Identifiability investigation of within-host models of acute virus infection.

Uncertainty in parameter estimates from fitting within-host models to empirical data limits the model's ability to uncover mechanisms of infection, disease progression, and to guide pharmaceutical interventions. Understanding the effect of model structure and data availability on model predictions is important for informing model development and experimental design. To address sources of uncertainty in parameter estimation, we used four mathematical models of influenza A infection with increased degrees of biological realism.

A novel within-host model of HIV and nutrition.

In this paper we develop a four compartment within-host model of nutrition and HIV. We show that the model has two equilibria: an infection-free equilibrium and infection equilibrium. The infection free equilibrium is locally asymptotically stable when the basic reproduction number $ \mathcal{R}_0 < 1 $, and unstable when $ \mathcal{R}_0 > 1 $.

Identifiability investigation of within-host models of acute virus infection.

Uncertainty in parameter estimates from fitting within-host models to empirical data limits the model's ability to uncover mechanisms of infection, disease progression, and to guide pharmaceutical interventions. Understanding the effect of model structure and data availability on model predictions is important for informing model development and experimental design. To address sources of uncertainty in parameter estimation, we use four mathematical models of influenza A infection with increased degrees of biological realism.

Optimal control of a multi-scale HIV-opioid model.

In this study, we apply optimal control theory to an immuno-epidemiological model of HIV and opioid epidemics. For the multi-scale model, we used four controls: treating the opioid use, reducing HIV risk behaviour among opioid users, entry inhibiting antiviral therapy, and antiviral therapy which blocks the viral production. Two population-level controls are combined with two within-host-level controls.

The effect of model structure and data availability on Usutu virus dynamics at three biological scales.

Understanding the epidemiology of emerging pathogens, such as Usutu virus (USUV) infections, requires systems investigation at each scale involved in the host-virus transmission cycle, from individual bird infections, to bird-to-vector transmissions, and to USUV incidence in bird and vector populations. For new pathogens field data are sparse, and predictions can be aided by the use of laboratory-type inoculation and transmission experiments combined with dynamical mathematical modelling. In this study, we investigated the dynamics of two strains of USUV by constructing mathematical models for the within-host scale, bird-to-vector transmission scale and vector-borne epidemiological scale.

Modeling the interplay between albumin-globulin metabolism and HIV infection.

Human immunodeficiency virus (HIV) infection is a major public health concern with 1.2 million people living with HIV in the United States. The role of nutrition in general, and albumin/globulin in particular in HIV progression has long been recognized.

Structural identifiability analysis of epidemic models based on differential equations: a tutorial-based primer.

The successful application of epidemic models hinges on our ability to estimate model parameters from limited observations reliably. An often-overlooked step before estimating model parameters consists of ensuring that the model parameters are structurally identifiable from the observed states of the system. In this tutorial-based primer, intended for a diverse audience, including students training in dynamic systems, we review and provide detailed guidance for conducting structural identifiability analysis of differential equation epidemic models based on a differential algebra approach using differential algebra for identifiability of systems (DAISY) and Mathematica (Wolfram Research).

A network immuno-epidemiological model of HIV and opioid epidemics.

In this paper, we introduce a novel multi-scale network model of two epidemics: HIV infection and opioid addiction. The HIV infection dynamics is modeled on a complex network. We determine the basic reproduction number of HIV infection, $ \mathcal{R}_{v} $, and the basic reproduction number of opioid addiction, $ \mathcal{R}_{u} $.

Identifiability of parameters in mathematical models of SARS-CoV-2 infections in humans.

Determining accurate estimates for the characteristics of the severe acute respiratory syndrome coronavirus 2 in the upper and lower respiratory tracts, by fitting mathematical models to data, is made difficult by the lack of measurements early in the infection. To determine the sensitivity of the parameter estimates to the noise in the data, we developed a novel two-patch within-host mathematical model that considered the infection of both respiratory tracts and assumed that the viral load in the lower respiratory tract decays in a density dependent manner and investigated its ability to match population level data. We proposed several approaches that can improve practical identifiability of parameters, including an optimal experimental approach, and found that availability of viral data early in the infection is of essence for improving the accuracy of the estimates.

Parameter identifiability and optimal control of an SARS-CoV-2 model early in the pandemic.

We fit an SARS-CoV-2 model to US data of COVID-19 cases and deaths. We conclude that the model is not structurally identifiable. We make the model identifiable by prefixing some of the parameters from external information.

Immuno-epidemiological co-affection model of HIV infection and opioid addiction.

In this paper, we present a multi-scale co-affection model of HIV infection and opioid addiction. The population scale epidemiological model is linked to the within-host model which describes the HIV and opioid dynamics in a co-affected individual. CD4 cells and viral load data obtained from morphine addicted SIV-infected monkeys are used to validate the within-host model.

Sensitivity Analysis in an Immuno-Epidemiological Vector-Host Model.

Sensitivity Analysis (SA) is a useful tool to measure the impact of changes in model parameters on the infection dynamics, particularly to quantify the expected efficacy of disease control strategies. SA has only been applied to epidemic models at the population level, ignoring the effect of within-host virus-with-immune-system interactions on the disease spread. Connecting the scales from individual to population can help inform drug and vaccine development.

Determining reliable parameter estimates for within-host and within-vector models of Zika virus.

In this paper, we introduce three within-host and one within-vector models of Zika virus. The within-host models are the target cell limited model, the target cell limited model with natural killer (NK) cells class, and a within-host-within-fetus model of a pregnant individual. The within-vector model includes the Zika virus dynamics in the midgut and salivary glands.

Effects of social-distancing on infectious disease dynamics: an evolutionary game theory and economic perspective.

We propose two models inspired by the COVID-19 pandemic: a coupled disease-human behaviour (or disease-game theoretic), and a coupled disease-human behaviour-economic model, both of which account for the impact of social-distancing on disease control and economic growth. The models exhibit rich dynamical behaviour including multistable equilibria, a backward bifurcation, and sustained bounded periodic oscillations. Analyses of the first model suggests that the disease can be eliminated if everybody practices full social-distancing, but the most likely outcome is some level of disease coupled with some level of social-distancing.

A Network Immuno-Epidemiological HIV Model.

In this paper we formulate a multi-scale nested immuno-epidemiological model of HIV on complex networks. The system is described by ordinary differential equations coupled with a partial differential equation. First, we prove the existence and uniqueness of the immunological model and then establish the well-posedness of the multi-scale model.

Comparison of Drug Inhibitory Effects ([Formula: see text]) in Monolayer and Spheroid Cultures.

Traditionally, the monolayer (two-dimensional) cell cultures are used for initial evaluation of the effectiveness of anticancer drugs. In particular, these experiments provide the [Formula: see text] curves that determine drug concentration that can inhibit growth of a tumor colony by half when compared to the cells grown with no exposure to the drug. Low [Formula: see text] value means that the drug is effective at low concentrations, and thus will show lower systemic toxicity when administered to the patient.

Efficacy of control measures in the control of Ebola, Liberia 2014-2015.

The largest outbreak of Ebola to date is the 2014 West Africa Ebola outbreak, with more than 10,000 cases and over 4000 deaths reported in Liberia alone. To control the spread of the outbreak, multiple interventions were implemented: identification and isolation of cases, contact tracing, quarantining of suspected contacts, proper personal protection, safely conducted burials, improved education, social awareness and individual protective measures. Devising rigorous methodologies for the evaluation of the effectiveness of the control measures implemented to stop an outbreak is of paramount importance.

Structural and Practical Identifiability Analysis of Zika Epidemiological Models.

The Zika virus (ZIKV) epidemic has caused an ongoing threat to global health security and spurred new investigations of the virus. Use of epidemiological models for arbovirus diseases can be a powerful tool to assist in prevention and control of the emerging disease. In this article, we introduce six models of ZIKV, beginning with a general vector-borne model and gradually including different transmission routes of ZIKV.

Structural and practical identifiability analysis of outbreak models.

Estimating the reproduction number of an emerging infectious disease from an epidemiological data is becoming more essential in evaluating the current status of an outbreak. However, these studies are lacking the fundamental prerequisite in parameter estimation problem, namely the structural identifiability of the epidemic model, which determines the possibility of uniquely determining the model parameters from the epidemic data. In this paper, we perform both structural and practical identifiability analysis to classical epidemic models such as SIR (Susceptible-Infected-Recovered), SEIR (Susceptible-Exposed-Infected-Recovered) and an epidemic model with the treatment class (SITR).

Backward bifurcation and oscillations in a nested immuno-eco-epidemiological model.

This paper introduces a novel partial differential equation immuno-eco-epidemiological model of competition in which one species is affected by a disease while another can compete with it directly and by lowering the first species' immune response to the infection, a mode of competition termed stress-induced competition. When the disease is chronic, and the within-host dynamics are rapid, we reduce the partial differential equation model (PDE) to a three-dimensional ordinary differential equation (ODE) model. The ODE model exhibits backward bifurcation and sustained oscillations caused by the stress-induced competition.

Efficacies of prevention and control measures applied during an outbreak in Southwest Madrid, Spain.

Leishmaniasis is a vector-borne disease of worldwide distribution, currently present in 98 countries. Since late 2010, an unusual increase of human visceral and cutaneous leishmaniasis cases has been observed in the south-western Madrid region, totaling more than 600 cases until 2015. Some hosts, such as human, domestic dog and cat, rabbit (Oryctolagus cuniculus), and hare (Lepus granatensis), were found infected by the parasite of this disease in the area.

Optimal control of a malaria model with asymptomatic class and superinfection.

In this paper, we introduce a malaria model with an asymptomatic class in human population and exposed classes in both human and vector populations. The model assumes that asymptomatic individuals can get re-infected and move to the symptomatic class. In the case of an incomplete treatment, symptomatic individuals move to the asymptomatic class.

Vector-Borne Pathogen and Host Evolution in a Structured Immuno-Epidemiological System.

Vector-borne disease transmission is a common dissemination mode used by many pathogens to spread in a host population. Similar to directly transmitted diseases, the within-host interaction of a vector-borne pathogen and a host's immune system influences the pathogen's transmission potential between hosts via vectors. Yet there are few theoretical studies on virulence-transmission trade-offs and evolution in vector-borne pathogen-host systems.

Structural and Practical Identifiability Issues of Immuno-Epidemiological Vector-Host Models with Application to Rift Valley Fever.

In this article, we discuss the structural and practical identifiability of a nested immuno-epidemiological model of arbovirus diseases, where host-vector transmission rate, host recovery, and disease-induced death rates are governed by the within-host immune system. We incorporate the newest ideas and the most up-to-date features of numerical methods to fit multi-scale models to multi-scale data. For an immunological model, we use Rift Valley Fever Virus (RVFV) time-series data obtained from livestock under laboratory experiments, and for an epidemiological model we incorporate a human compartment to the nested model and use the number of human RVFV cases reported by the CDC during the 2006-2007 Kenya outbreak.

On the principle of host evolution in host-pathogen interactions.

In this paper, we use a two-host one pathogen immuno-epidemiological model to argue that the principle for host evolution, when the host is subjected to a fatal disease, is minimization of the case fatality proportion [Formula: see text]. This principle is valid whether the disease is chronic or leads to recovery. In the case of continuum of hosts, stratified by their immune response stimulation rate a, we suggest that [Formula: see text] has a minimum because a trade-off exists between virulence to the host induced by the pathogen and virulence induced by the immune response.