A runtime alterable epidemic model with genetic drift, waning immunity and vaccinations.

We present methods for building a Java Runtime-Alterable-Model Platform (RAMP) of complex dynamical systems. We illustrate our methods by building a multivariant SEIR (epidemic) RAMP. Underlying our RAMP is an individual-based model that includes adaptive contact rates, pathogen genetic drift, waning and cross-immunity. Besides allowing parameter values, process descriptions and scriptable runtime drivers to be easily modified during simulations, our RAMP can used within R-Studio and other computational platforms. Process descriptions that can be runtime altered within our SEIR RAMP include pathogen variant-dependent host shedding, environmental persistence, host transmission and within-host pathogen mutation and replication. They also include adaptive social distancing and adaptive application of vaccination rates and variant-valency of vaccines. We present simulation results using parameter values and process descriptions relevant to the current COVID-19 pandemic. Our results suggest that if waning immunity outpaces vaccination rates, then vaccination rollouts may fail to contain the most transmissible variants, particularly if vaccine valencies are not adapted to deal with escape mutations. Our SEIR RAMP is designed for easy use by others. More generally, our RAMP concept facilitates construction of highly flexible complex systems models of all types, which can then be easily shared as stand-alone application programs.

Modeling the population effects of escape mutations in SARS-CoV-2 to guide vaccination strategies.

SARS-Cov-2 escape mutations (EM) have been detected and are spreading. Vaccines may need adjustment to respond to these or future mutations. We designed a population level model integrating both waning immunity and EM. We also designed a set of criteria for elaborating and fitting this model to cross-neutralization and other data with a goal of minimizing vaccine decision errors. We formulated four related models. These differ regarding which strains can drift to escape immunity in the host when that immunity was elicited by different strains. Across changing waning and escape mutation parameter values, these model variations led to patterns where: 1) EM are rare in the first epidemic, 2) rebound outbreaks after the first outbreak are accelerated by increasing waning and by increasing drifting, 3) the long term endemic level of infection is determined mostly by waning rates with small effects of the drifting parameter, 4) EM caused loss of vaccine effectiveness, and under some conditions: vaccines induced EM that caused higher levels of infection with vaccines than without them. The differences and similarities across the four models suggest paths for developing models specifying the epitopes where EM act. This model provides a base on which to construct epitope specific evolutionary models using new high-throughput assay data from population samples to guide vaccine decisions.

The geometry of reaction norms yields insights on classical fitness functions for Great Lakes salmon.

Life history theory examines how characteristics of organisms, such as age and size at maturity, may vary through natural selection as evolutionary responses that optimize fitness. Here we ask how predictions of age and size at maturity differ for the three classical fitness functions-intrinsic rate of natural increase r, net reproductive rate R0, and reproductive value Vx-for semelparous species. We show that different choices of fitness functions can lead to very different predictions of species behavior. In one's efforts to understand an organism's behavior and to develop effective conservation and management policies, the choice of fitness function matters. The central ingredient of our approach is the maturation reaction norm (MRN), which describes how optimal age and size at maturation vary with growth rate or mortality rate. We develop a practical geometric construction of MRNs that allows us to include different growth functions (linear growth and nonlinear von Bertalanffy growth in length) and develop two-dimensional MRNs useful for quantifying growth-mortality trade-offs. We relate our approach to Beverton-Holt life history invariants and to the Stearns-Koella categorization of MRNs. We conclude with a detailed discussion of life history parameters for Great Lakes Chinook Salmon and demonstrate that age and size at maturity are consistent with predictions using R0 (but not r or Vx) as the underlying fitness function.

Modeling the underlying dynamics of the spread of crime.

The spread of crime is a complex, dynamic process that calls for a systems level approach. Here, we build and analyze a series of dynamical systems models of the spread of crime, imprisonment and recidivism, using only abstract transition parameters. To find the general patterns among these parameters--patterns that are independent of the underlying particulars--we compute analytic expressions for the equilibria and for the tipping points between high-crime and low-crime equilibria in these models. We use these expressions to examine, in particular, the effects of longer prison terms and of increased incarceration rates on the prevalence of crime, with a follow-up analysis on the effects of a Three-Strike Policy.

A transmission model for the ecology of an avian blood parasite in a temperate ecosystem.

Most of our knowledge about avian haemosporidian parasites comes from the Hawaiian archipelago, where recently introduced Plasmodiumrelictum has contributed to the extinction of many endemic avian species. While the ecology of invasive malaria is reasonably understood, the ecology of endemic haemosporidian infection in mainland systems is poorly understood, even though it is the rule rather than the exception. We develop a mathematical model to explore and identify the ecological factors that most influence transmission of the common avian parasite, Leucocytozoonfringillinarum (Apicomplexa). The model was parameterized from White-crowned Sparrow (Zonotrichialeucophrys) and S. silvestre / craigi black fly populations breeding in an alpine ecosystem. We identify and examine the importance of altricial nestlings, the seasonal relapse of infected birds for parasite persistence across breeding seasons, and potential impacts of seasonal changes in black fly emergence on parasite prevalence in a high elevation temperate system. We also use the model to identify and estimate the parameters most influencing transmission dynamics. Our analysis found that relapse of adult birds and young of the year birds were crucial for parasite persistence across multiple seasons. However, distinguishing between nude nestlings and feathered young of the year was unnecessary. Finally, due to model sensitivity to many black fly parameters, parasite prevalence and sparrow recruitment may be most affected by seasonal changes in environmental temperature driving shifts in black fly emergence and gonotrophic cycles.

Modeling bacterial colonization and infection routes in health care settings: analytic and numerical approaches.

Health-care associated infections are a major problem in our society, accounting for tens of thousands of patient deaths and millions of dollars in wasted health care expenditures each year. Many of these infections are caused by bacteria that are transmitted from patient to patient either through direct contact or via the hands or clothing of health care workers. Because of the complexity of bacterial transmission routes in health care settings, computational approaches are essential, though often analytically intractable. Here we describe the construction and detailed analysis of a model for bacterial transmission in health care settings. Our model includes both colonization and disease stages for patients and health care workers, as well as an isolation ward and both patient-patient and patient-HCW-patient transmission pathways. We explicitly derive the basic reproductive ratio for this complex model, a nine-term expression that contains all nine ways with which a new colonization can occur. Using key parameters found in the medical literature, we use our model to gain insight into the relative importance of various bacterial transmission pathways within health care facilities, and to identify which forms of interventions are likely to prove most effective in hospitals and long-term care settings. We show that analytical and numerical approaches can complement each other as we seek to untangle the complex web of interactions that occur within a health care facility.

When to control endemic infections by focusing on high-risk groups.

BACKGROUND: For nontransmissible diseases, decisions between interventions focused on high-risk groups and unfocused interventions can be based on attributable-risk calculations. The assumptions of those calculations, however, are violated for infectious diseases. METHODS: We used deterministic compartmental models of infection transmission having both high- and low-risk groups and both susceptible and infected states to examine intervention effects on endemic infection levels. High risk is generated by increased susceptibility or contagiousness-factors that can be reduced by interventions. Population effects of focused and unfocused interventions are compared at settings where these would be equal if there were no transmission. RESULTS: In the most likely range of mixing between high- and low-risk groups, focused interventions have considerably larger effects than unfocused interventions. At all mixing levels, both interventions have greater effects on infectious than noninfectious diseases because a change in risk factor for one individual alters risk in others. Interventions on contagiousness in high-risk groups have greater effects than comparable interventions on susceptibility. CONCLUSIONS: Risk assessment for infectious disease requires analysis of the population system that is circulating the infection. Vaccine trials on individuals will miss important effects that trials on transmission units will detect. Focusing HIV control on contagiousness factors in high-risk groups will be especially productive.

Stochastic effects on endemic infection levels of disseminating versus local contacts.

The effects of two levels of mixing on endemic infection levels are shown to differ for identically conformed deterministic compartmental (DC) and stochastic compartmental (SC) models. Both DC and SC models give similar endemic levels when populations are large, immunity is short lived, and mixing is universal. But local transmissions and/or transient immunity decrease overall population infection levels in SC but not in DC models. DC models also fail to detect the greater effects of eliminating disseminating transmissions in comparison to eliminating local transmissions shown by SC models. These differences in model behavior arise because localities that encounter few infections from distant sites and that have stochastically low infection levels have decreased infection rates while localities with stochastically high levels of infection do not decrease the rate at which they lose infection. At the extreme this generates local stochastic die out with subsequent build up of susceptibility in SC but not DC models. This phenomenon should act upon all endemic infections that have changing geographic or social foci of infection. Neither standard epidemiological investigations nor sufficient-component cause models can capture these effects because they occur in the absence of differences between individuals.

Qualitative theory of compartmental systems with lags.

Dynamic models of many processes in the biological and physical sciences give systems of ordinary differential equations called compartmental systems. Often, these systems include time lags; in this context, continuous probability density functions (pdfs) of lags are far more important than discrete lags. There is a relatively complete theory of compartmental systems without lags, both linear and non-linear [SIAM Rev. 35 (1993) 43]. The authors extend their previous work on compartmental systems without lags to show that, for discrete lags and for a very large class of pdfs of continuous lags, compartmental systems with lags are equivalent to larger compartmental systems without lags. Consequently, the properties of compartmental systems with lags are the same as those of compartmental systems without lags. For a very large class of compartmental systems with time lags, one can show that the time lags themselves can be generated by compartmental systems without lags. Thus, such systems can be partitioned into a main system, which is the original system without the lags, plus compartmental subsystems without lags that generate the lags. The latter may be linear or non-linear and may be inserted into main systems that are linear or non-linear. The state variables of the compartmental lag subsystems are hidden variables in the formulation with explicit lags.

An evolutionary ecological perspective on demographic transitions: modeling multiple currencies.

Life history theory postulates tradeoffs of current versus future reproduction; today women face evolutionarily novel versions of these tradeoffs. Optimal age at first birth is the result of tradeoffs in fertility and mortality; ceteris paribus, early reproduction is advantageous. Yet modern women in developed nations experience relatively late first births; they appear to be trading off socioeconomic status and the paths to raised SES, education and work, against early fertility. Here, [1] using delineating parameter values drawn from data in the literature, we model these tradeoffs to determine how much socioeconomic advantage will compensate for delayed first births and lower lifetime fertility; and [2] we examine the effects of work and education on women's lifetime and age-specific fertility using data from seven cohorts in the Panel Study of Income Dynamics (PSID).