Finite Difference Method for Infection Model of HPV with Cervical Cancer under Caputo Operator

In this paper, a fractional model in the Caputo sense is used to characterize the dynamics of HPV with cervical cancer. Generalized mean value theorem has been used to examine whether the infection model has a unique positive solution. The model has two equilibrium points: the disease-free point and the endemic point. The examination of the system’s local and global stability is provided in terms of the basic reproductive number <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"><a:mfenced open="(" close=")" separators="|"><a:mrow><a:msub><a:mrow><a:msub><a:mrow><a:mi mathvariant="script">R</a:mi></a:mrow><a:mrow><a:mi>p</a:mi></a:mrow></a:msub></a:mrow><a:mrow><a:mo>°</a:mo></a:mrow></a:msub></a:mrow></a:mfenced></a:math> . The global stability analysis has been carried out using an appropriate Lyapunov function and the LaSalle invariant principle. The results demonstrate that in the infection model, if <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" id="M2"><g:msub><g:mrow><g:msub><g:mrow><g:mi mathvariant="script">R</g:mi></g:mrow><g:mrow><g:mi>p</g:mi></g:mrow></g:msub></g:mrow><g:mrow><g:mo>°</g:mo></g:mrow></g:msub><g:mo><</g:mo><g:mn>1</g:mn></g:math> , then the solution converges to the disease-free equilibrium, which is both locally and globally asymptotically stable. Whilst <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" id="M3"><j:msub><j:mrow><j:msub><j:mrow><j:mi mathvariant="script">R</j:mi></j:mrow><j:mrow><j:mi>p</j:mi></j:mrow></j:msub></j:mrow><j:mrow><j:mo>°</j:mo></j:mrow></j:msub><j:mo>></j:mo><j:mn>1</j:mn></j:math> , the endemic equilibrium is considered to exist. Simulations are implemented via a finite difference method with Grünwald-Letnikov discretization approach for Caputo derivative operator to define how changes in parameters impact the dynamic behavior of the system using Matlab.