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zApQa6KF%Hd@z4>=XnmT)WiuqFg4;mPy)(dKWF{gvbsMWZ7!rx!rn|j=^QlM1c_JC6qHj?Z(dcP$_GacD z09_^k8r#@uE?t6>AST~WFWmHZq z2<1T3F8K_NuWlGXbf$aj88RRdhta=HD2xxBbM^r`#DfY?^qViOi0OTOB_w-@i%bQx r4k7V-8Lkhi1epVnSO4d-I=dJHT|9uF3(3LE%*hN-K_RXv0snshO3%kY literal 0 HcmV?d00001 diff --git a/docs/ResourceAllocation.tex b/docs/ResourceAllocation.tex new file mode 100644 index 0000000..4bfbb0d --- /dev/null +++ b/docs/ResourceAllocation.tex @@ -0,0 +1,31 @@ +\documentclass{article} + +% External references +\usepackage{pgf} +\usepackage{tikz} +\usepackage{amsmath} +\usepackage{amssymb} +\usepackage{amsthm} +\usepackage{IEEEtrantools} +\usepackage{mathrsfs} + +% For the Markov chain diagrams +\usetikzlibrary{arrows,automata} + +\title{Resource Allocation Models} +\author{Aaron Geoffrey Sheldon} +\date{\today} +\begin{document} + \pagenumbering{gobble} + \begin{tikzpicture}[->,thick,node distance=3cm] + \node[state] (RA) {RA}; + \node[state] (RR) [below right of=RA] {RR}; + \node[state] (RO) [above right of=RR] {RO}; + \node[state] (RC) [below of=RR] {RC}; + \path + (RA) edge [bend left] node [above] {$\displaystyle\int_0^\infty \gamma\beta_\text{hos} e^{\gamma\alpha_\text{hos} a} n_\text{I} da$} (RO) + (RR) edge [bend left] node [below] {$\beta_\text{ref}$} (RA) + (RO) edge [bend left] node [right] {$\displaystyle\int_0^\infty \left(\gamma\beta_\text{age} e^{\gamma\alpha_\text{age} a} + \gamma\beta_\text{dis} e^{-\gamma\alpha_\text{dis} a}\right) n_{H} da$} (RR) + (RR) edge (RC); + \end{tikzpicture} +\end{document} \ No newline at end of file diff --git a/src/vonFoersterHazards.ipynb b/src/vonFoersterHazards.ipynb index 268c4f3..bd23c77 100644 --- a/src/vonFoersterHazards.ipynb +++ b/src/vonFoersterHazards.ipynb @@ -746,7 +746,7 @@ "\\end{array}\n", "$$\n", "\n", - "The scattering rates are normalized to be either greater than one $\\hat{\\sigma} \\ge 1$ or less than one $\\hat{\\sigma} \\le 1$ for all ages and can be of any form such as logistic or Gompertz. The hazard rate matrix $H$ can be a constant, representing the endogenous self interaction within a single age cohort, such as with ageing. It is from the modest observation that we construct the updating function inside the main loop of our engine.\n", + "The scattering rates are normalized to be either greater than one $\\hat{\\sigma} \\ge 1$ or less than one $\\hat{\\sigma} \\le 1$ for all ages and can be of any form such as logistic or exponential. The hazard rate matrix $H$ can be a constant, representing the endogenous self interaction within a single age cohort, such as with ageing. It is from the modest observation that we construct the updating function inside the main loop of our engine.\n", "\n", "By accumulating all the endogenous self interactions into a single matrix we can exploit the symmetry in age-age scattering cross section to write the exogenous term as a single product so that to first order the terms in our minimal age dependent communicable disease model are:\n", "\n", @@ -793,8 +793,8 @@ " & - \\gamma\\beta_\\text{hos} e^{\\gamma\\alpha_\\text{hos} a} \\int_0^\\infty n_\\text{RA} da & 0 & 0 & 0 & 0 & \\\\\n", " & \\gamma\\beta_\\text{hos} e^{\\gamma\\alpha_\\text{hos} a} \\int_0^\\infty n_\\text{RA} da & - \\gamma\\beta_\\text{age} e^{\\gamma\\alpha_\\text{age} a} - \\gamma\\beta_\\text{dis} e^{-\\gamma\\alpha_\\text{dis} a} & 0 & 0 & 0 & \\\\\n", " & 0 & 0 & -\\int_0^\\infty \\gamma\\beta_\\text{hos} e^{\\gamma\\alpha_\\text{hos} a} n_\\text{I} da & 0 & \\beta_{ref} & \\\\\n", - " & 0 & 0 & \\int_0^\\infty \\gamma\\beta_\\text{hos} e^{\\gamma\\alpha_\\text{hos} a} n_\\text{I} da & - \\int_0^\\infty \\gamma\\beta_\\text{age} e^{\\gamma\\alpha_\\text{age} a} - \\gamma\\beta_\\text{dis} e^{-\\gamma\\alpha_\\text{dis} a} n_{H} da & 0 & \\\\\n", - " & 0 & 0 & 0 & \\int_0^\\infty \\gamma\\beta_\\text{age} e^{\\gamma\\alpha_\\text{age} a} - \\gamma\\beta_\\text{dis} e^{-\\gamma\\alpha_\\text{dis} a} n_{H} da & -\\beta_{ref} & \\\\\n", + " & 0 & 0 & \\int_0^\\infty \\gamma\\beta_\\text{hos} e^{\\gamma\\alpha_\\text{hos} a} n_\\text{I} da & - \\int_0^\\infty \\left( \\gamma\\beta_\\text{age} e^{\\gamma\\alpha_\\text{age} a} + \\gamma\\beta_\\text{dis} e^{-\\gamma\\alpha_\\text{dis} a} \\right) n_{H} da & 0 & \\\\\n", + " & 0 & 0 & 0 & \\int_0^\\infty \\left(\\gamma\\beta_\\text{age} e^{\\gamma\\alpha_\\text{age} a} + \\gamma\\beta_\\text{dis} e^{-\\gamma\\alpha_\\text{dis} a} \\right) n_{H} da & -\\beta_{ref} & \\\\\n", " & & & & & & \\ddots\n", "\\end{bmatrix}\n", "$$\n", diff --git a/src/vonFoersterHazards.jl b/src/vonFoersterHazards.jl index a103df4..b71a620 100644 --- a/src/vonFoersterHazards.jl +++ b/src/vonFoersterHazards.jl @@ -95,7 +95,7 @@ struct evolve{R<:population, S<:Real, T<:Real} gestation::T count::Int64 end -Base.eltype(::Type{evolve{S, T}}) = S +Base.eltype(::Type{evolve{R, S, T}}) = R Base.length(E::evolve) = E.count Base.size(E::evolve, d=1) = ((d==1) ? length(E) : 1) function Base.iterate(E::evolve)