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Viral phylodynamics is the study of how epidemiological, immunological, and evolutionary processes act and potentially interact to shape viral phylogenies. [1] Since the term was coined in 2004, research on viral phylodynamics has focused on transmission dynamics in an effort to shed light on how these dynamics impact viral genetic variation.
For example, if a contact network can be approximated with an Erdős–Rényi graph with a Poissonian degree distribution, and the disease spreading parameters are as defined in the example above, such that is the transmission rate per person and the disease has a mean infectious period of , then the basic reproduction number is = [22] [23 ...
Viral evolution is a subfield of evolutionary biology and virology that is specifically concerned with the evolution of viruses. [ 1 ] [ 2 ] Viruses have short generation times, and many—in particular RNA viruses —have relatively high mutation rates (on the order of one point mutation or more per genome per round of replication).
For the full specification of the model, the arrows should be labeled with the transition rates between compartments. Between S and I, the transition rate is assumed to be (/) / = /, where is the total population, is the average number of contacts per person per time, multiplied by the probability of disease transmission in a contact between a susceptible and an infectious subject, and / is ...
Using these techniques, Malthus' population principle of growth was later transformed into a mathematical model known as the logistic equation: = (), where N is the population size, r is the intrinsic rate of natural increase, and K is the carrying capacity of the population. The formula can be read as follows: the rate of change in the ...
The Reed–Frost model is a mathematical model of epidemics put forth in the 1920s by Lowell Reed and Wade Hampton Frost, of Johns Hopkins University. [1] [2] While originally presented in a talk by Frost in 1928 and used in courses at Hopkins for two decades, the mathematical formulation was not published until the 1950s, when it was also made into a TV episode.
The "Kill the Winner" hypothesis relates to Lotka-Volterra equations. Viral lysis, which disproportionately targets the "winners" of marine ecosystems.. The "Kill the Winner" hypothesis (KtW) is an ecological model of population growth involving prokaryotes, viruses and protozoans that links trophic interactions to biogeochemistry. [1]
Firstly, a proportional measure of the extent of infection is chosen as the disease extent metric. For example, the metric might be the proportion of leaf area affected by mildew or the proportion of plants in a population showing dieback lesions. Measures of disease extent are then taken over time, and a mathematical model is fitted. The model ...