Treatment outcome in an SI model with evolutionary resistance: a Darwinian model for the evolution of resistance

Abstract

We consider a Darwinian (evolutionary game theoretic) version of a standard susceptible-infectious SI model in which the resistance of the disease causing pathogen to a treatment that prevents death to infected individuals is subject to evolutionary adaptation. We determine the existence and stability of all equilibria, both disease-free and endemic, and use the results to determine conditions under which the treatment will succeed or fail. Of particular interest are conditions under which a successful treatment in the absence of resistance adaptation (i.e. one that leads to a stable disease-free equilibrium) will succeed or fail when pathogen resistance is adaptive. These conditions are determined by the relative breadths of treatment effectiveness and infection transmission rate distributions as functions of pathogen resistance.

Keywords:

• SI model
• Darwinian dynamics
• evolutionary adaptation
• pathogen resistance to treatment

AMS Subject Classifications:

• 92D30
• 92D15

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Junpyo Park was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) [No. NRF-2021R1A4A1032924, NRF-2023R1A2C1004893]. Nakul Chitnis was supported by the Bill and Melinda Gates Foundation [INV025569].