Exploring the impact of inoculum dose on host immunity and morbidity to inform model-based vaccine design.

Vaccination is an effective method to protect against infectious diseases. An important consideration in any vaccine formulation is the inoculum dose, i.e., amount of antigen or live attenuated pathogen that is used. Higher levels generally lead to better stimulation of the immune response but might cause more severe side effects and allow for less population coverage in the presence of vaccine shortages. Determining the optimal amount of inoculum dose is an important component of rational vaccine design. A combination of mathematical models with experimental data can help determine the impact of the inoculum dose. We illustrate the concept of using data and models to inform inoculum dose determination for vaccines, wby fitting a mathematical model to data from influenza A virus (IAV) infection of mice and human parainfluenza virus (HPIV) infection of cotton rats at different inoculum doses. We use the model to map inoculum dose to the level of immune protection and morbidity and to explore how such a framework might be used to determine an optimal inoculum dose. We show how a framework that combines mathematical models with experimental data can be used to study the impact of inoculum dose on important outcomes such as immune protection and morbidity. Our findings illustrate that the impact of inoculum dose on immune protection and morbidity can depend on the specific pathogen and that both protection and morbidity do not necessarily increase monotonically with increasing inoculum dose. Once vaccine design goals are specified with required levels of protection and acceptable levels of morbidity, our proposed framework can help in the rational design of vaccines and determination of the optimal amount of inoculum.

Modeling within-host dynamics of influenza virus infection including immune responses.

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.

Correction: Within-Host Models of High and Low Pathogenic Influenza Virus Infections: The Role of Macrophages.

[This corrects the article DOI: 10.1371/journal.pone.0150568.].

Within-Host Models of High and Low Pathogenic Influenza Virus Infections: The Role of Macrophages.

The World Health Organization identifies influenza as a major public health problem. While the strains commonly circulating in humans usually do not cause severe pathogenicity in healthy adults, some strains that have infected humans, such as H5N1, can cause high morbidity and mortality. Based on the severity of the disease, influenza viruses are sometimes categorized as either being highly pathogenic (HP) or having low pathogenicity (LP). The reasons why some strains are LP and others HP are not fully understood. While there are likely multiple mechanisms of interaction between the virus and the immune response that determine LP versus HP outcomes, we focus here on one component, namely macrophages (MP). There is some evidence that MP may both help fight the infection and become productively infected with HP influenza viruses. We developed mathematical models for influenza infections which explicitly included the dynamics and action of MP. We fit these models to viral load and macrophage count data from experimental infections of mice with LP and HP strains. Our results suggest that MP may not only help fight an influenza infection but may contribute to virus production in infections with HP viruses. We also explored the impact of combination therapies with antivirals and anti-inflammatory drugs on HP infections. Our study suggests a possible mechanism of MP in determining HP versus LP outcomes, and how different interventions might affect infection dynamics.

Connecting within and between-hosts dynamics in the influenza infection-staged epidemiological models with behavior change.

Influenza viruses are a major public health problem worldwide. Although influenza has been extensively researched, there are still many aspects that are not fully understood such as the effects of within and between-hosts dynamics and their impact on behavior change. Here, we develop mathematical models with multiple infection stages and estimate parameters based on within-host data to investigate the impact of behavior change on influenza dynamics. We divide the infected population into three and four groups based on the age of the infection, which corresponds to viral load shedding. We consider within-host data on viral shedding to estimate the length and force of infection of the different infectivity stages. Our results show that behavior changes, due to exogenous events (e.g., media coverage) and disease symptoms, are effective in delaying and lowering an epidemic peak. We show that the dynamics of viral shedding and symptoms, during the infection, are key features when considering epidemic prevention strategies. This study improves our understanding of the spread of influenza virus infection in the population and provides information about the impact of emergent behavior and its connection to the within and between-hosts dynamics.

Modeling the impact of twitter on influenza epidemics.

Influenza remains a serious public-health problem worldwide. The rising popularity and scale of social networking sites such as Twitter may play an important role in detecting, affecting, and predicting influenza epidemics. In this paper, we develop a simple mathematical model including the dynamics of ``tweets'' --- short, 140-character Twitter messages that may enhance the awareness of disease, change individual's behavior, and reduce the transmission of disease among a population during an influenza season. We analyze the model by deriving the basic reproductive number and proving the stability of the steady states. A Hopf bifurcation occurs when a threshold curve is crossed, which suggests the possibility of multiple outbreaks of influenza. We also perform numerical simulations, conduct sensitivity test on a few parameters related to tweets, and compare modeling predictions with surveillance data of influenza-like illness reported cases and the percentage of tweets self-reporting flu during the 2009 H1N1 flu outbreak in England and Wales. These results show that social media programs like Twitter may serve as a good indicator of seasonal influenza epidemics and influence the emergence and spread of the disease.

Modeling dynamics of culex pipiens complex populations and assessing abatement strategies for West Nile Virus.

The primary mosquito species associated with underground stormwater systems in the United States are the Culex pipiens complex species. This group represents important vectors of West Nile virus (WNV) throughout regions of the continental U.S. In this study, we designed a mathematical model and compared it with surveillance data for the Cx. pipiens complex collected in Beaufort County, South Carolina. Based on the best fit of the model to the data, we estimated parameters associated with the effectiveness of public health insecticide (adulticide) treatments (primarily pyrethrin products) as well as the birth, maturation, and death rates of immature and adult Cx. pipiens complex mosquitoes. We used these estimates for modeling the spread of WNV to obtain more reliable disease outbreak predictions and performed numerical simulations to test various mosquito abatement strategies. We demonstrated that insecticide treatments produced significant reductions in the Cx. pipiens complex populations. However, abatement efforts were effective for approximately one day and the vector mosquitoes rebounded until the next treatment. These results suggest that frequent insecticide applications are necessary to control these mosquitoes. We derived the basic reproductive number (ℜ0) to predict the conditions under which disease outbreaks are likely to occur and to evaluate mosquito abatement strategies. We concluded that enhancing the mosquito death rate results in lower values of ℜ0, and if ℜ0<1, then an epidemic will not occur. Our modeling results provide insights about control strategies of the vector populations and, consequently, a potential decrease in the risk of a WNV outbreak.

A model of HIV-1 infection with two time delays: mathematical analysis and comparison with patient data.

Mathematical models have made considerable contributions to our understanding of HIV dynamics. Introducing time delays to HIV models usually brings challenges to both mathematical analysis of the models and comparison of model predictions with patient data. In this paper, we incorporate two delays, one the time needed for infected cells to produce virions after viral entry and the other the time needed for the adaptive immune response to emerge to control viral replication, into an HIV-1 model. We begin model analysis with proving the positivity and boundedness of the solutions, local stability of the infection-free and infected steady states, and uniform persistence of the system. By developing a few Lyapunov functionals, we obtain conditions ensuring global stability of the steady states. We also fit the model including two delays to viral load data from 10 patients during primary HIV-1 infection and estimate parameter values. Although the delay model provides better fits to patient data (achieving a smaller error between data and modeling prediction) than the one without delays, we could not determine which one is better from the statistical standpoint. This highlights the need of more data sets for model verification and selection when we incorporate time delays into mathematical models to study virus dynamics.