Effects of CCN1 and Macrophage Content on Glioma Virotherapy: A Mathematical Model.

Oncolytic virus (OV) is a genetically engineered virus that can selectively replicate in and kill tumor cells while not harming normal cells. OV therapy has been explored as a treatment for numerous cancers including glioblastoma, an aggressive and devastating brain tumor. Experiments show that extracellular matrix protein CCN1 limits OV therapy of glioma by orchestrating an antiviral response and enhancing the proinflammatory activation and migration of macrophages. Neutralizing CCN1 by antibody has been demonstrated to improve OV spread and tends to increase the time to disease progression. In this paper, we develop a mathematical model to investigate the effects of CCN1 on the treatment of glioma with oncolytic herpes simplex virus. We show that numerical simulations of the model are in agreement with the experimental results and then use the model to explore the anti-tumor effects of combining antibodies with OV therapy. Model simulations suggest that the macrophage content of the tumor is a critical factor to the success of OV therapy and to the reduction in tumor volume gained with the CCN1 antibody.

The large graph limit of a stochastic epidemic model on a dynamic multilayer network.

We consider a Markovian SIR-type (Susceptible → Infected → Recovered) stochastic epidemic process with multiple modes of transmission on a contact network. The network is given by a random graph following a multilayer configuration model where edges in different layers correspond to potentially infectious contacts of different types. We assume that the graph structure evolves in response to the epidemic via activation or deactivation of edges of infectious nodes. We derive a large graph limit theorem that gives a system of ordinary differential equations (ODEs) describing the evolution of quantities of interest, such as the proportions of infected and susceptible vertices, as the number of nodes tends to infinity. Analysis of the limiting system elucidates how the coupling of edge activation and deactivation to infection status affects disease dynamics, as illustrated by a two-layer network example with edge types corresponding to community and healthcare contacts. Our theorem extends some earlier results describing the deterministic limit of stochastic SIR processes on static, single-layer configuration model graphs. We also describe precisely the conditions for equivalence between our limiting ODEs and the systems obtained via pair approximation, which are widely used in the epidemiological and ecological literature to approximate disease dynamics on networks. The flexible modeling framework and asymptotic results have potential application to many disease settings including Ebola dynamics in West Africa, which was the original motivation for this study.

Network-based analysis of a small Ebola outbreak.

We present a method for estimating epidemic parameters in network-based stochastic epidemic models when the total number of infections is assumed to be small. We illustrate the method by reanalyzing the data from the 2014 Democratic Republic of the Congo (DRC) Ebola outbreak described in Maganga et al. (2014).

Analysis of a mathematical model for tumor therapy with a fusogenic oncolytic virus.

Oncolytic virotherapy is a tumor treatment which uses viruses to selectively target and destroy cancer cells. Fusogenic viruses, capable of causing cell-to-cell fusion upon infection of a tumor cell, have shown promise in experimental studies. Fusion causes the formation of large, multinucleated syncytia which eventually leads to cell death. We formulate a partial differential equations model with a moving boundary to describe the treatment of a spherical tumor with a fusogenic oncolytic virus. Fusion, lysis, and budding are incorporated as mechanisms of viral spread, resulting in nonlocal integral terms. A proof is presented for existence and uniqueness of global solutions to the nonlinear hyperbolic-parabolic system. Numerical simulations demonstrate convergence to spatially homogeneous solutions and exponential growth or decay of the tumor radius depending on viral burst size and rate of fusion. Long-term tumor radius is shown to decrease with increasing values of viral burst size while the effect of the rate of fusion on tumor growth is demonstrated to be nonmonotonic.

Mathematical modeling of citrus groves infected by huanglongbing.

Huanglongbing (citrus greening) is a bacterial disease that is significantly impacting the citrus industry in Florida and poses a risk to the remaining citrus-producing regions of the United States. A mathematical model of a grove infected by citrus greening is developed. An equilibrium stability analysis is presented. The basic reproductive number and its relation to the persistence of the disease is discussed. A numerical study is performed to illustrate the theoretical findings.