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<p>In this paper, we construct and formulate a novel mathematical model for the spread of epidemic diseases with vaccination especially for Chikungunya transmitted virally in Brazil. This model includes seven biological components consisting of susceptible (<i>S</i>), exposed (<i>E</i>), infected (<i>I</i>), recovered (<i>R</i>), vaccinated (<i>V</i>), quarantined (<i>Q</i>) and dead individuals (<i>D</i>). This study considers various parameters that affect the spread of the Chikungunya disease and fills gaps in other models and epidemiology data. According to the fluctuating essence of studying epidemic diseases, especially Chikungunya, implementation of stochastic differential equations and Brownian motion is one of the innovations of this comprehensive model compared to other simple models for Chikungunya transmission. Additionally, we calculate the basic reproduction number <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2025_1617_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">\((R_0)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msub> <mi>R</mi> <mn>0</mn> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> by the next-generation matrix method in order to demonstrate the level of the Chikungunya virus outbreak. Moreover, dynamical analysis is presented as a theoretical foundation of our proposed epidemic model. We introduce specific conditions in which the disease tends to extinct stochastically. Moreover, numerical simulation and data fitting are performed using Euler–Maruyama method to illustrate and validate the efficiency of the proposed model and its accordance using real data for the Chikungunya outbreak in Espirito Santo, Brazil.</p>

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Transmission dynamics of a stochastic model of Chikungunya virus: a case study of Brazil

  • 期刊论文

  • 发表日期：

    2025年3月2日

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  • Milad Fahimi,
  • Kazem Nouri,
  • Leila Torkzadeh

摘要

In this paper, we construct and formulate a novel mathematical model for the spread of epidemic diseases with vaccination especially for Chikungunya transmitted virally in Brazil. This model includes seven biological components consisting of susceptible (S), exposed (E), infected (I), recovered (R), vaccinated (V), quarantined (Q) and dead individuals (D). This study considers various parameters that affect the spread of the Chikungunya disease and fills gaps in other models and epidemiology data. According to the fluctuating essence of studying epidemic diseases, especially Chikungunya, implementation of stochastic differential equations and Brownian motion is one of the innovations of this comprehensive model compared to other simple models for Chikungunya transmission. Additionally, we calculate the basic reproduction number \((R_0)\) ( R 0 ) by the next-generation matrix method in order to demonstrate the level of the Chikungunya virus outbreak. Moreover, dynamical analysis is presented as a theoretical foundation of our proposed epidemic model. We introduce specific conditions in which the disease tends to extinct stochastically. Moreover, numerical simulation and data fitting are performed using Euler–Maruyama method to illustrate and validate the efficiency of the proposed model and its accordance using real data for the Chikungunya outbreak in Espirito Santo, Brazil.