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Optimal Virulence, Diffusion and Tradeoffs.

Esdras Jafet Aristides da Silva1, César Castilho2

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Summary

This study models pathogen evolution using a SIR model with random walk mutations. It reveals optimal evolutionary strategies predicting mild, short infections or acute, long-lasting ones based on virulence trade-offs.

Keywords:
EpidemicsEvolution theorySIR modelsTradeoffsVirulence

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Area of Science:

  • Epidemiology
  • Evolutionary Biology
  • Mathematical Biology

Background:

  • Classical SIR models track infectious disease spread.
  • Pathogen evolution, including virulence, is crucial for disease dynamics.
  • Understanding pathogen evolutionary strategies is key to predicting infection outcomes.

Purpose of the Study:

  • To investigate pathogen evolutionary strategies using a modified SIR model.
  • To explore how random walk mutations in pathogen traits influence epidemiological dynamics.
  • To interpret pathogen evolution as an optimal control problem aiming to maximize the basic reproductive number.

Main Methods:

  • Developed a variant of the SIR epidemiological model incorporating a phenotypic mutant trait.
  • Modeled trait mutation using a random walk process.
  • Applied Pontryagin's maximum principle to identify optimal evolutionary strategies.

Main Results:

  • Identified three distinct optimal evolutionary routes for pathogens.
  • Demonstrated that optimal strategies involve trade-offs among epidemiological parameters.
  • Predicted two primary infection types: short-term mild and long-term acute.

Conclusions:

  • Pathogen evolution can be mathematically modeled as an optimal control problem.
  • Virulence evolution is influenced by mutation processes and epidemiological trade-offs.
  • The model predicts distinct clinical outcomes based on pathogen evolutionary strategies.