An Epidemic Model with Infection Age and Vaccination Age Structure.

A model of epidemic dynamics is developed that incorporates continuous variables for infection age and vaccination age. The model analyzes pre-symptomatic and symptomatic periods of an infected individual in terms of infection age. This property is shown to be of major importance in the severity of the epidemic, when the infectious period of an infected individual precedes the symptomatic period. The model also analyzes the efficacy of vaccination in terms of vaccination age. The immunity to infection of vaccinated individuals varies with vaccination age and is also of major significance in the severity of the epidemic. Application of the model to the 2003 SARS epidemic in Taiwan and the COVID-19 epidemic in New York provides insights into the dynamics of these diseases. It is shown that the SARS outbreak was effectively contained due to the complete overlap of infectious and symptomatic periods, allowing for the timely isolation of affected individuals. In contrast, the pre-symptomatic spread of COVID-19 in New York led to a rapid, uncontrolled epidemic. These findings underscore the critical importance of the pre-symptomatic infectious period and the vaccination strategies in influencing the dynamics of an epidemic.

Bifurcation analysis of critical values for wound closure outcomes in wound healing experiments.

A nonlinear partial differential equation containing a nonlocal advection term and a diffusion term is analyzed to study wound closure outcomes in wound healing experiments. There is an extensive literature of similar models for wound healing experiments. In this paper we study the character of wound closure in these experiments in terms of the sensing radius of cells and the force of cell-cell adhesion. We prove a bifurcation result which differentiates uniform closure of the wound from nonuniform closure of the wound, based on a critical value [Formula: see text] of the force of cell-cell adhesion parameter [Formula: see text]. For [Formula: see text] the steady state solution [Formula: see text] of the model is stable and the wound closes uniformly. For [Formula: see text] the steady state solution [Formula: see text] of the model is unstable and the wound closes nonuniformly. We provide numerical simulations of the model to illustrate our results.

The force of cell-cell adhesion in determining the outcome in a nonlocal advection diffusion model of wound healing.

A model of wound healing is presented to investigate the connection of the force of cell-cell adhesion to the sensing radius of cells in their spatial environment. The model consists of a partial differential equation with nonlocal advection and diffusion terms, describing the movement of cells in a spatial environment. The model is applied to biological wound healing experiments to understand incomplete wound closure. The analysis demonstrates that for each value of the force of adhesion parameter, there is a critical value of the sensing radius above which complete wound healing does not occur.

Modeling Vaccine Efficacy for COVID-19 Outbreak in New York City.

In this article we study the efficacy of vaccination in epidemiological reconstructions of COVID-19 epidemics from reported cases data. Given an epidemiological model, we developed in previous studies a method that allowed the computation of an instantaneous transmission rate that produced an exact fit of reported cases data of the COVID-19 outbreak. In this article, we improve the method by incorporating vaccination data. More precisely, we develop a model in which vaccination is variable in its effectiveness. We develop a new technique to compute the transmission rate in this model, which produces an exact fit to reported cases data, while quantifying the efficacy of the vaccine and the daily number of vaccinated. We apply our method to the reported cases data and vaccination data of New York City.

A COVID-19 Epidemic Model Predicting the Effectiveness of Vaccination in the US.

A model of a COVID-19 epidemic is used to predict the effectiveness of vaccination in the US. The model incorporates key features of COVID-19 epidemics: asymptomatic and symptomatic infectiousness, reported and unreported cases data, and social measures implemented to decrease infection transmission. The model analyzes the effectiveness of vaccination in terms of vaccination efficiency, vaccination scheduling, and relaxation of social measures that decrease disease transmission. The model demonstrates that the subsiding of the epidemic as vaccination is implemented depends critically on the scale of relaxation of social measures that reduce disease transmission.

Predicting the cumulative number of cases for the COVID-19 epidemic in China from early data.

We model the COVID-19 coronavirus epidemic in China. We use early reported case data to predict the cumulative number of reported cases to a final size. The key features of our model are the timing of implementation of major public policies restricting social movement, the identification and isolation of unreported cases, and the impact of asymptomatic infectious cases.

Modelling the aqueous transport of an infectious pathogen in regional communities: application to the cholera outbreak in Haiti.

A mathematical model is developed to describe the dynamics of the spread of a waterborne disease among communities located along a flowing waterway. The model is formulated as a system of reaction-diffusion-advection partial differential equations in this spatial setting. The compartments of the model consist of susceptible, infected, and recovered individuals in the communities along the waterway, together with a term representing the pathogen load in each community and a term representing the spatial concentration of pathogens flowing along the waterway. The model is applied to the cholera outbreak in Haiti in 2010.

Understanding Unreported Cases in the COVID-19 Epidemic Outbreak in Wuhan, China, and the Importance of Major Public Health Interventions.

We develop a mathematical model to provide epidemic predictions for the COVID-19 epidemic in Wuhan, China. We use reported case data up to 31 January 2020 from the Chinese Center for Disease Control and Prevention and the Wuhan Municipal Health Commission to parameterize the model. From the parameterized model, we identify the number of unreported cases. We then use the model to project the epidemic forward with varying levels of public health interventions. The model predictions emphasize the importance of major public health interventions in controlling COVID-19 epidemics.

Predicting the long-term impact of voluntary medical male circumcision on HIV incidence among men who have sex with men in Beijing, China.

Using a deterministic compartmental modeling procedure to fit prevalence from 2005-2015, we projected new HIV cases during 2016-2026 under different coverage rates ranging from 0.0001 (at baseline) to 0.15 (an optimistic assumption) with simulations on varying transmission rates, model calibration to match historical data, and sensitivity analyses for different assumptions. Compared with the baseline (λ = 0.0001), we found the new HIV cases would reduce with the increase of coverage rates of the voluntary medical male circumcision (VMMC) among men who have sex wtih men (MSM). The higher the coverage rate, the lower the new HIV incidence would be. As one of the first studies to model the potential impact of VMMC among MSM in China, our model suggested a modest to the significant public health impact of VMMC. Even at just 15% VMMC annual uptake rate, the reduction in new infections is substantial. Therefore, there is a strong need to determine the efficacy of VMMC among MSM, to improve the evidence base for its potential use among MSM in low circumcision settings. Only then can policymakers decide whether to incorporate VMMC into a package of HIV prevention interventions targeting MSM.

Spatial models of vector-host epidemics with directed movement of vectors over long distances.

We investigate a time-dependent spatial vector-host epidemic model with non-coincident domains for the vector and host populations. The host population resides in small non-overlapping sub-regions, while the vector population resides throughout a much larger region. The dynamics of the populations are modeled by a reaction-diffusion-advection compartmental system of partial differential equations. The disease is transmitted through vector and host populations in criss-cross fashion. We establish global well-posedness and uniform a prior bounds as well as the long-term behavior. The model is applied to simulate the outbreak of bluetongue disease in sheep transmitted by midges infected with bluetongue virus. We show that the long-range directed movement of the midge population, due to wind-aided movement, enhances the transmission of the disease to sheep in distant sites.

Modeling economic and epidemiological impact of voluntary medical male circumcision among men who have sex with men in Beijing, China.

Voluntary medical male circumcision (VMMC) among men who have sex with men (MSM) may protect against HIV acquisition. We conducted a series of analyses to assess if expanded VMMC might reduce HIV incidence among MSM effectively and economically. We used a deterministic compartmental model to project new HIV cases (2016-2026) under annual VMMC coverage rates (λ) ranging from 0.0001 to 0.15. The 'number needed to avert' (NNA) is defined as the cumulative number of VMMCs conducted up to that year divided by the cumulative number of HIV cases averted in that specific year. Compared with the baseline circumcision coverage rate, we projected that new HIV cases would be reduced with increasing coverage. By 2026 (last year simulated), the model generated the lowest ratio (11.10) when the annual circumcision rate was the most optimistic (λ = 0.15). The breakeven point was observed at the year of 2019 with the annual VMMC coverage rate of 0.001. The total cost saved by averting HIV cases would range from 2.5 to 811 million US dollars by the end of 2026 with different hypothetical coverage rates. Our model suggests that acceleration in VMMC implementation among MSM could help stem the HIV/AIDS epidemic.

A dynamic model of CT scans for quantifying doubling time of ground glass opacities using histogram analysis.

We quantify a recent five-category CT histogram based classification of ground glass opacities using a dynamic mathematical model for the spatial-temporal evolution of malignant nodules. Our mathematical model takes the form of a spatially structured partial differential equation with a logistic crowding term. We present the results of extensive simulations and validate our model using patient data obtained from clinical CT images from patients with benign and malignant lesions.

Final size of a multi-group SIR epidemic model: Irreducible and non-irreducible modes of transmission.

A model of an epidemic outbreak incorporating multiple subgroups of susceptible and infected individuals is investigated. The asymptotic behavior of the model is analyzed and it is proved that the infected classes all converge to 0. A computational algorithm is developed for the cumulative final size of infected individuals over the course of the epidemic. The results are applied to the SARS epidemic in Singapore in 2003, where it is shown that the two-peak evolution of the infected population can be attributed to a two-group formulation of transmission.

The parameter identification problem for SIR epidemic models: identifying unreported cases.

A SIR epidemic model is analyzed with respect to identification of its parameters, based upon reported case data from public health sources. The objective of the analysis is to understand the relation of unreported cases to reported cases. In many epidemic diseases the ratio of unreported to reported cases is very high, and of major importance in implementing measures for controlling the epidemic. This ratio can be estimated by the identification of parameters for the model from reported case data. The analysis is applied to three examples: (1) the Hong Kong seasonal influenza epidemic in New York City in 1968-1969, (2) the bubonic plague epidemic in Bombay, India in 1906, and (3) the seasonal influenza epidemic in Puerto Rico in 2016-2017.

Optimal control applied to community-acquired methicillin-resistant Staphylococcus aureus in hospitals.

Optimal control methods are applied to a deterministic mathematical model to characterize the factors contributing to the replacement of hospital-acquired methicillin-resistant Staphylococcus aureus (HA-MRSA) with community-acquired methicillin-resistant Staphylococcus aureus (CA-MRSA), and quantify the effectiveness of three interventions aimed at limiting the spread of CA-MRSA in healthcare settings. Characterizations of the optimal control strategies are established, and numerical simulations are provided to illustrate the results.

Modeling contact tracing in outbreaks with application to Ebola.

Contact tracing is an important control strategy for containing Ebola epidemics. From a modeling perspective, explicitly incorporating contact tracing with disease dynamics presents challenges, and population level effects of contact tracing are difficult to determine. In this work, we formulate and analyze a mechanistic SEIR type outbreak model which considers the key features of contact tracing, and we characterize the impact of contact tracing on the effective reproduction number, Re, of Ebola. In particular, we determine how relevant epidemiological properties such as incubation period, infectious period and case reporting, along with varying monitoring protocols, affect the efficacy of contact tracing. In the special cases of either perfect monitoring of traced cases or perfect reporting of all cases, we derive simple formulae for the critical proportion of contacts that need to be traced in order to bring the effective reproduction number Re below one. Also, in either case, we show that Re can be expressed completely in terms of observable reported case/tracing quantities, namely Re = k((1-q)/q)+km where k is the number of secondary traced infected contacts per primary untraced reported case, km is the number of secondary traced infected contacts per primary traced reported case and (1-q)/q is the odds that a reported case is not a traced contact. These formulae quantify contact tracing as both an intervention strategy that impacts disease spread and a probe into the current epidemic status at the population level. Data from the West Africa Ebola outbreak is utilized to form real-time estimates of Re, and inform our projections of the impact of contact tracing, and other control measures, on the epidemic trajectory.

A nosocomial epidemic model with infection of patients due to contaminated rooms.

A model of epidemic bacterial infections in hospitals is developed. The model incorporates the infection of patients and the contamination of healthcare workers due to environmental causes. The model is analyzed with respect to the asymptotic behavior of solutions. The model is interpreted to provide insight for controlling these nosocomial epidemics.

A model of the 2014 ebola epidemic in west Africa with contact tracing.

A differential equations model is developed for the 2014 Ebola epidemics in Sierra Leone and Liberia. The model describes the dynamic interactions of the susceptible and infected populations of these countries. The model incorporates the principle features of contact tracing, namely, the number of contacts per identified infectious case, the likelihood that a traced contact is infectious, and the efficiency of the contact tracing process. The model is first fitted to current cumulative reported case data in each country. The data fitted simulations are then projected forward in time, with varying parameter regimes corresponding to contact tracing efficiencies. These projections quantify the importance of the identification, isolation, and contact tracing processes for containment of the epidemics.

Host demise as a beneficial function of indigenous microbiota in human hosts.

UNLABELLED: The age structure of human populations is exceptional among animal species. Unlike with most species, human juvenility is extremely extended, and death is not coincident with the end of the reproductive period. We examine the age structure of early humans with models that reveal an extraordinary balance of human fertility and mortality. We hypothesize that the age structure of early humans was maintained by mechanisms incorporating the programmed death of senescent individuals, including by means of interactions with their indigenous microorganisms. First, before and during reproductive life, there was selection for microbes that preserve host function through regulation of energy homeostasis, promotion of fecundity, and defense against competing high-grade pathogens. Second, we hypothesize that after reproductive life, there was selection for organisms that contribute to host demise. While deleterious to the individual, the presence of such interplay may be salutary for the overall host population in terms of resource utilization, resistance to periodic diminutions in the food supply, and epidemics due to high-grade pathogens. We provide deterministic mathematical models based on age-structured populations that illustrate the dynamics of such relationships and explore the relevant parameter values within which population viability is maintained. We argue that the age structure of early humans was robust in its balance of the juvenile, reproductive-age, and senescent classes. These concepts are relevant to issues in modern human longevity, including inflammation-induced neoplasia and degenerative diseases of the elderly, which are a legacy of human evolution. IMPORTANCE: The extended longevity of modern humans is a very recent societal artifact, although it is inherent in human evolution. The age structure of early humans was balanced by fertility and mortality, with an exceptionally prolonged juvenility. We examined the role of indigenous microbes in early humans as fundamental contributors to this age structure. We hypothesize that the human microbiome evolved mechanisms specific to the mortality of senescent individuals among early humans because their mortality contributed to the stability of the general population. The hypothesis that we present provides new bases for modern medical problems, such as inflammation-induced neoplasia and degenerative diseases of the elderly. We postulate that these mechanisms evolved because they contributed to the stability of early human populations, but their legacy is now a burden on human longevity in the changed modern world.

Modeling the impact on HIV incidence of combination prevention strategies among men who have sex with men in Beijing, China.

OBJECTIVE: To project the HIV/AIDS epidemics among men who have sex with men (MSM) under different combinations of HIV testing and linkage to care (TLC) interventions including antiretroviral therapy (ART) in Beijing, China. DESIGN: Mathematical modeling. METHODS: Using a mathematical model to fit prevalence estimates from 2000-2010, we projected trends in HIV prevalence and incidence during 2011-2020 under five scenarios: (S1) current intervention levels by averaging 2000-2010 coverage; (S2) increased ART coverage with current TLC; (S3) increased TLC/ART coverage; (S4) increased condom use; and (S5) increased TLC/ART plus increased condom use. RESULTS: The basic reproduction number based upon the current level of interventions is significantly higher than 1 (R0 = 2.09; 95% confidence interval (CI), 1.83-2.35), suggesting that the HIV epidemic will continue to increase to 2020. Compared to the 2010 prevalence of 7.8%, the projected HIV prevalence in 2020 for the five prevention scenarios will be: (S1) Current coverage: 21.4% (95% CI, 9.9-31.7%); (S2) Increased ART: 19.9% (95% CI, 9.9-28.4%); (S3) Increased TLC/ART: 14.5% (95% CI, 7.0-23.8%); (S4) Increased condom use: 13.0% (95% CI, 9.8-28.4%); and (S5) Increased TLC/ART and condom use: 8.7% (95% CI, 5.4-11.5%). HIV epidemic will continue to rise (R0 > 1) for S1-S4 even with hyperbolic coverage in the sensitivity analysis, and is expected to decline (R0 = 0.93) for S5. CONCLUSION: Our transmission model suggests that Beijing MSM will have a rapidly rising HIV epidemic. Even enhanced levels of TLC/ART will not interrupt epidemic expansion, despite optimistic assumptions for coverage. Promoting condom use is a crucial component of combination interventions.