• Part 1: Introduction
• Part 2: Past work
• Part 3: Norovirus
• Part 4: Influenza
• Part 5: More stuff

https://xkcd.com/

• Inoculum dose is an important determinant of infection and vaccination outcomes.
• For infection, higher dose is often associated with greater risk of infection (ID50) and more severe outcomes (LD50).
• For vaccines, dose is thought to impact both immunogenicity/efficacy and side effects (morbidity).

• Not much is known about the impact of dose given infection.
• There might be non-monotone relations between infection or vaccination dose and outcomes.
• There might be trade-offs between vaccine availability/safety and efficacy.

Adenovirus type 5 (ADV) infections of cotton rats.

\[ \begin{aligned} \dot U & = - bUV \\ \dot I & = bUV - dI \\ \dot V & = pI - cV \end{aligned} \]

Li & Handel 2014 JTB

\[ \begin{aligned} \textrm{Uninfected cells} \qquad \dot{U} & = - bUV \\ \textrm{Infected cells} \qquad \dot{I} & = bUV - d_I I \\ \textrm{Dead cells} \qquad \dot{D} & = d_I I \\ \textrm{Virus} \qquad \dot{V} & = \frac{pI}{1+s_F F} - (d_V V + k^{'}_{A}A + b^{'} U)V\\ \textrm{Innate response} \qquad \dot{F} & = p_F - d_F F + \frac{g_F (F_{max} - F)V}{V+h_V} \\ \textrm{B cells} \qquad \dot{B} & = \frac{F V}{FV+h_F} g_B B \\ \textrm{Antibodies} \qquad \dot{A} & = r_A B - d_A A - k_{A}AV \\ \end{aligned} \]