Effect of cross-immunity in a two-strain cholera model with aquatic component.

The bacteria Vibrio cholerae relies heavily upon an aquatic reservoir as a transmission route with two distinct serotypes observed in many recent outbreaks. In this paper, we extend previously studied ordinary differential equation epidemiological models to create a two-strain SIRP (susceptible-infectious-recovered-pathogen) system which incorporates both partial cross-immunity between disease strains and environmental pathogen transmission. Of particular interest are undamped anti-phase periodic solutions, as these display a type of coexistence where strains routinely switch dominance, and understanding what drives this switch can optimize the efficiency of the host population's control measures against the disease. We derive the basic reproduction number R0 and use stability analysis to examine the disease free and single-strain equilibria. We formulate a unique coexistence equilibrium and prove uniform persistence of both strains when R0>1. In addition, we simulate solutions to this system, along with seasonally forced versions of the model with and without host coinfection. Cross-immunity and transmission pathways influence damped or sustained oscillatory dynamics, where the presence of seasonality can modify, amplify or synchronize the period and phase of serotypes, driving epidemic waves. Cycling of serotypes over large time intervals, similar to observed data, is found for a range of cross-immunity levels, and the inclusion of coinfection in the model contributes to sustained anti-phase periodic solutions.

Data Note: The Digital Ludeme Project Database.

This document outlines the types of data collected for the Digital Ludeme Project, an ERC-funded research project that aims to improve our understanding of the development of games throughout human history through computational analysis of the available (partial) historical data of games. This document outlines how this data is collected, formatted and stored, and how it can be accessed. It is the aim of the Digital Ludeme Project to provide a data resource of unprecedented depth and scope for the benefit of historical games researchers worldwide. Special attention is paid to the FAIR Guiding Principles for scientific data management and stewardship.

Virus-immune dynamics determined by prey-predator interaction network and epistasis in viral fitness landscape.

Population dynamics and evolutionary genetics underly the structure of ecosystems, changing on the same timescale for interacting species with rapid turnover, such as virus (e.g. HIV) and immune response. Thus, an important problem in mathematical modeling is to connect ecology, evolution and genetics, which often have been treated separately. Here, extending analysis of multiple virus and immune response populations in a resource-prey (consumer)-predator model from Browne and Smith (2018), we show that long term dynamics of viral mutants evolving resistance at distinct epitopes (viral proteins targeted by immune responses) are governed by epistasis in the virus fitness landscape. In particular, the stability of persistent equilibrium virus-immune (prey-predator) network structures, such as nested and one-to-one, and bifurcations are determined by a collection of circuits defined by combinations of viral fitnesses that are minimally additive within a hypercube of binary sequences representing all possible viral epitope sequences ordered according to immunodominance hierarchy. Numerical solutions of our ordinary differential equation system, along with an extended stochastic version including random mutation, demonstrate how pairwise or multiplicative epistatic interactions shape viral evolution against concurrent immune responses and convergence to the multi-variant steady state predicted by theoretical results. Furthermore, simulations illustrate how periodic infusions of subdominant immune responses can induce a bifurcation in the persistent viral strains, offering superior host outcome over an alternative strategy of immunotherapy with strongest immune response.

Differential impacts of contact tracing and lockdowns on outbreak size in COVID-19 model applied to China.

The COVID-19 pandemic has led to widespread attention given to the notions of "flattening the curve" during lockdowns, and successful contact tracing programs suppressing outbreaks. However a more nuanced picture of these interventions' effects on epidemic trajectories is necessary. By mathematical modeling each as reactive quarantine measures, dependent on current infection rates, with different mechanisms of action, we analytically derive distinct nonlinear effects of these interventions on final and peak outbreak size. We simultaneously fit the model to provincial reported case and aggregated quarantined contact data from China. Lockdowns compressed the outbreak in China inversely proportional to population quarantine rates, revealing their critical dependence on timing. Contact tracing had significantly less impact on final outbreak size, but did lead to peak size reduction. Our analysis suggests that altering the cumulative cases in a rapidly spreading outbreak requires sustained interventions that decrease the reproduction number close to one, otherwise some type of swift lockdown measure may be needed.

Predator-Prey Dynamics of Intra-Host Simian Immunodeficiency Virus Evolution Within the Untreated Host.

The dynamic nature of the SIV population during disease progression in the SIV/macaque model of AIDS and the factors responsible for its behavior have not been documented, largely owing to the lack of sufficient spatial and temporal sampling of both viral and host data from SIV-infected animals. In this study, we detail Bayesian coalescent inference of the changing collective intra-host viral effective population size (Ne ) from various tissues over the course of infection and its relationship with what we demonstrate is a continuously changing immune cell repertoire within the blood. Although the relative contribution of these factors varied among hosts and time points, the adaptive immune response best explained the overall periodic dynamic behavior of the effective virus population. Data exposing the nature of the relationship between the virus and immune cell populations revealed the plausibility of an eco-evolutionary mathematical model, which was able to mimic the large-scale oscillations in Ne through virus escape from relatively few, early immunodominant responses, followed by slower escape from several subdominant and weakened immune populations. The results of this study suggest that SIV diversity within the untreated host is governed by a predator-prey relationship, wherein differing phases of infection are the result of adaptation in response to varying immune responses. Previous investigations into viral population dynamics using sequence data have focused on single estimates of the effective viral population size (Ne ) or point estimates over sparse sampling data to provide insight into the precise impact of immune selection on virus adaptive behavior. Herein, we describe the use of the coalescent phylogenetic frame- work to estimate the relative changes in Ne over time in order to quantify the relationship with empirical data on the dynamic immune composition of the host. This relationship has allowed us to expand on earlier simulations to build a predator-prey model that explains the deterministic behavior of the virus over the course of disease progression. We show that sequential viral adaptation can occur in response to phases of varying immune pressure, providing a broader picture of the viral response throughout the entire course of progression to AIDS.

SARS-CoV-2 shifting transmission dynamics and hidden reservoirs potentially limit efficacy of public health interventions in Italy.

We investigated SARS-CoV-2 transmission dynamics in Italy, one of the countries hit hardest by the pandemic, using phylodynamic analysis of viral genetic and epidemiological data. We observed the co-circulation of multiple SARS-CoV-2 lineages over time, which were linked to multiple importations and characterized by large transmission clusters concomitant with a high number of infections. Subsequent implementation of a three-phase nationwide lockdown strategy greatly reduced infection numbers and hospitalizations. Yet we present evidence of sustained viral spread among sporadic clusters acting as "hidden reservoirs" during summer 2020. Mathematical modelling shows that increased mobility among residents eventually catalyzed the coalescence of such clusters, thus driving up the number of infections and initiating a new epidemic wave. Our results suggest that the efficacy of public health interventions is, ultimately, limited by the size and structure of epidemic reservoirs, which may warrant prioritization during vaccine deployment.

AI for Ancient Games: Report on the Digital Ludeme Project.

This report summarises the Digital Ludeme Project, a recently launched 5-year research project being conducted at Maastricht University. This computational study of the world's traditional strategy games seeks to improve our understanding of early games, their development, and their role in the spread of related mathematical ideas throughout recorded human history.

Toxigenic Vibrio cholerae evolution and establishment of reservoirs in aquatic ecosystems.

The spread of cholera in the midst of an epidemic is largely driven by direct transmission from person to person, although it is well-recognized that Vibrio cholerae is also capable of growth and long-term survival in aquatic ecosystems. While prior studies have shown that aquatic reservoirs are important in the persistence of the disease on the Indian subcontinent, an epidemiological view postulating that locally evolving environmental V. cholerae contributes to outbreaks outside Asia remains debated. The single-source introduction of toxigenic V. cholerae O1 in Haiti, one of the largest outbreaks occurring this century, with 812,586 suspected cases and 9,606 deaths reported through July 2018, provided a unique opportunity to evaluate the role of aquatic reservoirs and assess bacterial transmission dynamics across environmental boundaries. To this end, we investigated the phylogeography of both clinical and aquatic toxigenic V. cholerae O1 isolates and show robust evidence of the establishment of aquatic reservoirs as well as ongoing evolution of V. cholerae isolates from aquatic sites. Novel environmental lineages emerged from sequential population bottlenecks, carrying mutations potentially involved in adaptation to the aquatic ecosystem. Based on such empirical data, we developed a mixed-transmission dynamic model of V. cholerae, where aquatic reservoirs actively contribute to genetic diversification and epidemic emergence, which underscores the complexity of transmission pathways in epidemics and endemic settings and the need for long-term investments in cholera control at both human and environmental levels.

Infection severity across scales in multi-strain immuno-epidemiological Dengue model structured by host antibody level.

Infection by distinct Dengue virus serotypes and host immunity are intricately linked. In particular, certain levels of cross-reactive antibodies in the host may actually enhance infection severity leading to Dengue hemorrhagic fever (DHF). The coupled immunological and epidemiological dynamics of Dengue calls for a multi-scale modeling approach. In this work, we formulate a within-host model which mechanistically recapitulates characteristics of antibody dependent enhancement in Dengue infection. The within-host scale is then linked to epidemiological spread by a vector-host partial differential equation model structured by host antibody level. The coupling allows for dynamic population-wide antibody levels to be tracked through primary and secondary infections by distinct Dengue strains, along with waning of cross-protective immunity after primary infection. Analysis of both the within-host and between-host systems are conducted. Stability results in the epidemic model are formulated via basic and invasion reproduction numbers as a function of immunological variables. Additionally, we develop numerical methods in order to simulate the multi-scale model and assess the influence of parameters on disease spread and DHF prevalence in the population.

Resonance of Periodic Combination Antiviral Therapy and Intracellular Delays in Virus Model.

There is a substantial interest in detailed models of viral infection and antiviral drug kinetics in order to optimize the treatment against viruses such as HIV. In this paper, we study within-viral dynamics under general intracellular distributed delays and periodic combination antiviral therapy. The basic reproduction number [Formula: see text] is established as a global threshold determining extinction versus persistence, and spectral methods are utilized for analytical and numerical computations of [Formula: see text]. We derive the critical maturation delay for virus and optimal phase difference between sinusoidally varying drug efficacies under various intracellular delays. Furthermore, numerical simulations are conducted utilizing realistic pharmacokinetics and gamma-distributed viral production delays for HIV. Our results demonstrate that the relative timing of the key viral replication cycle steps and periodic antiviral treatment schedule involving distinct drugs all can interact to critically affect the overall viral dynamics.

Age-structured viral dynamics in a host with multiple compartments.

Several studies have reported dual pathways for HIV cell infection, namely the binding of free virions to target cell receptors (cell-free), and direct transmission from infected cells to uninfected cells through virological synapse (cell-to-cell). Furthermore, understanding spread of the infection may require a relatively in-depth comprehension of how the connection between organs, each with characteristic cell composition and infection kinetics, affects viral dynamics. We propose a virus model consisting of multiple compartments with cell populations subject to distinct infectivity kernels as a function of cell infection-age, in order to imitate the infection spread through various organs. When the within-host structure is strongly connected, we formulate the basic reproduction number to be the threshold value determining the viral persistence or extinction. On the other hand, in non-strongly connected cases, we also formulate a sequence of threshold values to find out the infection pattern in the whole system. Numerical results of derivative examples show that: (1) In a strongly connected system but lacking some directional connection between compartments therein, the migration of cells certainly affects the viral dynamics and it may not monotonously depend on the value of migration rate. (2) In a non-strongly connected structure, increasing migration rate may first change persistence of the virus to extinction in the whole system, and then for even larger migration rate, trigger the infection in a subset of compartments. (3) For data-informed cases of intracellular delay and gamma-distributed cell infectivity kernels, compartments with faster kinetics representative of cell-to-cell transmission mode, as opposed to cell-free, can promote persistence of the virus.

Dynamics of virus and immune response in multi-epitope network.

The host immune response can often efficiently suppress a virus infection, which may lead to selection for immune-resistant viral variants within the host. For example, during HIV infection, an array of CTL immune response populations recognize specific epitopes (viral proteins) presented on the surface of infected cells to effectively mediate their killing. However HIV can rapidly evolve resistance to CTL attack at different epitopes, inducing a dynamic network of interacting viral and immune response variants. We consider models for the network of virus and immune response populations, consisting of Lotka-Volterra-like systems of ordinary differential equations. Stability of feasible equilibria and corresponding uniform persistence of distinct variants are characterized via a Lyapunov function. We specialize the model to a "binary sequence" setting, where for n epitopes there can be [Formula: see text] distinct viral variants mapped on a hypercube graph. The dynamics in several cases are analyzed and sharp polychotomies are derived characterizing persistent variants. In particular, we prove that if the viral fitness costs for gaining resistance to each epitope are equal, then the system of [Formula: see text] virus strains converges to a "perfectly nested network" with less than or equal to [Formula: see text] persistent virus strains. Overall, our results suggest that immunodominance, i.e. relative strength of immune response to an epitope, is the most important factor determining the persistent network structure.

Global properties of nested network model with application to multi-epitope HIV/CTL dynamics.

Mathematical modeling and analysis can provide insight on the dynamics of ecosystems which maintain biodiversity in the face of competitive and prey-predator interactions. Of primary interests are the underlying structure and features which stabilize diverse ecological networks. Recently Korytowski and Smith (Theor Ecol 8(1):111-120, 2015) proved that a perfectly nested infection network, along with appropriate life history trade-offs, leads to coexistence and persistence of bacteria-phage communities in a chemostat model. In this article, we generalize their model in order to apply it to the within-host dynamics virus and immune response, in particular HIV and CTL (Cytotoxic T Lymphocyte) cells. Our model can describe sequential viral escape from dominant immune responses and rise in subdominant immune responses, consistent with observed patterns of HIV/CTL evolution. We find a Lyapunov function for the system which leads to rigorous characterization of persistent viral and immune variants, along with informing upon equilibria stability and global dynamics. Results are interpreted in the context of within-host HIV/CTL evolution and numerical simulations are provided.

Immune response in virus model structured by cell infection-age.

This paper concerns modeling the coupled within-host population dynamics of virus and CTL (Cytotoxic T Lymphocyte) immune response. There is substantial evidence that the CTL immune response plays a crucial role in controlling HIV in infected patients. Recent experimental studies have demonstrated that certain CTL variants can recognize HIV infected cells early in the infected cell lifecycle before viral production, while other CTLs only detect viral proteins (epitopes) presented on the surface of infected cells after viral production. The kinetics of epitope presentation and immune recognition can impact the efficacy of the immune response. We extend previous virus models to include cell infection-age structure in the infected cell compartment and immune response killing/activation rates of a PDE-ODE system. We characterize solutions to our system utilizing semigroup theory, determine equilibria and reproduction numbers, and prove stability and persistence results. Numerical simulations show that ' early immune recognition' precipitates both enhanced viral control and sustained oscillations via a Hopf bifurcation. In addition to inducing oscillatory dynamics, considering immune process rates to be functions of cell infection-age can also lead to coexistence of multiple distinct immune effector populations.

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.

From regional pulse vaccination to global disease eradication: insights from a mathematical model of poliomyelitis.

Mass-vaccination campaigns are an important strategy in the global fight against poliomyelitis and measles. The large-scale logistics required for these mass immunisation campaigns magnifies the need for research into the effectiveness and optimal deployment of pulse vaccination. In order to better understand this control strategy, we propose a mathematical model accounting for the disease dynamics in connected regions, incorporating seasonality, environmental reservoirs and independent periodic pulse vaccination schedules in each region. The effective reproduction number, Re, is defined and proved to be a global threshold for persistence of the disease. Analytical and numerical calculations show the importance of synchronising the pulse vaccinations in connected regions and the timing of the pulses with respect to the pathogen circulation seasonality. Our results indicate that it may be crucial for mass-vaccination programs, such as national immunisation days, to be synchronised across different regions. In addition, simulations show that a migration imbalance can increase Re and alter how pulse vaccination should be optimally distributed among the patches, similar to results found with constant-rate vaccination. Furthermore, contrary to the case of constant-rate vaccination, the fraction of environmental transmission affects the value of Re when pulse vaccination is present.

Periodic multidrug therapy in a within-host virus model.

Floquet theory and perturbation techniques are used to analyze a classical within-host virus model with periodic drug treatment. Both single and multidrug treatment strategies are investigated. Specifically, the effects of both RT-inhibitors and P-inhibitors on the stability of the infection-free steady state are studied. It is found that when both classes of drugs have periodic drug efficacy functions, then shifting the phase of these functions can critically affect the stability of the infection-free steady state. A numerical study is conducted to illustrate the theoretical results and provide additional insights.