1 / 38

BUU 2014 Burapha University International Conference 2014

BUU 2014 Burapha University International Conference 2014. The transmission dynamics of SIR modeling for dengue fever with vector-born infection Pratchaya Chanprasopchai a , Puntani Pongsumpun b Email: a :pchanprasopcai@gmail.com, b : kppuntan@kmitl.ac.th. Presented by

shawna
Download Presentation

BUU 2014 Burapha University International Conference 2014

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. BUU 2014Burapha University International Conference 2014 The transmission dynamics of SIR modeling for dengue fever with vector-born infection Pratchaya Chanprasopchaia, Puntani Pongsumpunb Email: a:pchanprasopcai@gmail.com, b: kppuntan@kmitl.ac.th Presented by Pratchaya Chanprasopchai July 3-4, 2014

  2. AGENDA • INTRODUCTION • MATERIAL AND METHODS • RESULTS • DISCUSSION • CONCLUSION • FEFERENCES

  3. AGENDA • INTRODUCTION • MATERIAL AND METHODS • RESULTS • DISCUSSION • CONCLUSION • FEFERENCES

  4. INTRODUCTION • The geographic distribution of dengue cases reported in 2011, WHO.

  5. INTRODUCTION (CONT’D) • Dengue fever is a dangerous disease which is a problem in many parts of the world, including Africa, Asia, South America and Australia. • Dengue fever is an infectious disease caused by the dengue virus. • There are 4 serotypes virus (DEN 1 – 4), which are transmitted to human by the bite of infected female Aedes mosquitoes. • The 4 dengue viruses co-circulate in many areas of Africa, America and Asia.

  6. INTRODUCTION (CONT’D) • In Thailand, dengue fever appears the whole year whiles the peak period is during rainy season between May - August. There were reported cases of Dengue fever about 64,374 in 2011. In 2012, Thailand officials recorded 74,250 cases, and 79 deaths. In 2013, the numbers of cases are ballooning at a remarkable rate, were reporting 150,934 cases.

  7. INTRODUCTION (CONT’D) • Dengue cases reported in Thailand, Department of disease control, ministry of public health.

  8. INTRODUCTION (CONT’D) • Dengue fever is a disease caused by mosquito. • The mosquito can transmit the fluid within our body and subsequently gives the symptoms of headache, body pain, fever, rashes, bleeding skin and more. • It would take 8 to 15 days incubation period and the symptoms will manifest in our body but for people who have a weaker immunity like children may take only 5 to 7 days before the disease is shown.

  9. INTRODUCTION (CONT’D) • Dengue fever occurs around the world where the mosquitoes can breed in water. • It can be available in any places that have stagnant water which can be found anywhere and anytime in your home. • The danger of dengue fever is no antibiotic treatment and actually everyone can be affected by the transmission of dengue fever since the growths of mosquitoes are wide spreading.

  10. INTRODUCTION (CONT’D) • Dengue fever has become a major international public health concern since it has been reported in over 100 countries and is estimated to affected more than 100 million people/year. • It is estimated that 2.5 billion people live in dengue epidemic areas. • Given the disease’s widespread prevalence in Thailand, the need to better understand the epidemiology of dengue fever is most urgently needed. 11

  11. INTRODUCTION (CONT’D) • Estava and Vargus (1998) was proposed dengue fever model in 1998. • Pongsumpun (2006, 2007) proposed mathematical model of dengue fever with incubation period. • Naowarat et al. proposed and analyzed dynamical model for determining human susceptibility to dengue fever. 12

  12. INTRODUCTION (CONT’D) In this paper, we are considered infected vector caused by both biting of infected human and vector-born infection. The vector-born infection is caused by infected egg and will be the infected vector. 13

  13. AGENDA • INTRODUCTION • MATERIAL AND METHODS • RESULTS • DISCUSSION • CONCLUSION • FEFERENCES

  14. MATERIAL AND METHODS • We are assumed that human population and mosquito population are constant denoted by NH and NV. • The mathematical model is considered the infected vector by both biting of infected human and vector-born infection. • Human populations are separated into three classes, susceptible, infected and recovered human while the vector populations are separated into two classes, susceptible and infected vector populations.

  15. MATERIAL AND METHODS • The Dynamics of the disease is depicted in the compartment diagram, as shown in Fig. 1. Figure 1. Flow chart for the transmission of dengue disease

  16. MATERIAL AND METHODS (CONT’D) • Where: SH(t) = Number of susceptible humans population at time t, IH(t) = Number of infected humans population at time t, RH(t) = Number of recovered humans population at time t, SV(t) = Number of susceptible vector population at time t, IV (t) = Number of infected vector population at time t, A = Recruitment rate of vector population, B = Vector-born rate of vector population.

  17. MATERIAL AND METHODS (CONT’D) • The dengue fever transmission model with vector-born infection can be explained by mathematical equation as following: (1) (2) (3) (4) (5)

  18. MATERIAL AND METHODS (CONT’D) • Where: = Total number the human population, = Birth rate of the human population, = Biting rate of the vector population, = Transmission probability from vector to human population, = Transmission probability from human to vector population, = Death rate of the human population, = Death rate of the vector population, = Recovery rate of the human population. (6) (7)

  19. MATERIAL AND METHODS (CONT’D) • Total human and mosquito populations are constant, the time rate of change of human population is equal to zero. • Then, we can get the important conditions. (8) (9) (10) (11)

  20. MATERIAL AND METHODS (CONT’D) • To analyze the model, we can normalize the model of Eq. (1) – (5) and define new variable: • The reduce models are depicted as Eq. (13) –(15) as following: (12) (13) (14) (15)

  21. MATERIAL AND METHODS (CONT’D) , Analysis the model Equilibrium points • The solution can be found by setting the right hand side of equation (13) – (15) equal to zero. Then, we can get the two equilibrium points E1 and E2as following: (16) (17)

  22. MATERIAL AND METHODS (CONT’D) , (18) (19) (20) (21) (22) (23)

  23. MATERIAL AND METHODS (CONT’D) , • Where:

  24. MATERILA AND METHODS (CONT’D) • Local asymptotical stability: It is determined from Jacobian matrix of Eq. (13)-(15). The eigenvalues of Jacobian matrix are determined by solving: • The Routh-Hurwitz criteria stability conditions are as below: (e0 > 0), (e1 > 0) and (e0*e1> e2) • Thus, equilibrium point E1 is local stable. (24) (25) (26)

  25. AGENDA • INTRODUCTION • MATERIAL AND METHODS • RESULTS • DISCUSSION • CONCLUSION • FEFERENCES

  26. RESULTS • The system of Eq. (13)-(15) solved numerically using the parameters values are as below. A = 400, B = 200, = 10,000, b = 1/3 day-1, = 0.75, = 1.00, = 0.0000391 day-1, = 0.075 day-1, = 0.1428 day-1.

  27. RESULTS (CONT’D) • From Eq. (13)-(15) and (24), we obtained the characteristic equation as below: • The results of calculated values are: • All eigenvalues are negative that leads to the equilibrium state. R0is 1.07768, which is more than 1 that leads to be the endemic state. (27)

  28. RESULTS (CONT’D) • The equilibrium point E1 (Sh1*, Ih1*, IV1*) is shown as below. E1=(0.00055,0.00027,0.334188).

  29. RESULTS (CONT’D) • The relationship between biting rate and each variable are as below:

  30. AGENDA • INTRODUCTION • MATERIAL AND METHODS • RESULTS • DISCUSSION • CONCLUSION • FEFERENCES

  31. DISCUSSION • It establish the threshold parameter for this model is: • The basic reproductive number of the dengue fever in this study is . It is the average number of secondary case that one case can produce into a susceptible human.

  32. DISCUSSION • In this work, R0>1, the normalized individual populations converges to the endemic equilibrium point E1 (0.060569, 0.000257, 0.002870). • The basic reproductive numbers are used for controlling the disease. • The effective way to control the disease is decreasing the capacity of the environment for mosquitoes breeding sites and the mosquito biting rate.

  33. AGENDA • INTRODUCTION • MATERIAL AND METHODS • RESULTS • DISCUSSION • CONCLUSION • FEFERENCES

  34. CONCLUSION • This paper proposed and analyzed the transmission dynamics of SIR modeling for dengue fever with vector-born infection, which we are considered both infected vectored by biting infected human and vector born infection. • The equilibrium point converges to the endemic equilibrium state and the simulations of the biting rate of mosquitoes are investigated . • The value of R0 can control by decreasing the mosquitoes biting. The basic reproductive numbers are used to control the transmission of dengue fever.

  35. AGENDA • INTRODUCTION • MATERIAL AND METHODS • RESULTS • DISCUSSION • CONCLUSION • FEFERENCES

  36. REFFERENCES

  37. Q&A Thank you very much for your attention

More Related