Stability analysis and optimal control of HPV infection model with early-stage cervical cancer

Cervical cancer cells may develop from any cell infected by human papillomavirus (HPV). The aim of this paper is to study whether an optimal control of HPV infection can reduce those resulting cancer cells. To this end, the problem will be modelled by five differential equations that describe the interactions between healthy cells, infected cells, free virus, precancerous cells and cancer cells. A saturated infection rate and two treatments are incorporated into the model. The first therapy stands for the efficacy of drug treatment in blocking new infections, whereas the second serves as the drug effectiveness in inhibiting viral production. First, The problem well-posedness is fulfilled in terms of existence, positivity and boundedness of solution. Next, the existence for the two optimal control pair is established, Pontryagin's maximum principle is used to characterize these two optimal controls. Moreover, the optimality system is derived and solved numerically using the forward and backward difference approximation scheme. Finally, numerical simulations are established in order to show the role of optimal therapy in controlling cancer cells proliferation. It was revealed that the antiviral drug therapies do not act only on the viral infection spread but also on reducing the amount of precancerous and cancerous cells. Consequently, the antiviral therapies can be considered amongst the most promising measures to reduce cervical cancer cells invasion.