Advantage of Being Multicomponent and Spatial: Multipartite Viruses Colonize Structured Populations with Lower Thresholds

Multipartite viruses have a genome divided into different disconnected viral particles. A majority of multipartite viruses infect plants; very few target animals. To understand why, we use a simple, network-based susceptible-latent-infectious-recovered model. We show both analytically and numerically that, provided that the average degree of the contact network exceeds a critical value, even in the absence of an explicit microscopic advantage, multipartite viruses have a lower threshold to colonizing network-structured populations compared to a well-mixed population. We further corroborate this finding on two-dimensional lattice networks, which better represent the typical contact structures of plants.

Figure 1

Average density of recovered nodes ${\mathsf{R}}_{\infty }$ as a function of $\beta$ for the SLIR process taking place on (a) annealed ER networks with a mean degree $⟨k⟩=6$, and (b) static ER networks with $⟨k⟩=10$, 8, 6. In panel (a), lines are theoretical results, where the stable solutions are represented by solid lines and unstable solutions by dashed lines. The diamonds are the results from stochastic simulations. In panel (b), the solid lines are numerical solutions from pair approximation equations and the symbols are simulation results.

Figure 2

Epidemic (or colonization) thresholds of the SLIR model on annealed and static ER networks with the increase of mean degree $⟨k⟩$. The lines are theoretical results predicted, respectively, by Eqs. (2) and (3). The symbols represent the results from stochastic simulations.

Figure 3

Average density of recovered nodes ${\mathsf{R}}_{\infty }$ as a function of $\beta$ for the SLIR process with $n=3$ on static and annealed ER networks with a different mean degree $⟨k⟩$. Filled and open symbols correspond, respectively, to the results obtained through stochastic simulations on static and annealed networks. Vertical solid and dashed lines show the theoretical colonization thresholds for static and annealed networks, respectively.

Figure 4

Average density of recovered nodes ${\mathsf{R}}_{\infty }$ as a function of $\beta$ for the SLIR process on two-dimensional square lattices and their annealed counterparts (i.e., frequently rewiring regular random graphs) with different mean degree $⟨k⟩$. Panels (a) and (b) are for multipartite viruses with two and three viral segments, respectively. The filled and open symbols correspond, respectively, to the results obtained through stochastic simulations on static and annealed structures. The solid and dashed lines show the colonization thresholds yielded by theoretical predictions for static and annealed structures, respectively.