25 problems

Global asymptotic stability conjecture. The equilibrium $\tilde{E}$ is globally asymptotically stable.

Global-stability conjecture. The steady state $(1,0,z^*)$ remains globally asymptotically stable.

Natural-world existence conjecture. In the natural world, both the surface à godets and the pseudosphere have equal rights to exist.

Cis-reaction conjecture. This reaction does not lead to the type of Notch activation described above.

Let VSV denote vesicular stomatitis virus and VV denote vaccinia virus in the combined-therapy model. Compare changes in the VSV infection rate with comparable changes in the VV in…

Let VV denote vaccinia virus and VSV denote vesicular stomatitis virus. Consider systems in which VV and VSV are combined and compare systems with functional IFN-$\alpha$ signaling…

Let VSV denote vesicular stomatitis virus, VV denote vaccinia virus, and B18R denote the VV-encoded protein that suppresses the IFN-$\alpha$-mediated antiviral response. Consider t…

Immunotherapy conjecture. Immunotherapy and other immune-mediated mechanisms may be able to effectively counteract tumor growth in many cases.

A germinal-center cell lineage forms a phylogenetic tree of ancestries, whose terminal nodes are strains with no extant descendants. Low-affinity cells are cells classified as havi…

Hypoxia-design conjecture. Whether the tumour microenvironment is hypoxic should be considered when engineering OVs.

Activation of microglia is the proposed mechanism responsible for the appearance of Multiple Sclerosis lesions. Microglial activation conjecture. Activation of microglia is respons…

Zero-set conjecture.

Intraspecies competition conjecture. The intraspecies competition terms remove the unrealistic dynamic in which solutions become negative, since large populations attenuate the gro…

Gradient-flow extension conjecture. The same approach may allow many other stochastic variants of models from biological applications, including nonlocal Fisher–KPP equations, nonl…

Uniqueness conjecture. Such a reaction-diffusion equation should have a unique cline, rather than multiple clines.

Pseudospectra conjecture. Michaelis–Menten enzyme kinetics and a whole host of other important models in biology also exhibit significant pseudospectra.

Optimal-size conjecture. The optimal value of $L$ is close to

Global-infimum conjecture. For each fixed $N\geq4$ and $n\geq2$, the right-hand side of the displayed formula is a global infimum of all positive values of $(b/c)^*$ over all migra…

Let $N=N_1+N_2$ be the total population size, let $D=|N_1-N_2|$ be the difference in island sizes, and let $(b/c)^*$ denote the critical benefit-to-cost ratio for two islands with…

Torres's conjecture. The periodic solution is unique and asymptotically stable.

Consider the boundary value problem … where $p'(0)=0$, $p(\infty)<\infty$, $\Delta p$ is the $n$-dimensional Laplacian, $r$ is the distance from the origin of an $n$-dimensional ve…

Let $E_i$, $i=1,\ldots,n$, denote the single-strain equilibria, and let the reproduction numbers satisfy … The remaining reproduction numbers may be distinct and smaller, as in the…

In chronic hepatitis B virus infection, combination therapy uses a cocktail of antiviral drugs, whereas sequential monotherapy uses only one drug at a time and substitutes it if vi…

Critical-parameter conjecture. There exists a parameter value $\gamma_{\ast}$ such that (8.1) holds whenever

Ratchet power-law breakdown conjecture. For sufficiently large values of $N\lambda$, this power-law behaviour should break down.