# Mathematical Model Incorporating Individuals’ Trust, Vaccination Decision and Wane of Immunity for Establishing Herd Immunity

Halimatul Sa'adiah, Ja'ffar (2021) Mathematical Model Incorporating Individuals’ Trust, Vaccination Decision and Wane of Immunity for Establishing Herd Immunity. Masters thesis, Universiti Malaysia Sarawak (UNIMAS).

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## Abstract

Infectious diseases are the main public health concerns worldwide. In controlling the re-emergence of infectious diseases, public health relies on achieving the herd immunity establishment in the population. The herd immunity is formed by having enough number of immune individuals in the population to reduce the transmission of infectious diseases and indirectly protect susceptible individuals against infection. There are two factors that affect herd immunity namely individuals’ trust in public health and vaccines as well as wane of immunity in individuals. As these factors are modelled separately in most infectious disease models, this research aims to consolidate both individuals’ trust in public health and vaccines as well as wane of immunity in individuals into one epidemiological model in maintaining herd immunity. The model in the research is known as Susceptible-Infected-Recovered-Trust-Vaccinated-Waned (SIRTVW) model. The SIRTVW model formulation into Equation-Based Model (EBM) with non-linear Ordinary Differential Equation (ODE) and Individual-Based Model (IBM) with rules assigned to the individuals have been implemented by using MATLAB (function ODE solver: ode15s) and NetLogo respectively. In addition, the integration of imitation dynamics based on game theory into EBM and IBM assists the vaccination decision of individuals. The verification and validation of EBM and IBM apply parameter sensitivity analysis and performance indicators such as accuracy percentage measurement metric of Root Mean Square Percentage Error (RMSPE) and execution time. Based on EBM and IBM simulations by using the actual parameter of Pertussis infectious disease in Malaysia, around 70% of individuals in EBM and 80% of individuals in IBM must acquire trust towards public health and vaccines to generate the optimum simulation results when validated to the actual prevalence. The RMSPE of 22.31% in IBM is lower than RMSPE of 56.12% in EBM due to the heterogeneity of individuals in IBM of which EBM does not consider. As IBM mimics the actual prevalence, the 36.36% slower IBM simulation than EBM is acceptable. Furthermore, the individuals’ trust towards public health and vaccines as well as the individuals’ tendency to protect themselves against infection can reduce the transmission of infectious diseases in the population. In relation with herd immunity, a modified herd immunity threshold formula has been derived from SIRTVW model. The modification on the herd immunity threshold formula results in different threshold values due to sensitivity of certain parameters included in the formula. As herd immunity threshold is used to determine the minimum number of individuals that should be immune to induce herd immunity, the herd immunity threshold from the modified formula provides new insights for the establishment of herd immunity. It is very important to maintain the herd immunity establishment in the population as the disappearance of herd immunity becomes a barrier in controlling the transmission of infectious diseases.

Item Type: Thesis (Masters) Thesis (MSc.) - Universiti Malaysia Sarawak, 2021. Herd immunity, herd immunity threshold, individuals’ trust, wane of immunity, infectious disease modelling, vaccination, mathematical model, equation-based model, individual-based model, UNIMAS, Universiti Malaysia Sarawak Q Science > QA Mathematics > QA75 Electronic computers. Computer science Academic Faculties, Institutes and Centres > Faculty of Computer Science and Information Technology HALIMATUL SA'ADIAH BINTI JA'FFAR 30 Mar 2021 01:11 30 Mar 2021 01:11 http://ir.unimas.my/id/eprint/34948

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