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

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

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

Schematic representation of the full model.

<p>A detailed description of the model, the set of differential equations, and meaning and values for variables, and parameters are given in the Materials and Methods section and Tables <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0150568#pone.0150568.t001" target="_blank">1</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0150568#pone.0150568.t002" target="_blank">2</a>.</p

Model predictions for the susceptible epithelial cells (<i>T</i>) and infected epithelial cells (<i>I</i>).

<p>The figure shows the LP and HP H1N1 and H5N1 scenarios corresponding to the viral load and macrophage model results shown in Figs <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0150568#pone.0150568.g002" target="_blank">2</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0150568#pone.0150568.g003" target="_blank">3</a>. Parameter values are listed in Tables <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0150568#pone.0150568.t002" target="_blank">2</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0150568#pone.0150568.t003" target="_blank">3</a>.</p

Best fits of the model to the experimental data for viral load and macrophages reported in [28].

<p>Macrophages as predicted by the model are <i>M</i>_<i>A</i><i>+M</i>_<i>I</i>. Parameter values for the best fit estimates are listed in Tables <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0150568#pone.0150568.t002" target="_blank">2</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0150568#pone.0150568.t003" target="_blank">3</a>.</p

Parameter definitions, units, values, and references.

<p>Parameter definitions, units, values, and references.</p

Best fit parameter values to the viral load and macrophage data.

<p>The best fits are displayed in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0150568#pone.0150568.g002" target="_blank">Fig 2</a>.</p

Impact of HP associated parameter values on total viral load and total activated macrophages.

<p>We individually varied each of the parameters <i>α</i>, <i>p</i>_<i>M</i>, and <i>γ</i> in a range of 0.01–100 times its original value for HP infections shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0150568#pone.0150568.t003" target="_blank">Table 3</a>. All other parameters were kept at the values reported for the HP scenario in Tables <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0150568#pone.0150568.t002" target="_blank">2</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0150568#pone.0150568.t003" target="_blank">3</a>.</p

Definitions of variables used in the model and their initial values.

<p>Definitions of variables used in the model and their initial values.</p