4 problems

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Jacobian factorization conjecture for the basic reproduction number
Consider a Jacobian factorization in which all rational factors of the characteristic polynomial are normalized to have positive leading term, negative linear eigenvalue factors ar…
Conjectureopenepidemic-modeling reproduction-numbers stability-theoryarXiv posted 2 days ago
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Hill–Longini conjecture on convexity and concavity of the effective reproduction number
Let $K$ be an $N\times N$ next-generation matrix with non-negative entries, let $\eta\in\Delta=[0,1]^N$ be a vaccination strategy, and let $R_e[K]$ denote the spectral radius of…
Conjectureopenmathematical-epidemiology reproduction-numbers spectral-theoryarXiv posted 2 days ago
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Augmented dynamical-systems conjecture for the basic reproduction number
Augmented dynamical-systems conjecture. This analysis should yield a value of $R_0$ equal to the general expression for $R_0$ defined earlier in the paper.
Conjectureopenconfiguration-model-networks reproduction-numbers stochastic-epidemicsarXiv posted 2 days ago
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Conjecture on the comparison of household reproduction numbers $R_0$ and $R_2$
Comparison conjecture. In a growing epidemic, $R_0\ge R_2$ , while in a declining epidemic, $R_0\le R_2$ . Both inequalities are strict if and only if $n_H>2$ ; equivalently, the ineq…
Conjectureopenepidemic-models households reproduction-numbersarXiv posted 2 days ago

Jacobian factorization conjecture for the basic reproduction number