2025_Modeling And Simulations Of Vector-Host Diseases With Integer And Fractional Order Derivatives
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| country | Malaysia |
| date | 2024-12-30 21:00 |
| format | General Document |
| id | 17258 |
| institution | UniSZA |
| originalfilename | 17258_cb05a27d9bec3c6.pdf |
| person | Muhammad Farooq Khan |
| recordtype | oai_dc |
| resourceurl | https://intelek.unisza.edu.my/intelek/pages/view.php?ref=17258 |
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| spelling | 17258 https://intelek.unisza.edu.my/intelek/pages/view.php?ref=17258 https://intelek.unisza.edu.my/intelek/pages/search.php?search=!collection3 General Document Malaysia Library Staff (Top Management) Library Staff (Management) Library Staff (Support) Terengganu Faculty of Informatics & Computing English application/pdf 1.6 158 Server storage Scanned document UniSZA Private Access UniSZA Copyright©PWB2025 Mathematical Modeling Fractional Calculus UniSZA Dissertations-Academic 2025_Modeling And Simulations Of Vector-Host Diseases With Integer And Fractional Order Derivatives Muhammad Farooq Khan Vector-Host Diseases Fractional Order Derivatives Integer Order Model Holling Type II Incidence Saturated Treatment Function Optimal Control Sensitivity Analysis (LHS, PRCC) Vector-borne diseases—Mathematical models Epidemiology—Mathematical models Differential equations—Mathematical models Control Theory 2024-12-30 21:00 uuid:8ed3a19e-a7ad-43ed-8471-cf945be98327 17258_cb05a27d9bec3c6.pdf pdfTeX-1.40.25 Introduction: Vector-host disease outbreaks are a major public health concern and affect not only human health but also livestock and crops. The most common approaches used for vector-host disease models are bilinear or saturated incidence and a linear treatment function. These approaches, however, are impractical when there are a growing number of infected people and minimal healthcare resources. One of the most critical instruments for comprehending the dynamics of transmission and establishing effective control measures for combating infection in a community is mathematical modeling. In order to analyze the dynamics of transmission and management of vector-host illness, the research intends to create new deterministic mathematical models based on nonlinear saturated incidence and treatment functions of the Holling type II form. Methodology: The foundation for the mathematical models is initially established by using traditional nonlinear integer-order differential equations. The Holling type II incidence and treatment functions are used in the model formulation. Then the model in the integer case is rigorously analyzed in terms of the stability of equilibria. The Latin Hypercube Sampling (LHS) and the Partial Rank Correlation Coefficient (PRCC) techniques were used to perform the global sensitivity analysis of the model parameters in order to develop time-dependent measures that represent prevention control. Secondly, the proposed model has been extended to fractional mathematical models to study the impact of memory effects on the dynamics of vector-host diseases. Three well-known fractional-order derivatives, namely Caputo, Caputo-Fabrizio, and Atangana-Baleanu, have been utilized to formulate the models in the fractional case. Moreover, an efficient numerical scheme is used to obtain the iterative solution of the proposed models. Finally, the results of the proposed models with Holling type II incidence and treatment functions are compared with those of existing models based on linear incidence and treatment functions. Results: The theoretical results of the integer case model with control parameters indicate the presence of two equilibria: the disease-free equilibrium and the endemic equilibrium point. Analysis shows that the disease-free equilibrium is both locally and globally asymptotically stable when the biological threshold number, R0 < 1. On other hand, when R0 > 1, the endemic equilibrium point is both locally and globally asymptotically stable. The accuracy of these theoretical findings is validated using simulation The sensitivity results showed that the most influential parameters for the disease incidence are the human recovery rate (γ), mosquito natural death rate (μ), mosquito biting rate (b), and transmission probability per contact of susceptible mosquitoes with infectious humans (β). Particularly, the results revealed that reducing β by (10%) reduces the disease incidence by 8.5%. On the other hand, increasing the parameters μ and γ by 10% reduces the disease incidence by 9.8% and 3.9%, respectively. A comparative analysis is conducted in terms of the compartmental model and its control parameters to assess the influence of incorporating optimal control strategy for the eradication of vector-host diseases. Graphical results are presented and analyzed, show casing the impact of different parameter values on the basic reproductive number R0, both with and without control measures. The implementation of suggested preventive measures leads to a significant reduction in the density of infected humans and vectors, as indicated by the simulation. The solutions of fractional models, when initialized with non-negative data, satisfy the criteria for existence and uniqueness. Additionally, the theoretical analysis establishes the positivity and boundedness of the approximations. Simulation studies further validate the accuracy of these theoretical findings. Moreover, numerical results showed that implementing the suggested time-dependent control measures significantly reduced the cumulative number of infected humans and mosquitoes. Overall, the results of this study offer significant insights to implement an optimal preventive strategy for minimizing vector-host disease transmission. Additionally, the study presents a comprehensive understanding of the most sensitive and influential factors affecting the spread and control of vector-host diseases. Moreover, considering the previous history (memory effects using fractional models) of disease dynamics plays a crucial role in comprehending and controlling infection incidence. Conclusion: The numerical results for all proposed mathematical models indicate that the models based on nonlinear saturated incidence and treatment functions of Holling type II provide better epidemiological insights into the disease dynamics. Further, the results revealed that the implementation of a three-fold control strategy is the most useful strategy against disease eradication. Moreover, the numerical results showed that by implementing a three-fold control strategy, the infected humans and infected vectors could vanish after 40 and 50 days, respectively. The outcomes of this study will be beneficial for the government and health departments in order to understand the dynamics and control of such diseases in the community. Thesis |
| spellingShingle | 2025_Modeling And Simulations Of Vector-Host Diseases With Integer And Fractional Order Derivatives |
| state | Terengganu |
| subject | Dissertations-Academic Vector-borne diseases—Mathematical models Epidemiology—Mathematical models Differential equations—Mathematical models Control Theory |
| summary | Introduction: Vector-host disease outbreaks are a major public health concern and affect not only human health but also livestock and crops. The most common approaches used for vector-host disease models are bilinear or saturated incidence and a linear treatment function. These approaches, however, are impractical when there are a growing number of infected people and minimal healthcare resources. One of the most critical instruments for comprehending the dynamics of transmission and establishing effective control measures for combating infection in a community is mathematical modeling. In order to analyze the dynamics of transmission and management of vector-host illness, the research intends to create new deterministic mathematical models based on nonlinear saturated incidence and treatment functions of the Holling type II form. Methodology: The foundation for the mathematical models is initially established by using traditional nonlinear integer-order differential equations. The Holling type II incidence and treatment functions are used in the model formulation. Then the model in the integer case is rigorously analyzed in terms of the stability of equilibria. The Latin Hypercube Sampling (LHS) and the Partial Rank Correlation Coefficient (PRCC) techniques were used to perform the global sensitivity analysis of the model parameters in order to develop time-dependent measures that represent prevention control. Secondly, the proposed model has been extended to fractional mathematical models to study the impact of memory effects on the dynamics of vector-host diseases. Three well-known fractional-order derivatives, namely Caputo, Caputo-Fabrizio, and Atangana-Baleanu, have been utilized to formulate the models in the fractional case. Moreover, an efficient numerical scheme is used to obtain the iterative solution of the proposed models. Finally, the results of the proposed models with Holling type II incidence and treatment functions are compared with those of existing models based on linear incidence and treatment functions. Results: The theoretical results of the integer case model with control parameters indicate the presence of two equilibria: the disease-free equilibrium and the endemic equilibrium point. Analysis shows that the disease-free equilibrium is both locally and globally asymptotically stable when the biological threshold number, R0 < 1. On other hand, when R0 > 1, the endemic equilibrium point is both locally and globally asymptotically stable. The accuracy of these theoretical findings is validated using simulation The sensitivity results showed that the most influential parameters for the disease incidence are the human recovery rate (γ), mosquito natural death rate (μ), mosquito biting rate (b), and transmission probability per contact of susceptible mosquitoes with infectious humans (β). Particularly, the results revealed that reducing β by (10%) reduces the disease incidence by 8.5%. On the other hand, increasing the parameters μ and γ by 10% reduces the disease incidence by 9.8% and 3.9%, respectively. A comparative analysis is conducted in terms of the compartmental model and its control parameters to assess the influence of incorporating optimal control strategy for the eradication of vector-host diseases. Graphical results are presented and analyzed, show casing the impact of different parameter values on the basic reproductive number R0, both with and without control measures. The implementation of suggested preventive measures leads to a significant reduction in the density of infected humans and vectors, as indicated by the simulation. The solutions of fractional models, when initialized with non-negative data, satisfy the criteria for existence and uniqueness. Additionally, the theoretical analysis establishes the positivity and boundedness of the approximations. Simulation studies further validate the accuracy of these theoretical findings. Moreover, numerical results showed that implementing the suggested time-dependent control measures significantly reduced the cumulative number of infected humans and mosquitoes. Overall, the results of this study offer significant insights to implement an optimal preventive strategy for minimizing vector-host disease transmission. Additionally, the study presents a comprehensive understanding of the most sensitive and influential factors affecting the spread and control of vector-host diseases. Moreover, considering the previous history (memory effects using fractional models) of disease dynamics plays a crucial role in comprehending and controlling infection incidence. Conclusion: The numerical results for all proposed mathematical models indicate that the models based on nonlinear saturated incidence and treatment functions of Holling type II provide better epidemiological insights into the disease dynamics. Further, the results revealed that the implementation of a three-fold control strategy is the most useful strategy against disease eradication. Moreover, the numerical results showed that by implementing a three-fold control strategy, the infected humans and infected vectors could vanish after 40 and 50 days, respectively. The outcomes of this study will be beneficial for the government and health departments in order to understand the dynamics and control of such diseases in the community. |
| title | 2025_Modeling And Simulations Of Vector-Host Diseases With Integer And Fractional Order Derivatives |
| title_full | 2025_Modeling And Simulations Of Vector-Host Diseases With Integer And Fractional Order Derivatives |
| title_fullStr | 2025_Modeling And Simulations Of Vector-Host Diseases With Integer And Fractional Order Derivatives |
| title_full_unstemmed | 2025_Modeling And Simulations Of Vector-Host Diseases With Integer And Fractional Order Derivatives |
| title_short | 2025_Modeling And Simulations Of Vector-Host Diseases With Integer And Fractional Order Derivatives |
| title_sort | 2025_modeling and simulations of vector-host diseases with integer and fractional order derivatives |