/RFP CX3CR1WT/GFP mice. Subsequently, an anti-CD31 injection was administered to label the vasculature. Fluorescent imaging and quantification of anti-CD3 stained sections were performed on a range of tumor sizes to acquire vasculature, tumor, T cell, and myeloid cell densities. In parallel, a system of ordinary differential equations was formulated based on biological assumptions to evaluate the change over time of tumor cells, T cells, and infiltrating myeloid cells. The model was then refined and validated by experimental results. RESULTS/ANTICIPATED RESULTS: Fluorescent imaging and quantification revealed a correlation between tumor size and abundance of (CX3CR1+, CCR2-) and (CX3CR1+, CCR2+) myeloid cell populations in the tumor microenvironment. The density of these cell populations and vasculature remained constant as the tumors increased in size. Computer simulations of the mathematical model will predict tumor, myeloid, and T cell dynamics. These simulations will be particularly useful to uncover information regarding myeloid cell dynamics, such as cell entry time into the tumor microenvironment. Parameter sensitivity analysis of the model will inform us of the biological processes driving these tumor-immune cell dynamics. DISCUSSION/SIGNIFICANCE OF FINDINGS: GBM is a challenge as current intervention are ineffective. This study improves the understanding of glioma infiltrating myeloid cells and their impact on tumor progression. The data will serve as a basis for quantitatively predicting therapeutic responses of a novel combination treatment.

The Middle East Respiratory Syndrome (MERS) has been identified in 2012 and since then outbreaks have been reported in various localities in the Middle East and in other parts of the world. To help predict the possible dynamics of MERS, as well as ways to contain it, this paper develops a mathematical model for the disease. It has a compartmental structure similar to SARS models and is in the form of a coupled system of nonlinear ordinary differential equations (ODEs). The model predictions are fitted to data from the outbreaks in Riyadh (Saudi Arabia) during 2013-2016. The results reveal that MERS will eventually be contained in the city. However, the containment time and the severity of the outbreaks depend crucially on the contact coefficients and the isolation rate constant. When randomness is added to the model coefficients, the simulations show that the model is sensitive to the scaled contact rate among people and to the isolation rate. The model is analyzed using stability theory for ODEs and indicates that when using only isolation, the endemic steady state is locally stable and attracting. Numerical simulations with parameters estimated from the city of Riyadh illustrate the analytical results and the model behavior, which may have important implications for the disease containment in the city. Indeed, the model highlights the importance of isolation of infected individuals and may be used to assess other control measures. The model is general and may be used to analyze outbreaks in other parts of the Middle East and other areas.

The progressive loss of CD4+ T cell population is the hallmark of HIV-1 infection but the mechanism underlying the slow T cell decline remains unclear. Some recent studies suggested that pyroptosis, a form of programmed cell death triggered during abortive HIV infection, is associated with the release of inflammatory cytokines, which can attract more CD4+ T cells to be infected. In this paper, we developed mathematical models to study whether this mechanism can explain the time scale of CD4+ T cell decline during HIV infection. Simulations of the models showed that cytokine induced T cell movement can explain the very slow decline of CD4+ T cells within untreated patients. The long-term CD4+ T cell dynamics predicted by the models were shown to be consistent with available data from patients in Rio de Janeiro, Brazil. Highly active antiretroviral therapy has the potential to restore the CD4+ T cell population but CD4+ response depends on the effectiveness of the therapy, when the therapy is initiated, and whether there are drug sanctuary sites. The model also showed that chronic inflammation induced by pyroptosis may facilitate persistence of the HIV latent reservoir by promoting homeostatic proliferation of memory CD4+ cells. These results improve our understanding of the long-term T cell dynamics in HIV-1 infection, and support that new treatment strategies, such as the use of caspase-1 inhibitors that inhibit pyroptosis, may maintain the CD4+ T cell population and reduce the latent reservoir size.

The current paradigm for studying hepatitis C virus (HCV) dynamics in patients utilizes a standard viral dynamic model that keeps track of uninfected (target) cells, infected cells, and virus. The model does not account for the dynamics of intracellular viral replication, which is the major target of direct-acting antiviral agents (DAAs). Here we describe and study a recently developed multiscale age-structured model that explicitly considers the potential effects of DAAs on intracellular viral RNA production, degradation, and secretion as virus into the circulation. We show that when therapy significantly blocks both intracellular viral RNA production and virus secretion, the serum viral load decline has three phases, with slopes reflecting the rate of serum viral clearance, the rate of loss of intracellular viral RNA, and the rate of loss of intracellular replication templates and infected cells, respectively. We also derive analytical approximations of the multiscale model and use one of them to analyze data from patients treated for 14 days with the HCV protease inhibitor danoprevir. Analysis suggests that danoprevir significantly blocks intracellular viral production (with mean effectiveness 99.2%), enhances intracellular viral RNA degradation about 5-fold, and moderately inhibits viral secretion (with mean effectiveness 56%). The multiscale model can be used to study viral dynamics in patients treated with other DAAs and explore their mechanisms of action in treatment of hepatitis C.

Influenza virus infection remains a public health problem worldwide. The mechanisms underlying viral control during an uncomplicated influenza virus infection are not fully understood. Here, we developed a mathematical model including both innate and adaptive immune responses to study the within-host dynamics of equine influenza virus infection in horses. By comparing modeling predictions with both interferon and viral kinetic data, we examined the relative roles of target cell availability, and innate and adaptive immune responses in controlling the virus. Our results show that the rapid and substantial viral decline (about 2 to 4 logs within 1 day) after the peak can be explained by the killing of infected cells mediated by interferon activated cells, such as natural killer cells, during the innate immune response. After the viral load declines to a lower level, the loss of interferon-induced antiviral effect and an increased availability of target cells due to loss of the antiviral state can explain the observed short phase of viral plateau in which the viral level remains unchanged or even experiences a minor second peak in some animals. An adaptive immune response is needed in our model to explain the eventual viral clearance. This study provides a quantitative understanding of the biological factors that can explain the viral and interferon kinetics during a typical influenza virus infection.

Widespread resistance among circulating influenza A strains to at least one of the anti-influenza drugs is a major public health concern. A triple combination antiviral drug (TCAD) regimen comprised of amantadine, oseltamivir, and ribavirin has been shown to have synergistic and broad spectrum activity against influenza A strains, including drug resistant strains. Here, we used mathematical modeling along with three different experimental approaches to understand the effects of single agents, double combinations, and the TCAD regimen on resistance in influenza in vitro, including: 1) serial passage at constant drug concentrations, 2) serial passage at escalating drug concentrations, and 3) evaluation of the contribution of each component of the TCAD regimen to the suppression of resistance. Consistent with the modeling which demonstrated that three drugs were required to suppress the emergence of resistance in influenza A, treatment with the TCAD regimen resulted in the sustained suppression of drug resistant viruses, whereas treatment with amantadine alone or the amantadine-oseltamivir double combination led to the rapid selection of resistant variants which comprised ∼100% of the population. Furthermore, the TCAD regimen imposed a high genetic barrier to resistance, requiring multiple mutations in order to escape the effects of all the drugs in the regimen. Finally, we demonstrate that each drug in the TCAD regimen made a significant contribution to the suppression of virus breakthrough and resistance at clinically achievable concentrations. Taken together, these data demonstrate that the TCAD regimen was superior to double combinations and single agents at suppressing resistance, and that three drugs at a minimum were required to impede the selection of drug resistant variants in influenza A virus. The use of mathematical modeling with multiple experimental designs and molecular readouts to evaluate and optimize combination drug regimens for the suppression of resistance may be broadly applicable to other infectious diseases.

For most HIV-infected patients, antiretroviral therapy controls viral replication. However, in some patients drug resistance can cause therapy to fail. Nonetheless, continued therapy with a failing regimen can preserve or even lead to increases in CD4+ T cell counts. To understand the biological basis of these observations, we used mathematical models to explain observations made in patients with drug-resistant HIV treated with enfuvirtide (ENF/T-20), an HIV-1 fusion inhibitor. Due to resistance emergence, ENF was removed from the drug regimen, drug-sensitive virus regrown, and ENF was re-administered. We used our model to study the dynamics of plasma-viral RNA and CD4+ T cell levels, and the competition between drug-sensitive and resistant viruses during therapy interruption and re-administration. Focusing on resistant viruses carrying the V38A mutation in gp41, we found ENF-resistant virus to be 17±3% less fit than ENF-sensitive virus in the absence of the drug, and that the loss of resistant virus during therapy interruption was primarily due to this fitness cost. Using viral dynamic parameters estimated from these patients, we show that although re-administration of ENF cannot suppress viral load, it can, in the presence of resistant virus, increase CD4+ T cell counts, which should yield clinical benefits. This study provides a framework to investigate HIV and T cell dynamics in patients who develop drug resistance to other antiretroviral agents and may help to develop more effective strategies for treatment.

Although potent combination therapy is usually able to suppress plasma viral loads in HIV-1 patients to below the detection limit of conventional clinical assays, a low level of viremia frequently can be detected in plasma by more sensitive assays. Additionally, many patients experience transient episodes of viremia above the detection limit, termed viral blips, even after being on highly suppressive therapy for many years. An obstacle to viral eradication is the persistence of a latent reservoir for HIV-1 in resting memory CD4(+) T cells. The mechanisms underlying low viral load persistence, slow decay of the latent reservoir, and intermittent viral blips are not fully characterized. The quantitative contributions of residual viral replication to viral and the latent reservoir persistence remain unclear. In this paper, we probe these issues by developing a mathematical model that considers latently infected cell activation in response to stochastic antigenic stimulation. We demonstrate that programmed expansion and contraction of latently infected cells upon immune activation can generate both low-level persistent viremia and intermittent viral blips. Also, a small fraction of activated T cells revert to latency, providing a potential to replenish the latent reservoir. By this means, occasional activation of latently infected cells can explain the variable decay characteristics of the latent reservoir observed in different clinical studies. Finally, we propose a phenomenological model that includes a logistic term representing homeostatic proliferation of latently infected cells. The model is simple but can robustly generate the multiphasic viral decline seen after initiation of therapy, as well as low-level persistent viremia and intermittent HIV-1 blips. Using these models, we provide a quantitative and integrated prospective into the long-term dynamics of HIV-1 and the latent reservoir in the setting of potent antiretroviral therapy.

In this paper, we study a predator--prey mite model of Leslie type with generalized Holling IV functional response. The model is shown to have very rich bifurcation dynamics, including subcritical and supercritical Hopf bifurcations, degenerate Hopf bifurcation, focustype and cusp-type degenerate Bogdanov--Takens bifurcations of codimension 3, originating from a nilpotent focus or cusp of codimension 3 that acts as the organizing center for the bifurcation set. Coexistence of multiple steady states, multiple limit cycles, and homoclinic cycles is also found. Interestingly, the coexistence of two limit cycles is guaranteed by investigating generalized Hopf bifurcation and degenerate homoclinic bifurcation, and we also find that two generalized Hopf bifurcation points are connected by a saddle-node bifurcation curve of limit cycles, which indicates the existence of global regime for two limit cycles. Our work extends some results in the literature. [ABSTRACT FROM AUTHOR]