Infectious Disease Models Research Articles

Nathan Lo—translating infectious disease models into policy

Nathan Lo—translating infectious disease models into policy

Rhesus Macaque Killer Cell Ig-like Receptor Domain 0 Glycans Impact Surface Expression and Ligand Specificity.

Defining the MHC class I ligands of rhesus macaque killer cell Ig-like receptors (KIRs) is fundamental to NK cell biology in this species as a model for infectious diseases and comparative immunogenetics. Several rhesus macaque KIRs belong to a phylogenetically distinct group with a three-amino acid deletion in domain 0 (D0). This deletion results in polymorphic differences in potential N-linked glycosylation (PNG) sites adjacent to a predicted KIR-MHC class I contact site. Whereas most KIRs have two tandem PNG sites in D0 (N36FTN39FT), the KIRs containing the deletion only have a single site in this region (N36FT). To discern the contribution of glycosylation to KIR expression and ligand recognition, we constructed PNG mutants for six lineage II KIR genes that eliminate or create sites for N-glycan addition at these locations. The impact of these mutations on total and surface expression was determined by immunoblotting and flow cytometry. Ligand engagement was assessed by coincubating reporter cell lines bearing chimeric KIR-CD3ζ receptors with target cells expressing individual MHC class I molecules and were corroborated by staining with KIR IgG-Fc fusion proteins. We found that N36FT is glycosylated in KIR with a single site, and at least one site is glycosylated in KIRs with two tandem sites. In general, for rhesus KIRs with a single D0 glycosylation site, that site contributes to surface expression. For KIRs with two tandem sites, the first site can contribute to ligand specificity. This study establishes that D0 glycosylation of rhesus macaque KIRs modulates surface expression and contributes to ligand specificity.

Dynamical behaviors of a stochastic SIVS epidemic model with the Ornstein-Uhlenbeck process and vaccination of newborns.

In this paper, we study a stochastic SIVS infectious disease model with the Ornstein-Uhlenbeck process and newborns with vaccination. First, we demonstrate the theoretical existence of a unique global positive solution in accordance with this model. Second, adequate conditions are inferred for the infectious disease to die out and persist. Then, by classic Lynapunov function method, the stochastic model is allowed to obtain the sufficient condition so that the stochastic model has a stationary distribution represents illness persistence in the absence of endemic equilibrium. Calculating the associated Fokker-Planck equations yields the precise expression of the probability density function for the linearized system surrounding the quasi-endemic equilibrium. In the end, the theoretical findings are shown by numerical simulations.

A fractional order mathematical model for the omicron: a new variant of COVID-19

For the purpose of analyzing the Omicron pandemic, we build a novel SEIaIsIoHR mathematical model. The fundamental properties of the model are studied, including boundedness, uniqueness, and existence. The boundedness of the model’s solution is examined by solving the fractional Gronwall’s inequality using the Laplace transform method. Using the Picard-Lindelöf theorem, we verify the solution’s existence and uniqueness. The next-generation matrix is used to compute Ro (the basic reproduction number), which is significant in the mathematical modeling of infectious diseases. It is demonstrated that both the endemic and disease-free equilibrium solutions are globally and locally asymptotically stable. We also conducted a sensitivity analysis of the parameters based on Ro . Moreover, the model is extended by employing optimal control theory to examine the effects of certain control strategies. Finally, numerical simulations are performed to validate the model.

Single cell-inductively coupled plasma-mass spectrometry (SC-ICP-MS) reveals metallic heterogeneity in a macrophage model of infectious diseases.

Single cell-inductively coupled plasma-mass spectrometry (SC-ICP-MS) offers an attractive option for rapidly measuring trace metal heterogeneity at the single cell level. Chemical fixation has been previously applied to mammalian cells prior to sample introduction so that they can be resuspended in a solution suitable for SC-ICP-MS. However, the effect of fixation on the elemental composition of suspended cells is unknown, and robust methodologies are urgently needed so that the community can measure the effects of intracellular pathogens on elemental composition of their host cells. We demonstrate that different fixatives impact measured cell elemental composition. We have compared suspensions treated using different fixatives (methanol 60-100% in H2O and 4% paraformaldehyde in phosphate-buffered saline solution), and the number of distinguishable single cell events, keeping a constant particle number concentration. Significantly more single cell events (n = 3, P ≤ 0.05) were observed for Ca and Mg when cells were fixed in 4% paraformaldehyde than for the methanol-based fixatives, confirming the hypothesis that methanol fixatives cause leaching of these elements from the cells. The impact of fixation on Mn and Zn was less pronounced. Microbial and viral infection of eukaryotic cells can have profound effects on their elemental composition, but chemical fixation is necessary to render infected cells safe before analysis. We have successfully applied our methodology to a macrophage model of tuberculosis demonstrating utility in understanding metal homeostasis during microbial infection of mammalian cells.

Exploring the dynamics of leprosy transmission with treatment through a fractal–fractional differential model

Leprosy continues to be a significant public health challenge in many parts of the world, necessitating novel approaches to understanding and controlling its transmission. The dynamics of leprosy are examined in this study by means of a caputo fabrizio fractal–fractional differential system model. Leprosy transmission and treatment are complex and non-linear processes that can be captured by fractal–fractional derivatives. The temporal progression of the disease is the primary focus of our mathematical analysis, which evaluates a variety of parameter values, including initial population densities and compartmental transitions. Through simulations, we examine the impact of critical parameters on the severity and spread of diseases, as well as the rates of recovery and treatment. Numerical results of the model offer valuable insights into the impact of these parameters on leprosy dynamics, which is beneficial for public health interventions. The stability analysis of the model identifies supplementary conditions that are necessary for the success of disease control. By incorporating these novel mathematical techniques, we hope to improve our understanding of leprosy transmission and ultimately contribute to more effective control strategies. Based on our findings, additional studies investigating the relation between population density, treatment accessibility, and recovery rates are warranted. We hope that by graphically representing the relationships between these factors, we can draw attention to the possibility of targeted interventions that can reduce the transmission of leprosy. This study provides a strong basis for future studies on infectious disease modeling and aids leprosy-affected communities in developing strategies to mitigate the disease’s impact.

Air pollution’s numerical, spatial, and temporal heterogeneous impacts on childhood hand, foot and mouth disease: a multi-model county-level study from China

BackgroundWhile stationary links between childhood hand, foot and mouth disease (HFMD) and air pollution are known, a comprehensive study on their heterogeneous relationships (nonstationarity), jointly considering numerical, temporal and spatial dimensions, has not been reported.MethodsMonthly HFMD incidence and air pollution data were collected at the county level from Sichuan-Chongqing, China (2009–2011), alongside meteorological and social environmental covariates. Key influential factors were identified using random forest (RF) under the stationary assumption. Factors’ numerically, temporally, and spatially heterogeneous relationships with HFMD were assessed using generalized additive model (GAM) and geographically and temporally weighted regression (GTWR).ResultsOur findings highlighted the relatively higher stationary contributions of fine particulate matter (PM2.5) and ozone (O3) to HFMD incidence across Sichuan-Chongqing counties. We further uncovered heterogeneous impacts of PM2.5 and O3 from three nonstationary perspectives. Numerically, PM2.5 showed an inverse ‘V’-shaped relationship with HFMD incidence, while O3 exhibited a complex pattern, with increased HFMD incidence at low PM2.5 and moderate O3 concentrations. Temporally, PM2.5’s impact peaked in autumn and was weakest in spring, whereas O3’s effect was strongest in summer. Spatially, hotspot mapping revealed high-risk clusters for PM2.5 impact across all seasons, with notable geographical variations, and for O3 in spring, summer, and autumn, concentrated in specific regions of Sichuan-Chongqing.ConclusionsThis study underscores the nuanced and three-perspective heterogeneous influences of air pollution on HFMD in small areas, emphasizing the need for differentiated, localized, and time-sensitive prevention and control strategies to enhance the precision of dynamic early warnings and predictive models for HFMD and other infectious diseases, particularly in the fields of environmental and spatial epidemiology.

Stability and Optimality Criteria for an SVIR Epidemic Model with Numerical Simulation

The mathematical modeling of infectious diseases plays a vital role in understanding and predicting disease transmission, as underscored by recent global outbreaks; to delve deep into the dynamic of infectious disease considering latent period presciently is inevitable as it bridges the gap between realistic nature and mathematical modeling. This study extended the classical Susceptible–Infected–Recovered (SIR) model by incorporating vaccination strategies during incubation. We introduced multiple time delays to an account incubation period to capture realistic disease dynamics better. The model is formulated as a system of delay differential equations that describe the transmission dynamics of diseases such as polio or COVID-19, or diseases for which vaccination exists. Critical aspects of the study include proving the positivity of the model’s solutions, calculating the basic reproduction number (R0) using next-generation matrix theory, and identifying disease-free and endemic equilibrium points. The local stability of these equilibria is then analyzed using the Routh–Hurwitz criterion. Due to the complexity introduced by the delay components, we examine the stability by studying the roots of a fourth-degree exponential polynomial. The effects of educational campaigns and vaccination efficacy are also investigated as control measures. Furthermore, an optimization problem is formulated, based on Pontryagin’s maximum principle, to minimize the number of infections and associated intervention costs. Numerical simulations of the delay differential equations are conducted, and a modified Runge–Kutta method with delays is used to solve the optimal control problem. Finally, we present a few simulation results to illustrate the analytical findings.

Optimal switching of vaccination for an infectious disease model

We study a switched SIHR (Susceptible Infected Hospitalized Recovered) model for infectious diseases. The aim is to find the most effective switching signal to manage the disease's effects as effectively as maintaining a continuous vaccination program. A nonlinear, non-convex optimal control problem of the switched system is converted into a linear and convex optimal control problem by applying the theory of moments and semi-definite programming. Finally, some numerical simulations are performed to compare continuous vaccination programs and optimal switching of vaccination control. For more information see https://ejde.math.txstate.edu/Volumes/2024/59/abstr.html

Trade risk transmission of global cobalt industrial chain based on multi-layer network

In order to study the potential systemic risk transmission in cobalt trade, this paper combined the infectious disease model with complex networks to build a multi-layer network trade risk transmission model for cobalt trade based on the transmission of export restrictions and bilateral friction in a single country, in order to simulate the degree of impact of risk transmission in cobalt industry chain, identify key countries and risk transmission paths. The results show that multi-layer network risk transmission of global cobalt trade based on two communication forms has the characteristics of “robust and fragile”. In addition, the risk transmission situation based on bilateral frictions is mainly transmitted by core countries and direct contacts. The risk transmission based on the export restriction of a single country is mainly through direct contact, indirect contact and regional transmission. We also find that the multi-layer trade network of global cobalt trade can resist the bilateral frictional transmission mode better than the transmission mode of single country export restriction. The results can support policy makers to optimize the cobalt trade structure and mitigate the negative impact of trade disruptions.

Dynamics and backward bifurcations of SEI tuberculosis models in homogeneous and heterogeneous populations

The main difference between tuberculosis (TB) and other infectious diseases is that the transmission of the bacterium should be considered not only as the development of a primary infection, but also as exogenous reinfection or endogenous reactivation. Moreover, individuals in the population may have heterogeneous contact rates, which can be described by complex networks. To this end, we present two differential equation-based TB models in homogeneous and heterogeneous populations. The first model assumes that the number of contacts per unit time is constant for the whole population, whereas the second model considers the heterogeneous number of contacts per unit time for each individual. We derive the basic reproduction number of each model using the next-generation matrix method, and analyze the dynamical properties of each model in detail. We find that the two models undergo backward bifurcations and have the same threshold condition for backward bifurcation. From this threshold condition, we see that the reduced rate of exogenous reinfection of individuals plays an important role in causing the backward bifurcation. Interestingly, the second model allows the threshold condition for backward bifurcation to be independent of network parameters. Thus, unlike other infectious disease models on complex networks, in controlling the spread of tuberculosis among populations with different numbers of contacts, we only need to focus on disease parameters during treatment. Finally, numerical simulations more intuitively demonstrate the impact of parameter changes on the prevalence of tuberculosis and reveal the model's richer and more interesting dynamical properties, such as bistability. Sensitivity analysis indicates that the basic reproduction number is highly correlated with both the relapse rate of latent individuals progressing to active infection and the probability of healthy individuals becoming infected after contact with the pathogen. Therefore, enhancing the detection and treatment of latent cases and reducing contact between infected and uninfected individuals are the most crucial public health interventions.

Quantifying age-specific household contacts in Aotearoa New Zealand for infectious disease modelling.

Accounting for population age structure and age-specific contact patterns is crucial for accurate modelling of human infectious disease dynamics and impact. A common approach is to use contact matrices, which estimate the number of contacts between individuals of different ages. These contact matrices are frequently based on data collected from populations with very different demographic and socio-economic characteristics from the population of interest. Here we use a comprehensive household composition dataset based on Aotearoa New Zealand census and administrative data to construct a household contact matrix and a synthetic population that can be used for modelling. We investigate the behaviour of a compartment-based and an agent-based epidemic model parametrized using these data, compared with a commonly used contact matrix that was constructed by projecting international data onto New Zealand's population. We find that using the New Zealand household data, either in a compartment-based model or in an agent-based model, leads to lower attack rates in older age groups compared with using the projected contact matrix. This difference becomes larger when household transmission is more dominant relative to non-household transmission. We provide electronic versions of the synthetic population and household contact matrix for other researchers to use in infectious disease models.

Mathematical modelling for pandemic preparedness in Canada: Learning from COVID-19.

The COVID-19 pandemic underlined the need for pandemic planning but also brought into focus the use of mathematical modelling to support public health decisions. The types of models needed (compartment, agent-based, importation) are described. Best practices regarding biological realism (including the need for multidisciplinary expert advisors to modellers), model complexity, consideration of uncertainty and communications to decision-makers and the public are outlined. A narrative review was developed from the experiences of COVID-19 by members of the Public Health Agency of Canada External Modelling Network for Infectious Diseases (PHAC EMN-ID), a national community of practice on mathematical modelling of infectious diseases for public health. Modelling can best support pandemic preparedness in two ways: 1) by modelling to support decisions on resource needs for likely future pandemics by estimating numbers of infections, hospitalized cases and cases needing intensive care, associated with epidemics of "hypothetical-yet-plausible" pandemic pathogens in Canada; and 2) by having ready-to-go modelling methods that can be readily adapted to the features of an emerging pandemic pathogen and used for long-range forecasting of the epidemic in Canada, as well as to explore scenarios to support public health decisions on the use of interventions. There is a need for modelling expertise within public health organizations in Canada, linked to modellers in academia in a community of practice, within which relationships built outside of times of crisis can be applied to enhance modelling during public health emergencies. Key challenges to modelling for pandemic preparedness include the availability of linked public health, hospital and genomic data in Canada.

On a Symmetry-Based Structural Deterministic Fractal Fractional Order Mathematical Model to Investigate Conjunctivitis Adenovirus Disease

In the last few years, the conjunctivitis adenovirus disease has been investigated by using the concept of mathematical models. Hence, researchers have presented some mathematical models of the mentioned disease by using classical and fractional order derivatives. A complementary method involves analyzing the system of fractal fractional order equations by considering the set of symmetries of its solutions. By characterizing structures that relate to the fundamental dynamics of biological systems, symmetries offer a potent notion for the creation of mechanistic models. This study investigates a novel mathematical model for conjunctivitis adenovirus disease. Conjunctivitis is an infection in the eye that is caused by adenovirus, also known as pink eye disease. Adenovirus is a common virus that affects the eye’s mucosa. Infectious conjunctivitis is most common eye disease on the planet, impacting individuals across all age groups and demographics. We have formulated a model to investigate the transmission of the aforesaid disease and the impact of vaccination on its dynamics. Also, using mathematical analysis, the percentage of a population which needs vaccination to prevent the spreading of the mentioned disease can be investigated. Fractal fractional derivatives have been widely used in the last few years to study different infectious disease models. Hence, being inspired by the importance of fractal fractional theory to investigate the mentioned human eye-related disease, we derived some adequate results for the above model, including equilibrium points, reproductive number, and sensitivity analysis. Furthermore, by utilizing fixed point theory and numerical techniques, adequate requirements were established for the existence theory, Ulam–Hyers stability, and approximate solutions. We used nonlinear functional analysis and fixed point theory for the qualitative theory. We have graphically simulated the outcomes for several fractal fractional order levels using the numerical method.

Incorporating Social Determinants of Health in Infectious Disease Models: A Systematic Review of Guidelines.

Infectious disease (ID) models have been the backbone of policy decisions during the COVID-19 pandemic. However, models often overlook variation in disease risk, health burden, and policy impact across social groups. Nonetheless, social determinants are becoming increasingly recognized as fundamental to the success of control strategies overall and to the mitigation of disparities. To underscore the importance of considering social heterogeneity in epidemiological modeling, we systematically reviewed ID modeling guidelines to identify reasons and recommendations for incorporating social determinants of health into models in relation to the conceptualization, implementation, and interpretations of models. After identifying 1,372 citations, we found 19 guidelines, of which 14 directly referenced at least 1 social determinant. Age (n = 11), sex and gender (n = 5), and socioeconomic status (n = 5) were the most commonly discussed social determinants. Specific recommendations were identified to consider social determinants to 1) improve the predictive accuracy of models, 2) understand heterogeneity of disease burden and policy impact, 3) contextualize decision making, 4) address inequalities, and 5) assess implementation challenges. This study can support modelers and policy makers in taking into account social heterogeneity, to consider the distributional impact of infectious disease outbreaks across social groups as well as to tailor approaches to improve equitable access to prevention, diagnostics, and therapeutics. Infectious disease (ID) models often overlook the role of social determinants of health (SDH) in understanding variation in disease risk, health burden, and policy impact across social groups.In this study, we systematically review ID guidelines and identify key areas to consider SDH in relation to the conceptualization, implementation, and interpretations of models.We identify specific recommendations to consider SDH to improve model accuracy, understand heterogeneity, estimate policy impact, address inequalities, and assess implementation challenges.

Respiratory pathogen dynamics in community fever cases: Jiangsu Province, China (2023–2024)

BackgroundRespiratory infectious diseases have the highest incidence among infectious diseases worldwide. Currently, global monitoring of respiratory pathogens primarily focuses on influenza and coronaviruses. This study included influenza and other common respiratory pathogens to establish a local respiratory pathogen spectrum. We investigated and analyzed the co-infection patterns of these pathogens and explored the impact of lifting non-pharmaceutical interventions (NPIs) on the transmission of influenza and other respiratory pathogens. Additionally, we used a predictive model for infectious diseases, utilizing the commonly used An autoregressive comprehensive moving average model (ARIMA), which can effectively forecast disease incidence.MethodsFrom June 2023 to February 2024, we collected influenza-like illness (ILI) cases weekly from the community in Xuanwu District, Nanjing, and obtained 2046 samples. We established a spectrum of respiratory pathogens in Nanjing and analysed the age distribution and clinical symptom distribution of various pathogens. We compared age, gender, symptom counts, and viral loads between individuals with co-infections and those with single infections. An autoregressive comprehensive moving average model (ARIMA) was constructed to predict the incidence of respiratory infectious diseases.ResultsAmong 2046 samples, the total detection rate of respiratory pathogen nucleic acids was 53.37% (1092/2046), with influenza A virus 479 cases (23.41%), influenza B virus 224 cases (10.95%), and HCoV 95 cases (4.64%) being predominant. Some pathogens were statistically significant in age and number of symptoms. The positive rate of mixed infections was 6.11% (125/2046). There was no significant difference in age or number of symptoms between co-infection and simple infection. After multiple iterative analyses, an ARIMA model (0,1,4), (0,0,0) was established as the optimal model, with an R2 value of 0.930, indicating good predictive performance.ConclusionsThe spectrum of respiratory pathogens in Nanjing, Jiangsu Province, was complex in the past. The primary age groups of different viruses were different, causing various symptoms, and the co-infection of viruses did not correlate with the age and gender of patients. The ARIMA model estimated future incidence, which plateaued in subsequent months.

New results on asymptotic stability of time-varying nonlinear systems with applications

Abstract. In this paper, we present a converse Lyapunov theorem for the new notion of global generalized practical uniform h-stability of nonlinear systems of differential equations. We derive some sufficient conditions which guarantee the global generalized practical uniform h-stability of time-varying perturbed systems. In addition, these results are used to study the practical h-stability of models of infectious diseases and vaccination. Mathematics Subject Classification (2010): 35B40, 37B55, 34D20, 93D15, 92D30. Keywords: Epidemic models, generalized practical uniform h-stability, Gronwall’s inequalities, Lyapunov functions.

PROBLEMS OF MANAGING THE IMMUNE RESPONSE UNDER CONDITIONS OF COMPETITIVE ADSORPTION, DIFFUSION PERTURBATIONS AND TEMPERATURE RESPONSE OF THE ORGANISM

Analysis of the problems associated with the rapid spread of infectious diseases indicates the need for new approaches to the diagnosis and develop- ment of effective personalized treatment programs. One of the important aspects of solving this problem is the creation of a mathematical modeling toolkit for predicting the dynamics of infectious diseases, taking into account spatial effects, concentrated effects, various mechanisms of body protec- tion in the conditions of the application of various types of therapeutic methods of treatment. An important component of complex methods of treat- ment of a wide range of infectious diseases is the use of adsorption drugs, which, along with detoxification of the body, are able to provide an addi- tional mechanism of neutralization of viral elements. In the process of using such means, not only pathogenic elements and toxins will be adsorbed, but also various types of immune agents, which will affect the dynamics of the immune response. In the paper the infectious disease model is generalized to take into account the features of competitive adsorption of antigens and immune agents in the conditions of diffusion perturbations, concentrated influences and temperature reaction of the body. By synthesizing the ideas of step-by-step procedures, asymptotic and numerical methods, an effective computational technology of step-by-step approximation of the solution of the original model singularly perturbed problem was built. The results of the computer experiments presented in the paper illustrate the features of reducing the predicted concentration of viral elements during their competi- tive adsorption together with immune agents, in particular, the effect of reducing the efficiency of the use of non-specific adsorbents. It is emphasized that taking into account the features of the action of competitive adsorption is important for making decisions regarding the formation of rational treatment programs with the complex use of adsorbing substances and immunological drugs.

Fast Computer Model Calibration using Annealed and Transformed Variational Inference

Computer models play a crucial role in numerous scientific and engineering domains. To ensure the accuracy of simulations, it is essential to properly calibrate the input parameters of these models through statistical inference. While Bayesian inference is the standard approach for this task, employing Markov chain Monte Carlo methods often encounters computational hurdles due to the costly evaluation of likelihood functions and slow mixing rates. Although variational inference (VI) can be a fast alternative to traditional Bayesian approaches, VI has limited applicability due to boundary issues and local optima problems. To address these challenges, we propose flexible VI methods based on deep generative models that do not require parametric assumptions on the variational distribution. We embed a surjective transformation in our framework to avoid posterior truncation at the boundary. Additionally, we provide theoretical conditions that guarantee the success of the algorithm. Furthermore, our temperature annealing scheme and fine-tuning can prevent being trapped in local optima through a series of intermediate posteriors and weight adjustment. We apply our method to infectious disease models and a geophysical model, illustrating that the proposed method can provide fast and accurate inference compared to its competitors.

Near-infrared in vivo imaging system for dynamic visualization of lung-colonizing bacteria in mouse pneumonia.

Conventional animal models of infectious diseases have traditionally relied upon average assessments involving numerous individuals, meaning they do not directly reflect changes in the pathology of an individual. Moreover, in recent years, ethical concerns have resulted in the demand to reduce the number of animals used in such models. Although in vivo imaging offers an effective approach for longitudinally evaluating the pathogenesis of infectious diseases in individual animals, a standardized method has not yet been established. To our knowledge, this study is the first to develop a highly versatile in vivo pulmonary bacterial quantification system utilizing near-infrared luminescence, plasmid-mediated expression of firefly luciferase in bacteria, and a scientific complementary metal-oxide semiconductor camera. Our research holds promise as a useful tool for assessing the efficacy of therapeutic drugs and pathogenesis of infectious diseases.