Mathematical Analysis of Mpox in HumanPopulation:TheEffectsof Vaccination Strategies
Mlyashimbi Helikumi, Philipina Shayo, Herman Trazias
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Source: Crossref
Published: Aug 30, 2026
DOI: 10.62277/mjrd2026v7i30003
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In this researchwork,afractional-ordermodelofmonkeypoxdiseasetransmissionwithinthe human population isformulatedandstudied.Theformulatedmodelincorporatestwocontrol strategies namely; vaccination and health education campaign. In model analysis, the disease free-equilibrium and basic reproduction number, are computed. The existence and unique ness 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 showedthatthemodel isstablewhen 0 < 1andunstablewhen 0 > 1.Inmodelsim ulations, parameter estimation using reported cases of monkeypox disease from Democratic Republic of Congo have been performed to compare the results for fractional ( = 0.5) and integer ( = 1) order derivatives. The results showed that fitting the model at = 0.5 had good results compared to when = 1.Implyingthatfractional model presented good results comparedtointeger-orderderivatives.Besides,weperformedSensitivityanalysisofthebasic reproduction number using computed partial rank correlation coefficients to investigate the impactofeachparameteronthedisease transmission.Furthermore,weperformednumerical 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 whentheefficacyoffirst-dosevaccinationwaschangedfrom75%to95%andtherateofhealth education campaign retained at 0.1thethresholdquantity 0 remainedgreaterthanunity.In contrastwhentheefficacyoffirst-dosevaccinationwaschangedfrom75%to95%andtherate ofhealtheducationcampaignchangedfrom0.1to0.9thethresholdquantity 0 wasobserved to be less than unity. The results have implication that the efficacy of first-dose vaccination must be greater than 95%andrateofhealtheducation campaignmustbegreaterthat 0.9 for the disease to eliminated in the population Monkeypox virus (MPXV) transmission remains an important public health concern, particularly in populations where vaccination coverage, disease surveillance, and access to effective preventive measures are limited. Mathematical modelling provides a valuable framework for understanding MPXV transmission dynamics and assessing the effectiveness of control interventions by describing the interactions among susceptible, vaccinated, exposed,andinfectiouspopulations.Inparticular,incorporatingfirst andsecond-dose vaccination into transmission models allows the differential protection pro videdbysuccessivevaccinedosestobeexamined,togetherwithvaccinationratesandvaccine efficacy. Parameter estimation using reported MPXV cases is essential for calibrating the modelandimproving itsabilitytodescribeobserveddiseasepatterns.Suchmodelscanalsobe used to determine key epidemiological quantities, including the basic reproduction number, and to evaluate the effects of vaccination and other interventions on disease transmission. Therefore,integratingMPXVmodelformulation,parameterestimation,andfirst-andsecond dose vaccination provides a useful mathematical framework for identifying effective control strategies and establishing conditions under which MPXV transmission can be reduced and potentially eliminated from the population.
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