A Two Strain Mutation Model with Temporary and Permanent Recovery

Abstract

Mutation occurs when there is a change in the sequence of the genetic code of an organism. Such changes pose some challenges especially in the development of drugs. A good understating of the dynamics of the strains will help to understand the variant of concern. In this research work, we examined a two strain mutation model in which the first strain has a SIS dynamics and the second strain a SIR dynamics. The disease-free equilibrium, endemic equilibrium and the basic reproduction number of each strain are derived. Suitable Lyapunov functions are used to determine the global stability of the disease free equilibrium of each strain. The equilibrium point and the basic reproduction number of the joint model are determined. The possibility for the coexistence of the endemic equilibrium is also determined. It was found out that both strains have direct variation between them. However, it will be difficult to eradicate the disease in the population if the basic reproduction number of strain 1 is greater than strain 2. The effect of degree of transmissibility of the two strains on the population is carried out through numerical simulation.