<p>Hepatitis C is among the major viral infectious diseases that are major traits with high human morbidity and mortality impacts and it has detrimental effects on the economies and health of nations worldwide. In the current study, we formulated and analysed a compartmental Hepatitis C epidemic model by dividing the entire susceptible human population into two groups, such as aware susceptible and unaware susceptible stage structure groups with optimal control strategies, since Hepatitis C has been a cause of death for individuals in different age groups. Qualitatively, we computed the model's unique disease-free and endemic equilibrium points, using the next-generation matrix operator approach we calculated the model basic reproduction number, and we proved the local stabilities of both the model disease-free and endemic equilibrium points using by applying the Routh-Hurwitz stability criteria, we also proved the global stabilities of the model's disease-free and endemic equilibrium points by building the suitable representative Lyapunov function. Using Pontryagin's Maximum Principle, the Hepatitis C model's optimality system which determines the necessary circumstances to improve the control over the spread of the Hepatitis C disease is built and examined. We performed numerical simulations to validate the qualitative analysis of the optimal control and explore the effects of the suggested optimal control techniques. Finally, without considering the effect of cost incurred we verified that implementing all the three control measures simultaneously will have very high impact to reduce and control the HCV infection spreading in the community.</p>

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Analyses of a stage structure hepatitis c virus compartmental model with optimal control theory

  • Shewafera Wondimagegnhu Teklu,
  • Tsegaye Simon Lachamo,
  • Tibebu Tulu Guya

摘要

Hepatitis C is among the major viral infectious diseases that are major traits with high human morbidity and mortality impacts and it has detrimental effects on the economies and health of nations worldwide. In the current study, we formulated and analysed a compartmental Hepatitis C epidemic model by dividing the entire susceptible human population into two groups, such as aware susceptible and unaware susceptible stage structure groups with optimal control strategies, since Hepatitis C has been a cause of death for individuals in different age groups. Qualitatively, we computed the model's unique disease-free and endemic equilibrium points, using the next-generation matrix operator approach we calculated the model basic reproduction number, and we proved the local stabilities of both the model disease-free and endemic equilibrium points using by applying the Routh-Hurwitz stability criteria, we also proved the global stabilities of the model's disease-free and endemic equilibrium points by building the suitable representative Lyapunov function. Using Pontryagin's Maximum Principle, the Hepatitis C model's optimality system which determines the necessary circumstances to improve the control over the spread of the Hepatitis C disease is built and examined. We performed numerical simulations to validate the qualitative analysis of the optimal control and explore the effects of the suggested optimal control techniques. Finally, without considering the effect of cost incurred we verified that implementing all the three control measures simultaneously will have very high impact to reduce and control the HCV infection spreading in the community.