Advances in Epidemiological Modeling and Control of Viruses covers recent and advanced research works in the field of epidemiological modeling, with special emphasis on new strategies to control the occurrence and reoccurrence of viruses. The models included in this book can be used to study the dynamics of different viruses, searching for control measures, and epidemic models under various effects and environments. This book covers different models and methods of modeling, including data-driven approaches. The authors and editors are experienced researchers, and each chapter has been designed to provide readers with leading-edge information on topics discussed.
1. 1.1: Introduction - p. 1 2. 1.2: Global convergence to the homogeneous solution - p. 3 3. 1.3: Numerical simulations - p. 18 4. 1.4: Spatiotemporal pattern formation - p. 20 5. 1.5: Conclusion and open problems - p. 25 6. Acknowledgements - p. 26 7. References - p. 26 8. 2 Hepatitis B virus transmission via epidemic model - p. 29 9. 2.1: Introduction - p. 29 10. 2.2: Model formulation - p. 31 11. 2.3: Stability analysis - p. 33 12. 2.4: Simulation and concluding remarks - p. 49 13. References - p. 53 14. 3 Global dynamics of an HCV model with full logistic terms and the host immune system - p. 55 15. 3.1: Introduction - p. 55 16. 3.2: Previous works - p. 57 17. 3.3: Mathematical preliminaries - p. 59 18. 3.4: Modelling virus-immune system interaction with full logistic terms in both uninfected and infected cells - p. 63 19. 3.5: Analysis of the model - p. 65 20. 3.5.1: Dissipativity, basic reproduction number, and equilibria - p. 65 21. 3.5.2: Local and global stability analysis - p. 70 22. 3.6: Numerical simulations - p. 89 23. 3.7: Conclusion and discussion - p. 91 24. Acknowledgements - p. 92 25. References - p. 92 26. 4 On a Novel SVEIRS Markov chain epidemic model with multiple discrete delays and infection rates: modeling and sensitivity analysis to determine vaccination effects - p. 95 27. 4.1: Introduction - p. 95 28. 4.2: Description of the SVEIRS epidemic and the delays in the disease dynamics - p. 98 29. 4.3: Discretization of time and decomposition of the SVEIRS population over time - p. 99 30. 4.4: The SVEIRS stochastic process - p. 110 31. 4.5: Some special SVEIRS epidemic models - p. 115 32. 4.6: Numerical study: some prototype SVEIRS epidemic models and sensitivity analysis to determine the effects of infection and vaccination - p. 122 33. 4.7: Conclusion - p. 141 34. References - p. 142 35. 5 Hopf bifurcation in an SIR epidemic model with psychological effect and distributed time delay - p. 145 36. 5.1: Introduction - p. 145 37. 5.2: Model - p. 149 38. 5.3: Direction of bifurcation and stability of periodic solution - p. 152 39. 5.4: Example: a truncated exponential distribution - p. 161 40. 5.5: Numerical simulation - p. 164 41. 5.6: Discussion - p. 166 42. Acknowledgements - p. 166 43. Appendix 5.A: Matlab code for Fig. 5.8(b) - p. 166 44. References - p. 167 45. 6 Modeling of the effects of media in the course of vaccination of rotavirus - p. 169 46. 7 Mathematical models of early stage Covid-19 transmission in Sri Lanka - p. 191 47. 7.1: Introduction - p. 191 48. 7.2: Mathematical model to estimate initial parameters - p. 194 49. 7.3: Mathematical models with heterogeneity of cases - p. 203 50. 7.4: Mathematical model with imported cases - p. 219 51. 7.5: Conclusion - p. 226 52. References - p. 228 53. 8 Global stability of a diffusive HTLV-I infection model with mitosis and CTL immune response - p. 231 54. 8.1: Introduction - p. 231 55. 8.2: Model formulation - p. 236 56. 8.3: Well-posedness of solutions - p. 237 57. 8.4: Steady state analysis - p. 239 58. 8.5: Global stability analysis - p. 240 59. 8.6: Numerical simulations - p. 246 60. 8.7: Conclusion and discussion - p. 248 61. References - p. 250 62. 9 Mathematical tools and their applications in dengue epidemic data analytics - p. 253 63. 10 Covid-19 pandemic model: a graph theoretical perspective - p. 285 64. 11 Towards nonmanifest chaos and order in biological structures by means of the multifractal paradigm - p. 305 65. 12 Global stability of epidemic models under discontinuous treatment strategy - p. 323 66. 12.1: Impact of discontinuous treatments on disease dynamics in an SIR epidemic model - p. 323 67. 12.1.1: Introduction - p. 323 68. 12.1.2: Model description and preliminaries - p. 324 69. 12.1.3: Equilibria and their stability - p. 327 70. 12.1.4: Global convergence in finite time - p. 332 71. 12.1.5: Conclusion and discussion - p. 336 72. 12.2: Global stability of an SIS epidemic model with discontinuous treatment strategy - p. 337 73. 12.3: Global stability of an SEIR epidemic model with infectious force in latent period and infected period under discontinuous treatment strategy - p. 346 74. Index - p. 365
Advances in Epidemiological Modeling and Control of Viruses covers recent and advanced research works in the field of epidemiological modeling, with special emphasis on new strategies to control the occurrence and reoccurrence of viruses. The models included in this book can be used to study the dynamics of different viruses, searching for control measures, and epidemic models under various effects and environments. This book covers different models and methods of modeling, including data-driven approaches. The authors and editors are experienced researchers, and each chapter has been designed to provide readers with leading-edge information on topics discussed.
1. 1.1: Introduction - p. 1 2. 1.2: Global convergence to the homogeneous solution - p. 3 3. 1.3: Numerical simulations - p. 18 4. 1.4: Spatiotemporal pattern formation - p. 20 5. 1.5: Conclusion and open problems - p. 25 6. Acknowledgements - p. 26 7. References - p. 26 8. 2 Hepatitis B virus transmission via epidemic model - p. 29 9. 2.1: Introduction - p. 29 10. 2.2: Model formulation - p. 31 11. 2.3: Stability analysis - p. 33 12. 2.4: Simulation and concluding remarks - p. 49 13. References - p. 53 14. 3 Global dynamics of an HCV model with full logistic terms and the host immune system - p. 55 15. 3.1: Introduction - p. 55 16. 3.2: Previous works - p. 57 17. 3.3: Mathematical preliminaries - p. 59 18. 3.4: Modelling virus-immune system interaction with full logistic terms in both uninfected and infected cells - p. 63 19. 3.5: Analysis of the model - p. 65 20. 3.5.1: Dissipativity, basic reproduction number, and equilibria - p. 65 21. 3.5.2: Local and global stability analysis - p. 70 22. 3.6: Numerical simulations - p. 89 23. 3.7: Conclusion and discussion - p. 91 24. Acknowledgements - p. 92 25. References - p. 92 26. 4 On a Novel SVEIRS Markov chain epidemic model with multiple discrete delays and infection rates: modeling and sensitivity analysis to determine vaccination effects - p. 95 27. 4.1: Introduction - p. 95 28. 4.2: Description of the SVEIRS epidemic and the delays in the disease dynamics - p. 98 29. 4.3: Discretization of time and decomposition of the SVEIRS population over time - p. 99 30. 4.4: The SVEIRS stochastic process - p. 110 31. 4.5: Some special SVEIRS epidemic models - p. 115 32. 4.6: Numerical study: some prototype SVEIRS epidemic models and sensitivity analysis to determine the effects of infection and vaccination - p. 122 33. 4.7: Conclusion - p. 141 34. References - p. 142 35. 5 Hopf bifurcation in an SIR epidemic model with psychological effect and distributed time delay - p. 145 36. 5.1: Introduction - p. 145 37. 5.2: Model - p. 149 38. 5.3: Direction of bifurcation and stability of periodic solution - p. 152 39. 5.4: Example: a truncated exponential distribution - p. 161 40. 5.5: Numerical simulation - p. 164 41. 5.6: Discussion - p. 166 42. Acknowledgements - p. 166 43. Appendix 5.A: Matlab code for Fig. 5.8(b) - p. 166 44. References - p. 167 45. 6 Modeling of the effects of media in the course of vaccination of rotavirus - p. 169 46. 7 Mathematical models of early stage Covid-19 transmission in Sri Lanka - p. 191 47. 7.1: Introduction - p. 191 48. 7.2: Mathematical model to estimate initial parameters - p. 194 49. 7.3: Mathematical models with heterogeneity of cases - p. 203 50. 7.4: Mathematical model with imported cases - p. 219 51. 7.5: Conclusion - p. 226 52. References - p. 228 53. 8 Global stability of a diffusive HTLV-I infection model with mitosis and CTL immune response - p. 231 54. 8.1: Introduction - p. 231 55. 8.2: Model formulation - p. 236 56. 8.3: Well-posedness of solutions - p. 237 57. 8.4: Steady state analysis - p. 239 58. 8.5: Global stability analysis - p. 240 59. 8.6: Numerical simulations - p. 246 60. 8.7: Conclusion and discussion - p. 248 61. References - p. 250 62. 9 Mathematical tools and their applications in dengue epidemic data analytics - p. 253 63. 10 Covid-19 pandemic model: a graph theoretical perspective - p. 285 64. 11 Towards nonmanifest chaos and order in biological structures by means of the multifractal paradigm - p. 305 65. 12 Global stability of epidemic models under discontinuous treatment strategy - p. 323 66. 12.1: Impact of discontinuous treatments on disease dynamics in an SIR epidemic model - p. 323 67. 12.1.1: Introduction - p. 323 68. 12.1.2: Model description and preliminaries - p. 324 69. 12.1.3: Equilibria and their stability - p. 327 70. 12.1.4: Global convergence in finite time - p. 332 71. 12.1.5: Conclusion and discussion - p. 336 72. 12.2: Global stability of an SIS epidemic model with discontinuous treatment strategy - p. 337 73. 12.3: Global stability of an SEIR epidemic model with infectious force in latent period and infected period under discontinuous treatment strategy - p. 346 74. Index - p. 365
