Two-sex logistic model for human papillomavirus and optimal vaccine

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We formulate a two-gender susceptible-infectious-susceptible (SIS) model to search for optimal childhood and catch-up vaccines over a 20-year period. The optimal vaccines should minimize the cost of Human Papillomavirus (HPV) disease in random logistically growing population. We find the basic reproduction number R0 for the model and use it to describe the local-asymptotic stability of the disease-free equilibrium (DFE). We estimate the solution of the model to show the role of vaccine in reducing R0 and controlling the disease. We formulate some optimal control problems to find the optimal vaccines needed to control HPV under limited resources. The optimal vaccines needed to keep R0 ≤ 1 are the catch-up vaccine rates of 0.004 and 0.005 for females and males, respectively; 100% is needed to reduce R0 to its minimum value. To reduce the expenses for HPV disease and its vaccines, we need 100% childhood vaccines (both genders) for the first 13-14 years and then gradually reduce the vaccine to reach 0% at year 20. For adults (both genders), we need maximum rates (one) for the first 9 years, then 0.2 for the next 3-4 years before reducing gradually to zero rate at year 20. Although the childhood vaccines provide very early protection strategy against HPV, its time to control HPV is longer than that for adult vaccines. Thus, full adults' only vaccines for enough period is a viable choice to control HPV at minimal cost and short time.

Original languageBritish English
Article number2150011
JournalInternational Journal of Biomathematics
Issue number3
StatePublished - Mar 2021


  • adult vaccine
  • childhood vaccine
  • Human papillomavirus
  • logistic model
  • mathematical model
  • optimal vaccine


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