Mathematical Analysis of Mpox in HumanPopulation:TheEffectsof Vaccination Strategies

Abstract

 In this research work, a fractional-order model of monkeypox disease transmission within the human  population is formulated and studied. The formulated model incorporates two control strategies  namely; vaccination and health education campaign. In model analysis, the disease free-equilibrium  and basic reproduction number, was computed. The existence and uniqueness of model solution  using fixed point theorem have been analyzed. Meanwhile, the global stability of the model have  been performed using well formulated Lyapunov function and the results showed that the model  is stable when R0 < 1 and unstable when R0 > 1. In model simulations, parameter estimation  using reported cases of Monkeypox disease from Democratic Republic of Congo have been performed to compare the results for fractional (z = 0.5) and integer (z = 1) order derivatives. The  results showed that fitting the model at z = 0.5 had good results compared to when z = 1. Implying that fractional model presented good results compared to integer-order derivatives. Besides,  we performed Sensitivity analysis of the basic reproduction number using computed partial rank  correlation coefficients to investigate the impact of each parameter on the disease transmission.  Furthermore, we performed numerical simulation of the model to assess the impact of memory  effects on the spread of Monkeypox virus transmission in the population. Additionally, numerical  simulation to investigate the effects of health education and vaccination was performed. Overall,  the results showed that when the efficacy of first-dose vaccination was changed from 75% to 95%  and the rate of health education campaign retained at 0.1 the threshold quantity R0 remained  greater than unity. In contrast when the efficacy of first-dose vaccination was changed from 75% to 95% and the rate of health education campaign changed from 0.1 to 0.9 the threshold quantity  R0 was observed to be less than unity. The results have implication that the efficacy of first-dose  vaccination must be greater than 95% and rate of health education campaign must be greater that  0.9 for the disease to eliminated in the population