# Modeling the transmission dynamics of Hantavirus infection under the effect of vaccination and other optimal controls

Mohamed Yusof, Fauzi and Musiliu Folarin, Farayola (2023) Modeling the transmission dynamics of Hantavirus infection under the effect of vaccination and other optimal controls. Menemui Matematik, 45 (1). pp. 56-75. ISSN 2231-7023

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## Abstract

This article presents a nonlinear deterministic mathematical model which simulates the transmission dynamics of hantavirus infection in the presence of vaccination as well as other optimal control measures. The model is formulated by improving the previous models and including vaccination as an essential component of its optimal control variable. The model is then analyzed for local stability and the disease reproduction number is obtained. Subsequently, the analysis of the model’s optimal controls is done using the Pontryagin maximum principle. The necessary conditions for the optimal solution are obtained and used to formulate the adjoint equations and characterize the optimal controls. The model equations and adjoint equations are then solved in the MATLAB environment and used to simulate the population dynamics of the infected and susceptible humans and rodents. The values for the model parameters used for the simulations are obtained from previous works of literature. Thereafter, the global sensitivity analysis of the model's optimal control variables is performed using infected humans and rodents as the expected outputs. The simulation results indicate that within five months, the populations of rodents and infected humans had approached zero. The population of susceptible humans increased initially but the rate of increase later slowed down. As for the susceptible rodents, the population increased for the first two months to a maximum point, then it decreased and approached zero. The results of the global sensitivity analysis show that the first-order sensitivity index for the vaccination in the infected human is 1.0 and 0.9935 in the infected rodents. Similarly, the total-effect sensitivity index for the vaccination in the infected humans is 0.0142 and -0.0691 in the infected rodents. Lastly, based on the simulation and sensitivity analysis results, the presented model, which integrated vaccination with other optimal control strategies, is the most viable model for Hantavirus.

Item Type: Article (Journal) Hantavirus; Vaccination; Pontryagin Maximum Principle; Biodiversity; Sensitivity Analysis Q Science > QA MathematicsT Technology > T Technology (General) > T55.4 Industrial engineering.Management engineering. > T57 Applied mathematics. Quantitative methods. Operation research. System analysisT Technology > TA Engineering (General). Civil engineering (General) > TA329 Engineering mathematics. Engineering analysis Kulliyyah of EngineeringKulliyyah of Engineering > Department of Science Dr. Musiliu Farayola 09 Oct 2023 09:08 21 Dec 2023 14:06 http://irep.iium.edu.my/id/eprint/107340