Sensitivity Analysis in an Immuno-Epidemiological Vector-Host Model.

Sensitivity Analysis (SA) is a useful tool to measure the impact of changes in model parameters on the infection dynamics, particularly to quantify the expected efficacy of disease control strategies. SA has only been applied to epidemic models at the population level, ignoring the effect of within-host virus-with-immune-system interactions on the disease spread. Connecting the scales from individual to population can help inform drug and vaccine development. Thus the value of understanding the impact of immunological parameters on epidemiological quantities. Here we consider an age-since-infection structured vector-host model, in which epidemiological parameters are formulated as functions of within-host virus and antibody densities, governed by an ODE system. We then use SA for these immuno-epidemiological models to investigate the impact of immunological parameters on population-level disease dynamics such as basic reproduction number, final size of the epidemic or the infectiousness at different phases of an outbreak. As a case study, we consider Rift Valley Fever Disease utilizing parameter estimations from prior studies. SA indicates that [Formula: see text] increase in within-host pathogen growth rate can lead up to [Formula: see text] increase in [Formula: see text] up to [Formula: see text] increase in steady-state infected host abundance, and up to [Formula: see text] increase in infectiousness of hosts when the reproduction number [Formula: see text] is larger than one. These significant increases in population-scale disease quantities suggest that control strategies that reduce the within-host pathogen growth can be important in reducing disease prevalence.

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.

A delay model for persistent viral infections in replicating cells.

Persistently infecting viruses remain within infected cells for a prolonged period of time without killing the cells and can reproduce via budding virus particles or passing on to daughter cells after division. The ability for populations of infected cells to be long-lived and replicate viral progeny through cell division may be critical for virus survival in examples such as HIV latent reservoirs, tumor oncolytic virotherapy, and non-virulent phages in microbial hosts. We consider a model for persistent viral infection within a replicating cell population with time delay in the eclipse stage prior to infected cell replicative form. We obtain reproduction numbers that provide criteria for the existence and stability of the equilibria of the system and provide bifurcation diagrams illustrating transcritical (backward and forward), saddle-node, and Hopf bifurcations, and provide evidence of homoclinic bifurcations and a Bogdanov-Takens bifurcation. We investigate the possibility of long term survival of the infection (represented by chronically infected cells and free virus) in the cell population by using the mathematical concept of robust uniform persistence. Using numerical continuation software with parameter values estimated from phage-microbe systems, we obtain two parameter bifurcation diagrams that divide parameter space into regions with different dynamical outcomes. We thus investigate how varying different parameters, including how the time spent in the eclipse phase, can influence whether or not the virus survives.

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.

Viral invasion fitness across a continuum from lysis to latency.

The prevailing paradigm in ecological studies of viruses and their microbial hosts is that the reproductive success of viruses depends on the proliferation of the 'predator', that is, the virus particle. Yet, viruses are obligate intracellular parasites, and the virus genome-the actual unit of selection-can persist and proliferate from one cell generation to the next without lysis or the production of new virus particles. Here, we propose a theoretical framework to quantify the invasion fitness of viruses using an epidemiological cell-centric metric that focuses on the proliferation of viral genomes inside cells instead of virus particles outside cells. This cell-centric metric enables direct comparison of viral strategies characterized by obligate killing of hosts (e.g. via lysis), persistence of viral genomes inside hosts (e.g. via lysogeny), and strategies along a continuum between these extremes (e.g. via chronic infections). As a result, we can identify environmental drivers, life history traits, and key feedbacks that govern variation in viral propagation in nonlinear population models. For example, we identify threshold conditions given relatively low densities of susceptible cells and relatively high growth rates of infected cells in which lysogenic and other chronic strategies have higher potential viral reproduction than lytic strategies. Altogether, the theoretical framework helps unify the ongoing study of eco-evolutionary drivers of viral strategies in natural environments.

Heterogeneous viral strategies promote coexistence in virus-microbe systems.

Viral infections of microbial cells often culminate in lysis and the release of new virus particles. However, viruses of microbes can also initiate chronic infections, in which new viruses particles are released via budding and without cell lysis. In chronic infections, viral genomes may also be passed on from mother to daughter cells during division. The consequences of chronic infections for the population dynamics of viruses and microbes remains under-explored. In this paper we present a model of chronic infections as well as a model of interactions between lytic and chronic viruses competing for the same microbial population. In the chronic only model, we identify conditions underlying complex bifurcations such as saddle-node, backward and Hopfbifurcations, leading to parameter regions with multiple attractors and/or oscillatory behavior. We then utilize invasion analysis to examine the coupled nonlinear system of microbes, lytic viruses, and chronic viruses. In so doing we find unexpected results, including a regime in which the chronic virus requires the lytic virus for survival, invasion, and persistence. In this regime, lytic viruses decrease total cell densities, so that a subpopulation of chronically infected cells experience decreased niche competition. As such, even when chronically infected cells have a growth disadvantage, lytic viruses can, paradoxically, enable the proliferation of both chronically infected cells and chronic viruses. We discuss the implications of our results for understanding the ecology and long-term evolution of heterogeneous viral strategies.

Vector-Borne Pathogen and Host Evolution in a Structured Immuno-Epidemiological System.

Vector-borne disease transmission is a common dissemination mode used by many pathogens to spread in a host population. Similar to directly transmitted diseases, the within-host interaction of a vector-borne pathogen and a host's immune system influences the pathogen's transmission potential between hosts via vectors. Yet there are few theoretical studies on virulence-transmission trade-offs and evolution in vector-borne pathogen-host systems. Here, we consider an immuno-epidemiological model that links the within-host dynamics to between-host circulation of a vector-borne disease. On the immunological scale, the model mimics antibody-pathogen dynamics for arbovirus diseases, such as Rift Valley fever and West Nile virus. The within-host dynamics govern transmission and host mortality and recovery in an age-since-infection structured host-vector-borne pathogen epidemic model. By considering multiple pathogen strains and multiple competing host populations differing in their within-host replication rate and immune response parameters, respectively, we derive evolutionary optimization principles for both pathogen and host. Invasion analysis shows that the [Formula: see text] maximization principle holds for the vector-borne pathogen. For the host, we prove that evolution favors minimizing case fatality ratio (CFR). These results are utilized to compute host and pathogen evolutionary trajectories and to determine how model parameters affect evolution outcomes. We find that increasing the vector inoculum size increases the pathogen [Formula: see text], but can either increase or decrease the pathogen virulence (the host CFR), suggesting that vector inoculum size can contribute to virulence of vector-borne diseases in distinct ways.

Structural and Practical Identifiability Issues of Immuno-Epidemiological Vector-Host Models with Application to Rift Valley Fever.

In this article, we discuss the structural and practical identifiability of a nested immuno-epidemiological model of arbovirus diseases, where host-vector transmission rate, host recovery, and disease-induced death rates are governed by the within-host immune system. We incorporate the newest ideas and the most up-to-date features of numerical methods to fit multi-scale models to multi-scale data. For an immunological model, we use Rift Valley Fever Virus (RVFV) time-series data obtained from livestock under laboratory experiments, and for an epidemiological model we incorporate a human compartment to the nested model and use the number of human RVFV cases reported by the CDC during the 2006-2007 Kenya outbreak. We show that the immunological model is not structurally identifiable for the measurements of time-series viremia concentrations in the host. Thus, we study the non-dimensionalized and scaled versions of the immunological model and prove that both are structurally globally identifiable. After fixing estimated parameter values for the immunological model derived from the scaled model, we develop a numerical method to fit observable RVFV epidemiological data to the nested model for the remaining parameter values of the multi-scale system. For the given (CDC) data set, Monte Carlo simulations indicate that only three parameters of the epidemiological model are practically identifiable when the immune model parameters are fixed. Alternatively, we fit the multi-scale data to the multi-scale model simultaneously. Monte Carlo simulations for the simultaneous fitting suggest that the parameters of the immunological model and the parameters of the immuno-epidemiological model are practically identifiable. We suggest that analytic approaches for studying the structural identifiability of nested models are a necessity, so that identifiable parameter combinations can be derived to reparameterize the nested model to obtain an identifiable one. This is a crucial step in developing multi-scale models which explain multi-scale data.

A touch of sleep: biophysical model of contact-mediated dormancy of archaea by viruses.

The canonical view of the interactions between viruses and their microbial hosts presumes that changes in host and virus fate requires the initiation of infection of a host by a virus. Infection may lead to the death of the host cell and release of viruses, to the elimination of the viral genome through cellular defence mechanisms or the integration of the viral genome with the host as a chromosomal or extrachromosomal element. Here, we revisit this canonical view, inspired by recent experimental findings in which the majority of target host cells can be induced into a dormant state when exposed to either active or deactivated viruses, even when viruses are present at low relative titre. We propose that both the qualitative phenomena and the quantitative timescales of dormancy induction are consistent with the hypothesis that cellular physiology can be altered by contact on the surface of host cells rather than strictly by infection In order to test this hypothesis, we develop and study a biophysical model of contact-mediated dynamics involving virus particles and target cells. We show how virus particles can catalyse cellular transformations among many cells, even if they ultimately infect only one (or none). We also find that population-scale dormancy is robust to variation in the representation of model dynamics, including cell growth, death and recovery.

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 structured avian influenza model with imperfect vaccination and vaccine-induced asymptomatic infection.

We introduce a model of avian influenza in domestic birds with imperfect vaccination and age-since-vaccination structure. The model has four components: susceptible birds, vaccinated birds (stratified by vaccination age), asymptomatically infected birds, and infected birds. The model includes reduction in the probability of infection, decreasing severity of disease of vaccinated birds and vaccine waning. The basic reproduction number, [Formula: see text], is calculated. The disease-free equilibrium is found to be globally stable under certain conditions when [Formula: see text]. When [Formula: see text], existence of an endemic equilibrium is proved (with uniqueness for the ODE case and local stability under stricter conditions) and uniform persistence of the disease is established. The inclusion of reduction in susceptibility of vaccinated birds, reduction in infectiousness of asymptomatically infected birds and vaccine waning can have important implications for disease control. We analytically and numerically demonstrate that vaccination can paradoxically increase the total number of infected, resulting in the "silent spread" of the disease. We also study the effects of vaccine efficacy on disease prevalence and the minimum critical vaccination coverage, a threshold value for vaccination coverage to avoid an increase in total disease prevalence due to asymptomatic infection.

Forward hysteresis and backward bifurcation caused by culling in an avian influenza model.

The emerging threat of a human pandemic caused by the H5N1 avian influenza virus strain magnifies the need for controlling the incidence of H5N1 infection in domestic bird populations. Culling is one of the most widely used control measures and has proved effective for isolated outbreaks. However, the socio-economic impacts of mass culling, in the face of a disease which has become endemic in many regions of the world, can affect the implementation and success of culling as a control measure. We use mathematical modeling to understand the dynamics of avian influenza under different culling approaches. We incorporate culling into an SI model by considering the per capita culling rates to be general functions of the number of infected birds. Complex dynamics of the system, such as backward bifurcation and forward hysteresis, along with bi-stability, are detected and analyzed for two distinct culling scenarios. In these cases, employing other control measures temporarily can drastically change the dynamics of the solutions to a more favorable outcome for disease control.