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.

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.

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.

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.

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.

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.

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.