Structural and Practical Identifiability Analysis of Zika Epidemiological Models

Exploring Zika's dynamics: A scoping review journey from epidemic to equations through mathematical modelling

Zika virus (ZIKV) infection, along with the concurrent circulation of other arboviruses, presents a great public health challenge, reminding the utilization of mathematical modelling as a crucial tool for explaining its intricate dynamics and interactions with co-circulating pathogens. Through a scoping review, we aimed to discern current mathematical models investigating ZIKV dynamics, focusing on its interplay with other pathogens, and to identify underlying assumptions and deficiencies supporting attention, particularly regarding the epidemiological attributes characterizing Zika outbreaks. Following the PRISMA-Sc guidelines, a systematic search across PubMed, Web of Science, and MathSciNet provided 137 pertinent studies from an initial pool of 2446 papers, showing a diversity of modelling approaches, predominantly centered on vector-host compartmental models, with a notable concentration on the epidemiological landscapes of Colombia and Brazil during the 2015-2016 Zika epidemic. While modelling studies have been important in explaining Zika transmission dynamics and their intersections with diseases such as Dengue, Chikungunya, and COVID-19 so far, future Zika models should prioritize robust data integration and rigorous validation against diverse datasets to improve the accuracy and reliability of epidemic prediction. In addition, models could benefit from adaptable frameworks incorporating human behavior, environmental factors, and stochastic parameters, with an emphasis on open-access tools to foster transparency and research collaboration.

Structural and Practical Identifiability of Phenomenological Growth Models for Epidemic Forecasting

Phenomenological models are highly effective tools for forecasting disease dynamics using real-world data, particularly in scenarios where detailed knowledge of disease mechanisms is limited. However, their reliability depends on the model parameters' structural and practical identifiability. In this study, we systematically analyze the identifiability of six commonly used growth models in epidemiology: the generalized growth model (GGM), the generalized logistic model (GLM), the Richards model, the generalized Richards model (GRM), the Gompertz model, and a modified SEIR model with inhomogeneous mixing. To address challenges posed by non-integer power exponents in these models, we reformulate them by introducing additional state variables. This enables rigorous structural identifiability analysis using the StructuralIdentifiability.jl package in JULIA. We validated the structural identifiability results by performing parameter estimation and forecasting using the GrowthPredict MATLAB Toolbox. This toolbox is designed to fit and forecast time series trajectories based on phenomenological growth models. We applied it to three epidemiological datasets: weekly incidence data for monkeypox, COVID-19, and Ebola. Additionally, we assessed practical identifiability through Monte Carlo simulations to evaluate parameter estimation robustness under varying levels of observational noise. Our results confirm that all six models are structurally identifiable under the proposed reformulation. Furthermore, practical identifiability analyses demonstrate that parameter estimates remain robust across different noise levels, though sensitivity varies by model and dataset. These findings provide critical insights into the strengths and limitations of phenomenological models to characterize epidemic trajectories, emphasizing their adaptability to real-world challenges and their role in informing public health interventions.

The role of viral interference in shaping RSV epidemics following the 2009 H1N1 influenza pandemic

Background

Disruptions in respiratory syncytial virus (RSV) activity were observed in different countries following the 2009 influenza pandemic. Given the limited use of non-pharmaceutical interventions, these disruptions do provide an opportunity to probe viral interference due to the out-of-season epidemics. The objectives of the study are twofold: to characterize atypical RSV activity in the United States (US) and to explore the mechanisms underlying changes in RSV epidemics following the pandemic.

Methods

Laboratory-confirmed RSV cases across 10 US regions from June 2007 to July 2019 were analyzed. A dynamic time warping method was used to characterize RSV activity in different seasons. A two-pathogen model was constructed to explore viral interference mechanisms. A sampling-importance resampling method was applied to estimate the effects of viral interference.

Results

We found that RSV activity was reduced following the influenza pandemic in the 2009/10 season across all regions in the US. By contrast, we found an enhanced but delayed RSV epidemic across the US in the 2010/11 season. Using a mathematical model, we identified three potential viral interference mechanisms that could explain the change of RSV activity following the pandemic. The pandemic influenza may interfere with RSV to reduce susceptibility to RSV coinfection, or shorten the RSV infectious period, or decrease RSV infectivity in co-infections.

Conclusions

This study provides statistical evidence for atypical RSV seasons following the influenza pandemic in the US and sheds light on viral interference mechanisms affecting RSV epidemics, offering a model-fitting framework for analyzing surveillance data at the population level.

Quantifying trade-offs between therapeutic efficacy and resistance dissemination for enrofloxacin dose regimens in cattle

The use of antimicrobial drugs in food-producing animals contributes to the selection pressure on pathogenic and commensal bacteria to become resistant. This study aims to evaluate the existence of trade-offs between treatment effectiveness, cost, and the dynamics of resistance in gut commensal bacteria. We developed a within-host ordinary differential equation model to track the dynamics of antimicrobial drug concentrations and bacterial populations in the site of infection (lung) and the gut. The model was parameterized to represent enrofloxacin treatment for bovine respiratory disease (BRD) caused by Pastereulla multocida in cattle. Three approved enrofloxacin dosing regimens were compared for their effects on resistance on P. multocida and commensal E. coli: 12.5 mg/kg and 7.5 mg/kg as a single dose, and 5 mg/kg as three doses. Additionally, we explored non-FDA-approved regimes. Our results indicated that both 12.5 mg/kg and 7.5 mg/kg as a single dose scenario increased the most the treatment costs and prevalence of P. multocida resistance in the lungs, while 5 mg/kg as three doses increased resistance in commensal E. coli bacteria in the gut the most out of the approved scenarios. A proposed non-FDA-approved scenario (7.5 mg/kg, two doses 24 h apart) showed low economic costs, minimal P. multocida, and moderate effects on resistant E. coli. Overall, the scenarios that decrease P. multocida, including resistant P. multocida did not coincide with those that decrease resistant E. coli the most, suggesting a trade-off between both outcomes. The sensitivity analysis suggests that bacterial populations were the most sensitive to drug conversion factors into plasma ( β ), elimination of the drug from the colon ( ϑ ), fifty percent sensitive bacteria (P. multocida) killing effect ( L s50 ), fifty percent of bacteria (E. coli) above ECOFF killing effect ( C r50 ), and net drug transfer rate in the lung ( γ ) parameters.

Parameter identifiability of a within-host SARS-CoV-2 epidemic model

Parameter identification involves the estimation of undisclosed parameters within a system based on observed data and mathematical models. In this investigation, we employ DAISY to meticulously examine the structural identifiability of parameters of a within-host SARS-CoV-2 epidemic model, taking into account an array of observable datasets. Furthermore, Monte Carlo simulations are performed to offer a comprehensive practical analysis of model parameters. Lastly, sensitivity analysis is employed to ascertain that decreasing the replication rate of the SARS-CoV-2 virus and curbing the infectious period are the most efficacious measures in alleviating the dissemination of COVID-19 amongst hosts.

Quantifying trade-offs between therapeutic efficacy and resistance dissemination for enrofloxacin dose regimens in cattle

The use of antimicrobial drugs in food-producing animals increases the selection pressure on pathogenic and commensal bacteria to become resistant. This study aims to evaluate the existence of trade-offs between treatment effectiveness, cost, and the dissemination of resistance in gut commensal bacteria. We developed a within-host ordinary differential equation model to track the dynamics of antimicrobial drug concentrations and bacterial populations in the site of infection (lung) and the gut. The model was parameterized to represent enrofloxacin treatment for bovine respiratory disease (BRD) caused by Pastereulla multocida in cattle. Three approved enrofloxacin dosing regimens were compared for their effects on resistance on P. multocida and commensal E. coli: 12.5 mg/kg and 7.5 mg/kg as a single dose, and 5 mg/kg as three doses. Additionally, we explored non-approved regimes. Our results indicated that both 12.5 mg/kg and 7.5 mg/kg as a single dose scenario increased the most the treatment costs and prevalence of P. multocida resistance in the lungs, while 5 mg/kg as three doses increased resistance in commensal E. coli bacteria in the gut the most out of the approved scenarios. A proposed scenario (7.5 mg/kg, two doses 24 hours apart) showed low economic costs, minimal P. multocida, and moderate effects on resistant E. coli. Overall, the scenarios that decrease P. multocida, including resistant P. multocida did not coincide with the scenarios that decrease resistant E. coli the most, suggesting a trade-off between both outcomes. The sensitivity analysis indicates that bacterial populations were the most sensitive to drug conversion factors into plasma (β), elimination of the drug from the colon (υ), fifty percent sensitive bacteria (P. multocida) killing effect (Ls50), fifty percent of bacteria (E. coli) above ECOFF killing effect (Cr50), and net drug transfer rate in the lung (γ) parameters.

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 $. The infection equilibrium is locally asymptotically stable if $ \mathcal{R}_0 > 1 $ and an additional condition holds. We show that the within-host model of HIV and nutrition is structured to reveal its parameters from the observations of viral load, CD4 cell count and total protein data. We then estimate the model parameters for these 3 data sets. We have also studied the practical identifiability of the model parameters by performing Monte Carlo simulations, and found that the rate of clearance of the virus by immunoglobulins is practically unidentifiable, and that the rest of the model parameters are only weakly identifiable given the experimental data. Furthermore, we have studied how the data frequency impacts the practical identifiability of model parameters.

Optimal control applied to Zika virus epidemics in Colombia and Puerto Rico

Zika virus (ZIKV) is a mostly non-lethal disease in humans transmitted by mosquitoes or humans that can produce severe brain defects such as microcephaly in babies and Guillain-Barré syndrome in elderly adults. The use of optimal control strategies involving information campaigns about insect repellents and condoms alongside an available safe and effective vaccine can prevent the number of infected humans with ZIKV. A system of nonlinear ordinary differential equations is formulated for the transmission dynamics of ZIKV in the presence of three control strategies to evaluate the impact of various scenarios during a ZIKV epidemic. In addition, we estimate parameters using weekly incidence data from previous ZIKV outbreaks in Colombia and Puerto Rico to capture the dynamics of an epidemic in each country when control measures are available. The basic reproduction number, R0, of each country is calculated using estimated parameters (without the controls). The vector-borne transmission threshold (Rv) is dominant in both countries , but the sexual transmission threshold (Rd) in Colombia is considerably higher than in Puerto Rico. Numerical simulations for Colombia show that the most effective strategies are to use three controls since the start of the outbreak. However, for Puerto Rico only information campaigns about mosquito repellents and vaccination are the most effective ways to mitigate the epidemic.

Mathematical Modeling for the Assessment of Public Policies in the Cancer Health-Care System Implemented for the Colombian Case

The incidence of cancer has been constantly growing worldwide, placing pressure on health systems and increasing the costs associated with the treatment of cancer. In particular, low- and middle-income countries are expected to face serious challenges related to caring for the majority of the world's new cancer cases in the next 10 years. In this study, we propose a mathematical model that allows for the simulation of different strategies focused on public policies by combining spending and epidemiological indicators. In this way, strategies aimed at efficient spending management with better epidemiological indicators can be determined. For validation and calibration of the model, we use data from Colombia-which, according to the World Bank, is an upper-middle-income country. The results of the simulations using the proposed model, calibrated and validated for Colombia, indicate that the most effective strategy for reducing mortality and financial burden consists of a combination of early detection and greater efficiency of treatment in the early stages of cancer. This approach is found to present a 38% reduction in mortality rate and a 20% reduction in costs (% GDP) when compared to the baseline scenario. Hence, Colombia should prioritize comprehensive care models that focus on patient-centered care, prevention, and early detection.

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. Practical identifiability of the model through Monte Carlo simulations reveals that two of the parameters may not be practically identifiable. With thus identified parameters, we set up an optimal control problem with social distancing and isolation as control variables. We investigate two scenarios: the controls are applied for the entire duration and the controls are applied only for the period of time. Our results show that if the controls are applied early in the epidemic, the reduction in the infected classes is at least an order of magnitude higher compared to when controls are applied with 2-week delay. Further, removing the controls before the pandemic ends leads to rebound of the infected classes.

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. Our findings can be useful for designing interventions.

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. AIDS diagnoses, HIV death and opioid mortality data are used to fit the between-host model. When the rates of viral clearance and morphine uptake are fixed, the within-host model is structurally identifiable. If in addition the morphine saturation and clearance rates are also fixed the model becomes practical identifiable. Analytical results of the multi-scale model suggest that in addition to the disease-addiction-free equilibrium, there is a unique HIV-only and opioid-only equilibrium. Each of the boundary equilibria is stable if the invasion number of the other epidemic is below one. Elasticity analysis suggests that the most sensitive number is the invasion number of opioid epidemic with respect to the parameter of enhancement of HIV infection of opioid-affected individual. We conclude that the most effective control strategy is to prevent opioid addicted individuals from getting HIV, and to treat the opioid addiction directly and independently from HIV.

Lack of practical identifiability may hamper reliable predictions in COVID-19 epidemic models

Compartmental models are widely adopted to describe and predict the spreading of infectious diseases. The unknown parameters of these models need to be estimated from the data. Furthermore, when some of the model variables are not empirically accessible, as in the case of asymptomatic carriers of coronavirus disease 2019 (COVID-19), they have to be obtained as an outcome of the model. Here, we introduce a framework to quantify how the uncertainty in the data affects the determination of the parameters and the evolution of the unmeasured variables of a given model. We illustrate how the method is able to characterize different regimes of identifiability, even in models with few compartments. Last, we discuss how the lack of identifiability in a realistic model for COVID-19 may prevent reliable predictions of the epidemic dynamics.

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. The within-host models are not structurally identifiable with respect to data on viral load and NK cell counts. After rescaling, the scaled within-host models are locally structurally identifiable. The within-vector model is structurally identifiable with respect to viremia data in the midgut and salivary glands. Using Monte Carlo Simulations, we find that target cell limited model is practically identifiable from data on viremia; the target cell limited model with NK cell class is practically identifiable, except for the rescaled half saturation constant. The within-host-within-fetus model has all fetus-related parameters not practically identifiable without data on the fetus, as well as the rescaled half saturation constant is also not practically identifiable. The remaining parameters are practically identifiable. Finally we find that none of the parameters of the within-vector model is practically identifiable.

Competition between RSV and influenza: Limits of modelling inference from surveillance data

Respiratory Syncytial Virus (RSV) and Influenza cause a large burden of disease. Evidence of their interaction via temporary cross-protection implies that prevention of one could inadvertently lead to an increase in the burden of the other. However, evidence for the public health impact of such interaction is sparse and largely derives from ecological analyses of peak shifts in surveillance data. To test the robustness of estimates of interaction parameters between RSV and Influenza from surveillance data we conducted a simulation and back-inference study. We developed a two-pathogen interaction model, parameterised to simulate RSV and Influenza epidemiology in the UK. Using the infection model in combination with a surveillance-like stochastic observation process we generated a range of possible RSV and Influenza trajectories and then used Markov Chain Monte Carlo (MCMC) methods to back-infer parameters including those describing competition. We find that in most scenarios both the strength and duration of RSV and Influenza interaction could be estimated from the simulated surveillance data reasonably well. However, the robustness of inference declined towards the extremes of the plausible parameter ranges, with misleading results. It was for instance not possible to tell the difference between low/moderate interaction and no interaction. In conclusion, our results illustrate that in a plausible parameter range, the strength of RSV and Influenza interaction can be estimated from a single season of high-quality surveillance data but also highlights the importance to test parameter identifiability a priori in such situations.

The susceptible-unidentified infected-confirmed (SUC) epidemic model for estimating unidentified infected population for COVID-19

In this article, we propose the Susceptible-Unidentified infected-Confirmed (SUC) epidemic model for estimating the unidentified infected population for coronavirus disease 2019 (COVID-19) in China. The unidentified infected population means the infected but not identified people. They are not yet hospitalized and still can spread the disease to the susceptible. To estimate the unidentified infected population, we find the optimal model parameters which best fit the confirmed case data in the least-squares sense. Here, we use the time series data of the confirmed cases in China reported by World Health Organization. In addition, we perform the practical identifiability analysis of the proposed model using the Monte Carlo simulation. The proposed model is simple but potentially useful in estimating the unidentified infected population to monitor the effectiveness of interventions and to prepare the quantity of protective masks or COVID-19 diagnostic kit to supply, hospital beds, medical staffs, and so on. Therefore, to control the spread of the infectious disease, it is essential to estimate the number of the unidentified infected population. The proposed SUC model can be used as a basic building block mathematical equation for estimating unidentified infected population.

Sensitivity, uncertainty and identifiability analyses to define a dengue transmission model with real data of an endemic municipality of Colombia

Dengue disease is a major problem for public health surveillance entities in tropical and subtropical regions having a significant impact not only epidemiological but social and economical. There are many factors involved in the dengue transmission process. We can evaluate the importance of these factors through the formulation of mathematical models. However, the majority of the models presented in the literature tend to be overparameterized, with considerable uncertainty levels and excessively complex formulations. We aim to evaluate the structure, complexity, trustworthiness, and suitability of three models, for the transmission of dengue disease, through different strategies. To achieve this goal, we perform structural and practical identifiability, sensitivity and uncertainty analyses to these models. The results showed that the simplest model was the most appropriate and reliable when the only available information to fit them is the cumulative number of reported dengue cases in an endemic municipality of Colombia.