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Susceptibility governs the dynamics of contagion. The classical SIR model is one of the simplest compartmental models of contagion spread, assuming a single shared susceptibility level. However, variation in susceptibility over a population can fundamentally affect the dynamics of contagion and thus the ultimate outcome of a pandemic. We develop mathematical machinery which explicitly considers susceptibility variation, illuminates how the susceptibility distribution is sculpted by contagion, and thence how such variation affects the SIR differential questions that govern contagion. Our methods allow us to derive closed form expressions for herd immunity thresholds as a function of initial susceptibility distributions and suggests an intuitively satisfying approach to inoculation when only a fraction of the population is accessible to such intervention. Of particular interest, if we assume static susceptibility of individuals in the susceptible pool, ignoring susceptibility diversity {em always} results in overestimation of the herd immunity threshold and that difference can be dramatic. Therefore, we should develop robust measures of susceptibility variation as part of public health strategies for handling pandemics.
The dynamics of a mosquito population depends heavily on climatic variables such as temperature and precipitation. Since climate change models predict that global warming will impact on the frequency and intensity of rainfall, it is important to unde
Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture notes, we introduce fundamental concepts of evoluti
Many questions that we have about the history and dynamics of organisms have a geographical component: How many are there, and where do they live? How do they move and interbreed across the landscape? How were they moving a thousand years ago, and wh
Population dynamics of a competitive two-species system under the influence of random events are analyzed and expressions for the steady-state population mean, fluctuations, and cross-correlation of the two species are presented. It is shown that ran
We consider age-structured models with an imposed refractory period between births. These models can be used to formulate alternative population control strategies to Chinas one-child policy. By allowing any number of births, but with an imposed dela