Impact of immune evasion, waning and boosting on dynamics of population mixing between a vaccinated majority and unvaccinated minority.

BACKGROUND: We previously demonstrated that when vaccines prevent infection, the dynamics of mixing between vaccinated and unvaccinated sub-populations is such that use of imperfect vaccines markedly decreases risk for vaccinated people, and for the population overall. Risks to vaccinated people accrue disproportionately from contact with unvaccinated people. In the context of the emergence of Omicron SARS-CoV-2 and evolving understanding of SARS-CoV-2 epidemiology, we updated our analysis to evaluate whether our earlier conclusions remained valid. METHODS: We modified a previously published Susceptible-Infectious-Recovered (SIR) compartmental model of SARS-CoV-2 with two connected sub-populations: vaccinated and unvaccinated, with non-random mixing between groups. Our expanded model incorporates diminished vaccine efficacy for preventing infection with the emergence of Omicron SARS-CoV-2 variants, waning immunity, the impact of prior immune experience on infectivity, "hybrid" effects of infection in previously vaccinated individuals, and booster vaccination. We evaluated the dynamics of an epidemic within each subgroup and in the overall population over a 10-year time horizon. RESULTS: Even with vaccine efficacy as low as 20%, and in the presence of waning immunity, the incidence of COVID-19 in the vaccinated subpopulation was lower than that among the unvaccinated population across the full 10-year time horizon. The cumulative risk of infection was 3-4 fold higher among unvaccinated people than among vaccinated people, and unvaccinated people contributed to infection risk among vaccinated individuals at twice the rate that would have been expected based on the frequency of contacts. These findings were robust across a range of assumptions around the rate of waning immunity, the impact of "hybrid immunity", frequency of boosting, and the impact of prior infection on infectivity in unvaccinated people. INTERPRETATION: Although the emergence of the Omicron variants of SARS-CoV-2 has diminished the protective effects of vaccination against infection with SARS-CoV-2, updating our earlier model to incorporate loss of immunity, diminished vaccine efficacy and a longer time horizon, does not qualitatively change our earlier conclusions. Vaccination against SARS-CoV-2 continues to diminish the risk of infection among vaccinated people and in the population as a whole. By contrast, the risk of infection among vaccinated people accrues disproportionately from contact with unvaccinated people.

R 0 May Not Tell Us Everything: Transient Disease Dynamics of Some SIR Models Over Patchy Environments.

This paper examines the short-term or transient dynamics of SIR infectious disease models in patch environments. We employ reactivity of an equilibrium and amplification rates, concepts from ecology, to analyze how dispersals/travels between patches, spatial heterogeneity, and other disease-related parameters impact short-term dynamics. Our findings reveal that in certain scenarios, due to the impact of spatial heterogeneity and the dispersals, the short-term disease dynamics over a patch environment may disagree with the long-term disease dynamics that is typically reflected by the basic reproduction number. Such an inconsistence can mislead the public, public healthy agencies and governments when making public health policy and decisions, and hence, these findings are of practical importance.

Estimating household contact matrices structure from easily collectable metadata.

Contact matrices are a commonly adopted data representation, used to develop compartmental models for epidemic spreading, accounting for the contact heterogeneities across age groups. Their estimation, however, is generally time and effort consuming and model-driven strategies to quantify the contacts are often needed. In this article we focus on household contact matrices, describing the contacts among the members of a family and develop a parametric model to describe them. This model combines demographic and easily quantifiable survey-based data and is tested on high resolution proximity data collected in two sites in South Africa. Given its simplicity and interpretability, we expect our method to be easily applied to other contexts as well and we identify relevant questions that need to be addressed during the data collection procedure.

Final epidemic size of a two-community SIR model with asymmetric coupling.

Communities are commonly not isolated but interact asymmetrically with each other, allowing the propagation of infectious diseases within the same community and between different communities. To reveal the impact of asymmetrical interactions and contact heterogeneity on disease transmission, we formulate a two-community SIR epidemic model, in which each community has its contact structure while communication between communities occurs through temporary commuters. We derive an explicit formula for the basic reproduction number R 0 , give an implicit equation for the final epidemic size z, and analyze the relationship between them. Unlike the typical positive correlation between R 0 and z in the classic SIR model, we find a negatively correlated relationship between counterparts of our model deviating from homogeneous populations. Moreover, we investigate the impact of asymmetric coupling mechanisms on R 0 . The results suggest that, in scenarios with restricted movement of susceptible individuals within a community, R 0 does not follow a simple monotonous relationship, indicating that an unbending decrease in the movement of susceptible individuals may increase R 0 . We further demonstrate that network contacts within communities have a greater effect on R 0 than casual contacts between communities. Finally, we develop an epidemic model without restriction on the movement of susceptible individuals, and the numerical simulations suggest that the increase in human flow between communities leads to a larger R 0 .

Predicting Drug-Drug Interactions Involving Rifampicin Using a Semi-mechanistic Hepatic Compartmental Model.

AIMS: To develop a semi-mechanistic hepatic compartmental model to predict the effects of rifampicin, a known inducer of CYP3A4 enzyme, on the metabolism of five drugs, in the hope of informing dose adjustments to avoid potential drug-drug interactions. METHODS: A search was conducted for DDI studies on the interactions between rifampicin and CYP substrates that met specific criteria, including the availability of plasma concentration-time profiles, physical and absorption parameters, pharmacokinetic parameters, and the use of healthy subjects at therapeutic doses. The semi-mechanistic model utilized in this study was improved from its predecessors, incorporating additional parameters such as population data (specifically for Chinese and Caucasians), virtual individuals, gender distribution, age range, dosing time points, and coefficients of variation. RESULTS: Optimal parameters were identified for our semi-mechanistic model by validating it with clinical data, resulting in a maximum difference of approximately 2-fold between simulated and observed values. PK data of healthy subjects were used for most CYP3A4 substrates, except for gilteritinib, which showed no significant difference between patients and healthy subjects. Dose adjustment of gilteritinib co-administered with rifampicin required a 3-fold increase of the initial dose, while other substrates were further tuned to achieve the desired drug exposure. CONCLUSIONS: The pharmacokinetic parameters AUCR and CmaxR of drugs metabolized by CYP3A4, when influenced by Rifampicin, were predicted by the semi-mechanistic model to be approximately twice the empirically observed values, which suggests that the semi-mechanistic model was able to reasonably simulate the effect. The doses of four drugs adjusted via simulation to reduce rifampicin interaction.

Impact of ontogenic changes on the dynamics of a fungal crop disease model motivated by coffee leaf rust.

Ontogenic resistance has been described for many plant-pathogen systems. Conversely, coffee leaf rust, a major fungal disease that drastically reduces coffee production, exhibits a form of ontogenic susceptibility, with a higher infection risk for mature leaves. To take into account stage-dependent crop response to phytopathogenic fungi, we developed an SEIR-U epidemiological model, where U stands for spores, which differentiates between young and mature leaves. Based on this model, we also explored the impact of ontogenic resistance on the sporulation rate. We computed the basic reproduction number [Formula: see text], which classically determines the stability of the disease-free equilibrium. We identified forward and backward bifurcation cases. The backward bifurcation is generated by the high sporulation of young leaves compared to mature ones. In this case, when the basic reproduction number is less than one, the disease can persist. These results provide useful insights on the disease dynamics and its control. In particular, ontogenic resistance may require higher control efforts to eradicate the disease.

The role of natural recovery category in malaria dynamics under saturated treatment.

In the process of malaria transmission, natural recovery individuals are slightly infectious compared with infected individuals. Our concern is whether the infectivity of natural recovery category can be ignored in areas with limited medical resources, so as to reveal the epidemic pattern of malaria with simpler analysis. To achieve this, we incorporate saturated treatment into two-compartment and three-compartment models, and the infectivity of natural recovery category is only reflected in the latter. The non-spatial two-compartment model can admit backward bifurcation. Its spatial version does not possess rich dynamics. Besides, the non-spatial three-compartment model can undergo backward bifurcation, Hopf bifurcation and Bogdanov-Takens bifurcation. For spatial three-compartment model, due to the complexity of characteristic equation, we apply Shengjin's Distinguishing Means to realize stability analysis. Further, the model exhibits Turing instability, Hopf bifurcation and Turing-Hopf bifurcation. This makes the model may admit bistability or even tristability when its basic reproduction number less than one. Biologically, malaria may present a variety of epidemic trends, such as elimination or inhomogeneous distribution in space and periodic fluctuation in time of infectious populations. Notably, parameter regions are given to illustrate substitution effect of two-compartment model for three-compartment model in both scenarios without or with spatial movement. Finally, spatial three-compartment model is used to present malaria transmission in Burundi. The application of efficiency index enables us to determine the most effective method to control the number of cases in different scenarios.

Stochastic transmission in epidemiological models.

Recent empirical evidence suggests that the transmission coefficient in susceptible-exposed-infected-removed-like (SEIR-like) models evolves with time, presenting random patterns, and some stylized facts, such as mean-reversion and jumps. To address such observations we propose the use of jump-diffusion stochastic processes to parameterize the transmission coefficient in an SEIR-like model that accounts for death and time-dependent parameters. We provide a detailed theoretical analysis of the proposed model proving the existence and uniqueness of solutions as well as studying its asymptotic behavior. We also compare the proposed model with some variations possibly including jumps. The forecast performance of the considered models, using reported COVID-19 infections from New York City, is then tested in different scenarios. Despite the simplicity of the epidemiological model, by considering stochastic transmission, the forecasted scenarios were fairly accurate.

A novel monolayer adsorption kinetic model based on adsorbates "infect" adsorbents inspired by epidemiological model.

Adsorption is a unit operation process with broad applications in environmental, pharmaceutical, and chemical fields, with its most significance in environmental fields for water and wastewater treatment. Adsorption involves continuous/batch modes with fixed/dispersed adsorbents, leading to diverse systems. The adsorption kinetic models provide essential insights for effectively designing these systems. However, many adsorption models are semi-empirical/empirical, making it challenging to identify the adsorption mechanisms. Additionally, a consistent method for modelling the adsorption kinetics of different processes would be helpful for the comparison and analysis of various adsorption systems, but no such unified model is available. In epidemiological modeling, populations are often categorized into susceptible, infected, and removed individuals, simplifying disease transmission dynamics without considering individual-level movement intricacies. Likewise, we have employed a similar approach within adsorption systems, classifying adsorbates into absorbable, adsorbed, and removed (to the effluent) segments, thus developing the Monolayer-Absorbable-Adsorbed-Removed (MPQR) kinetics model. This model is applicable to continuous/batch adsorption systems, regardless of whether fixed or dispersed adsorbents are employed. The model was validated using experimental data across water/wastewater treatment, drug separation/purification, metal recovery, and desalination. The results showed that our model successfully fitted the kinetic data from various adsorption systems. It outperformed commonly used models for continuous/batch adsorption. The model allowed us to directly compare the parameters among various adsorption processes. The solving method based on Excel was provided and can be used by the researchers. Our model offers a versatile and unified approach to model adsorption kinetics, enabling the analysis and design of various adsorption systems.

A Generalized Kinetic Model of Fractional Order Transport Dynamics with Transit Time Heterogeneity in Microvascular Space.

The aim of this study is to develop and validate a unifying kinetic model for microvascular transport by introducing an impulse response function that incorporates essential physiological parameters and integrates key features of existing models. This new methodology combines a one-compartment model of fractional order with a model that uses the gamma distribution to describe the distribution of capillary transit times. Central to this model are two primary parameters: [Formula: see text], representing the kurtosis of residue times, and [Formula: see text], signifying the width of the distribution of capillary transit times within a tissue voxel. To validate this proposed model, data from dynamic contrast-enhanced magnetic resonance imaging (DCI-MRI) were employed and the findings were compared with three existing models. Using the Akaike information criterion for model selection, the results demonstrate that the integrative model, especially at elevated blood flow rates, frequently offers superior fits in comparison to constrained models.

Markets as drivers of selection for highly virulent poultry pathogens.

Theoretical models have successfully predicted the evolution of poultry pathogen virulence in industrialized farm contexts of broiler chicken populations. Whether there are ecological factors specific to more traditional rural farming that affect virulence is an open question. Within non-industrialized farming networks, live bird markets are known to be hotspots of transmission, but whether they could shift selection pressures on the evolution of poultry pathogen virulence has not been addressed. Here, we revisit predictions for the evolution of virulence for viral poultry pathogens, such as Newcastle's disease virus, Marek's disease virus, and influenza virus, H5N1, using a compartmental model that represents transmission in rural markets. We show that both the higher turnover rate and higher environmental persistence in markets relative to farms could select for higher optimal virulence strategies. In contrast to theoretical results modeling industrialized poultry farms, we find that cleaning could also select for decreased virulence in the live poultry market setting. Additionally, we predict that more virulent strategies selected in markets could circulate solely within poultry located in markets. Thus, we recommend the close monitoring of markets not only as hotspots of transmission, but as potential sources of more virulent strains of poultry pathogens.

Quantifying health risks from ESBL-producing Escherichia coli in Dutch broiler production chains and potential interventions using compartmental models.

Extended-spectrum beta-lactamase (ESBL)-producing Escherichia coli (E. coli) in animals are considered a human health threat, because this type of bacteria can serve as a reservoir of antibiotic resistant genes and act as a continuous threat of the emergence of new resistant bacteria, in addition to the direct effect of making infection untreatable. Although the prevalence of ESBL producing bacteria in broilers was drastically reduced in the Netherlands, chicken meat still has the highest prevalence among meat products. Therefore, further control of the ESBL-producing E. coli in the broiler production chain is important to reduce public health risks. The main objectives of this study were to evaluate the effectiveness of intervention scenarios to reduce the transmission of ESBL-producing E. coli in the broiler production chain and to quantitatively estimate the risk to public health. In this study, we developed two different types of transmission models that described the observed time-related decline in prevalence during a production round: one with time-dependent decline in susceptibility and one with partial immunity to phylogenetic groups. Both models incorporated the environmental contamination effect between production rounds and within flocks. The parameter values, including transmission rate and recovery rate, were estimated by Approximate Bayesian computation (ABC) method using data from a longitudinal study in a Dutch organic broiler farm. We applied the models to the three production stages in the broiler production chain, beginning from the Parent Stock (PS) farms, the hatcheries, and to the broiler farms. In our models, eggs were collected from different parent stock farms and transported to the hatchery and from there to a broiler farm.The size of a flock and the number of farms were adjusted to the Dutch situation. Both models were able to describe the observed dynamics within and between the production stages equally well, with estimated ESBL-producing E. coli prevalence of 8.98% and 11.47% in broilers at slaughter and 0.12% and 0.15% in humans due to chicken consumption. Both models indicated that improving farm management to eliminate the bacteria from the environment was the most effective intervention, making this outcome robust. Although chicken meat consumption is not a major risk factor for human carriage of the bacteria according to our models, reducing the bacteria in the PS and broiler farm environment to at least one percent can further decrease the prevalence in humans.

The probability of epidemic burnout in the stochastic SIR model with vital dynamics.

We present an approach to computing the probability of epidemic "burnout," i.e., the probability that a newly emergent pathogen will go extinct after a major epidemic. Our analysis is based on the standard stochastic formulation of the Susceptible-Infectious-Removed (SIR) epidemic model including host demography (births and deaths) and corresponds to the standard SIR ordinary differential equations (ODEs) in the infinite population limit. Exploiting a boundary layer approximation to the ODEs and a birth-death process approximation to the stochastic dynamics within the boundary layer, we derive convenient, fully analytical approximations for the burnout probability. We demonstrate-by comparing with computationally demanding individual-based stochastic simulations and with semi-analytical approximations derived previously-that our fully analytical approximations are highly accurate for biologically plausible parameters. We show that the probability of burnout always decreases with increased mean infectious period. However, for typical biological parameters, there is a relevant local minimum in the probability of persistence as a function of the basic reproduction number [Formula: see text]. For the shortest infectious periods, persistence is least likely if [Formula: see text]; for longer infectious periods, the minimum point decreases to [Formula: see text]. For typical acute immunizing infections in human populations of realistic size, our analysis of the SIR model shows that burnout is almost certain in a well-mixed population, implying that susceptible recruitment through births is insufficient on its own to explain disease persistence.

Vaccination compartmental epidemiological models for the delta and omicron SARS-CoV-2 variants.

We explore the inclusion of vaccination in compartmental epidemiological models concerning the delta and omicron variants of the SARS-CoV-2 virus that caused the COVID-19 pandemic. We expand on our earlier compartmental-model work by incorporating vaccinated populations. We present two classes of models that differ depending on the immunological properties of the variant. The first one is for the delta variant, where we do not follow the dynamics of the vaccinated individuals since infections of vaccinated individuals were rare. The second one for the far more contagious omicron variant incorporates the evolution of the infections within the vaccinated cohort. We explore comparisons with available data involving two possible classes of counts, fatalities and hospitalizations. We present our results for two regions, Andalusia and Switzerland (including the Principality of Liechtenstein), where the necessary data are available. In the majority of the considered cases, the models are found to yield good agreement with the data and have a reasonable predictive capability beyond their training window, rendering them potentially useful tools for the interpretation of the COVID-19 and further pandemic waves, and for the design of intervention strategies during these waves.

A compartmental model for Schistosoma japonicum transmission dynamics in the Philippines.

Schistosomiasis is a chronic and debilitating neglected tropical disease (NTD), second only to malaria as one of the most devastating parasitic diseases. Caused by a parasitic flatworm of the genus Schistosoma, infection occurs when skin comes in contact with contaminated freshwater that contains schistosome-hosting snails. The disease continues to be endemic in many regions of the Philippines, where it poses a significant public health challenge due to a lack of healthcare resources. In the Philippines, additional mammalian reservoirs for the S. japonicum parasite, especially bovines such as carabaos, also facilitate the spread of schistosomiasis. We extend existing compartment models to include human, snail, bovine, and free-living Schistosoma for a comprehensive look at the transmission dynamics of the disease. Sensitivity analysis of model parameters shows that the carabaos themselves can sustain the endemicity of schistosomiasis. Thus, we consider the control method of farming mechanization to avoid contaminated freshwater sources. We find that a reduction of contaminated water contacts by at least 77% will break the transmission cycle and eliminate the disease. However, reducing the contact by about 70% will still result in decrease of human schistosomiasis prevalence to under 1% in 15 years or less. Achieving such high reduction of contact rates could be a daunting task, especially in rural areas. Still, the potential to eliminate or at least reduce the schistosomiasis prevalence should be considered an additional benefit of mechanization efforts in the Philippines.

A compartment model for subcutaneous injection of monoclonal antibodies.

Despite the growing popularity of subcutaneous (SC) administration for monoclonal antibodies (mAbs), there remains a limited understanding of the significance of mAb transport rate constants within the interstitial space and the lymphatic system on their pharmacokinetics. To bridge this knowledge gap, we introduce a compartmental model for subcutaneously administered mAbs. Our model differentiates FcRn-expressing cells across various sites, and the model predictions agree with experimental data from both human and rat studies. Our findings indicate that the time to reach the maximum mAb concentration in the plasma, denoted by Tmax, displays a weak positive correlation with mAb half-life and a negligible correlation with bioavailability. In contrast, the half-life of mAbs exhibits a strong positive correlation with bioavailability. Moreover, the rate of mAb transport from lymph to plasma significantly affects the mAb half-life. Increasing the transport rates of mAbs from the injection site to the lymph or from lymph to plasma enhances bioavailability. These insights, combined with our compartmental model, contribute to a deeper understanding of the pharmacokinetics of subcutaneously administered mAbs.

An epidemiological model for analysing pandemic trends of novel coronavirus transmission with optimal control.

Symptomatic and asymptomatic individuals play a significant role in the transmission dynamics of novel Coronaviruses. By considering the dynamical behaviour of symptomatic and asymptomatic individuals, this study examines the temporal dynamics and optimal control of Coronavirus disease propagation using an epidemiological model. Biologically and mathematically, the well-posed epidemic problem is examined, as well as the threshold quantity with parameter sensitivity. Model parameters are quantified and their relative impact on the disease is evaluated. Additionally, the steady states are investigated to determine the model's stability and bifurcation. Using the dynamics and parameters sensitivity, we then introduce optimal control strategies for the elimination of the disease. Using real disease data, numerical simulations and model validation are performed to support theoretical findings and show the effects of control strategies.

Fundamental bound on epidemic overshoot in the SIR model.

We derive an exact upper bound on the epidemic overshoot for the Kermack-McKendrick SIR model. This maximal overshoot value of 0.2984 · · · occurs at [Formula: see text]. In considering the utility of the notion of overshoot, a rudimentary analysis of data from the first wave of the COVID-19 pandemic in Manaus, Brazil highlights the public health hazard posed by overshoot for epidemics with R0 near 2. Using the general analysis framework presented within, we then consider more complex SIR models that incorporate vaccination.

An immune memory-structured SIS epidemiological model for hyperdiverse pathogens.

A hyperdiverse class of pathogens of humans and wildlife, including the malaria parasite Plasmodium falciparum, relies on multigene families to encode antigenic variation. As a result, high (asymptomatic) prevalence is observed despite high immunity in local populations under high-transmission settings. The vast diversity of "strains" and genes encoding this variation challenges the application of established models for the population dynamics of such infectious diseases. Agent-based models have been formulated to address theory on strain coexistence and structure, but their complexity can limit application to gain insights into population dynamics. Motivated by P. falciparum malaria, we develop an alternative formulation in the form of a structured susceptible-infected-susceptible population model in continuous time, where individuals are classified not only by age, as is standard, but also by the diversity of parasites they have been exposed to and retain in their specific immune memory. We analyze the population dynamics and bifurcation structure of this system of partial-differential equations, showing the existence of alternative steady states and an associated tipping point with transmission intensity. We attribute the critical transition to the positive feedback between parasite genetic diversity and force of infection. Basins of attraction show that intervention must drastically reduce diversity to prevent a rebound to high infection levels. Results emphasize the importance of explicitly considering pathogen diversity and associated specific immune memory in the population dynamics of hyperdiverse epidemiological systems. This statement is discussed in a more general context for ecological competition systems with hyperdiverse trait spaces.