A Simple Epidemiological Model for Typhoid with Saturated Incidence Rate and Treatment Effect
Typhoid fever is a communicable disease, found only in man and occurs due to systemic infection mainly by Salmonella typhi organism. The disease is endemic in many developing countries and remains a substantial public health problem despite recent progress in water and sanitation coverage. Globally, it is estimated that typhoid causes over 16 million cases of illness each year, resulting in over 600,000 deaths. A mathematical model for assessing the impact of educational campaigns on controlling the transmission dynamics of typhoid in the community, has been formulated and analyzed. The reproductive number has been computed. Stability of the model steady-states has been examined. The impact of educational campaigns on controlling the transmission dynamics of typhoid has been discussed through the basic reproductive number and numerical simulations. At its best the study suggests that targeted education campaigns, which are effective at stopping transmission of typhoid more than 40% of the time, will be highly effective at controlling the disease in the community.
[1] C. Kidgell, U. Reichard, and J. Wain J, et al, “Salmonella typhi, the
causative agent of typhoid fever, is approximately 50,000 years old,”
Infect. Genet. Evol, vol. 2, pp. 39-45, 2002.
[2] M. K. Bhan, R. Bahl, and ,S. Bhatnagar, “Typhoid and paratyphoid fever,”
Lancet, vol. 366, pp. 749-762, 2005.
[3] D. S. Merrell, and S. Falkow, “Frontal and stealth attack strategies in
microbial pathogenesis,” Nature, vol. 430, pp. 250-26, 2004.
[4] S. Kariuki, G. Revathi, J. Muyodi, J. Mwituria, A. Munyalo, S. Mirza, and
C. A. Hart, “Characterization of Multidrug-Resistant Typhoid Outbreaks
in Kenya,” J. Clin. Microbiol, vol. 42(4), pp. 1477-1482, 2004.
[5] A. E. Fica, S. Prat-Miranda, A. Fernandez-Ricci, K. DOttone, and F.
C. Cabello, “ Epidemic typhoid in Chile: analysis by molecular and
conventional methods of Salmonella typhi strain diversity in epidemic
(1977 and 1981) and nonepidemic. 1990. years,” J. Clin. Microbiol, vol.
34, pp. 1701-1707, 1996.
[6] J. Olarte, and E. Galindo, “Salmonella typhi resistant to chloramphenicol,
ampicillin and other antimicrobial agents: strains isolated during an extensive
typhoid fever epidemic in Mexico,” Antimicrob. Agents Chemother,
vol. 4, pp. 597-601, 1973.
[7] J. M. Ling, N. W. Lo, Y. M. Ho, K. M. Kam, N. T. Hoa, L. T. Phi,
and A. F. Cheng, “Molecular methods for the epidemiological typing of
Salmonella enterica serotype Typhi from Hong Kong and Vietnam,” J.
Clin. Microbiol vol. 38, pp. 292-300, 2000.
[8] S. H. Mirza, N. J. Beeching, and C. A. Hart, “Multidrug resistant typhoid:
a global problem,” J. Med. Microbiol, vol. 44, pp. 317-319, 1996.
[9] S. Mirza, S. Kariuki, K. Z. Mamun, N. J. Beeching, and C. A. Hart,
“Analysis of plasmid and chromosomal DNA of multidrug-resistant
Salmonella enterica serovar Typhi from Asia”, J. Clin. Microbiol, vol.
38, pp. 1449-1452, 2000.
[10] M. Rahman, A. Ahmad, and S. Shoma, “Decline in epidemic of
multidrug resistant Salmonella typhi is not associated with increased incidence
of antibiotic-susceptible strain in Bangladesh,” Epidemiol. Infect,
vol. 129, pp. 29-34, 2002.
[11] P. M. Shanahan, K. A. Karamat, C. J. Thomson, and S. G. Amyes.
“Molecular analysis of and identification of antibiotic resistance genes in
clinical isolates of Salmonella typhi from India,” J. Clin. Microbiol, vol.
36, pp. 1595-1600, 1998.
[12] S. Kariuki, C. Gilks, G. Revathi, and C. A. Hart, “Genotypic analysis
of multidrug-resistant Salmonella enterica Serovar Typhi, Kenya”, Emerg.
Infect. Dis, vol. 6, pp. 649-651, 2000.
[13] F. Mills-Robertson, M. E. Addy, P. Mensah, and S. S. Crupper, “
Molecular characterization of antibiotic resistance in clinical Salmonella
typhi isolated in Ghana,” FEMS Microbiol. Lett, vol. 215, pp. 249-253,
2002
[14] B. Singh, “Typhoid Fever Epidemiology,” Journal Indian Academy of
Clinical Medicine, vol. 2(1)-(2), pp. 11-12, 2001
[15] D. T. Lauria, B. Maskery, C. Poulos, and D. Whittington, “An optimization
model for reducing typhoid cases in developing countries without
increasing public spending,” Vaccine JVAC-8805 (2009).
[16] I. A. Adetunde, “A Mathematical models for the dynamics of typhoid
fever in Kassena-Nankana district of upper east region of Ghana,” Journal
of Modern Mathematics and statistics, vol. 2(2), pp. 45-49, 2008.
[17] D. Kalajdzievska, and M. Y. LI, “Modeling the effects of carriers on
transmission dynamics of infectious disease”, Math. Biosci. Eng, vol.
8(3), pp. 711-722, 2011.
[18] S. Mushayabasa, C. P. Bhunu, and E. T. Ngarakana-Gwasira, “Mathematical
analysis of a typhoid model with carriers, direct and indirect
disease transmission,” IJMSEA,vol. 7(1), pp. 79-90, 2013.
[19] J. Gonzlez-Guzmn, “ An epidemiological model for direct and indirect
transmission of typhoid fever,” Math. Biosci, vol. 96(1), pp. 33-46, 1989.
[20] P. Katri, S. Ruan, “Dynamics of human T-cell lymphototropic virus I
(HTLV-I) infection of CD4+ T-cells,” C.R. Biol, vol. 327, pp. 1009-1016,
2004.
[21] Y. Kuang, Delay differentail equations springer, new York (1997).
[22] S. Buseng, and K. L. Cooke, Vertically transmitted diseases, models and
dynamics. Biomathematics, vol. 23. Springer, New York (1993)
[23] H. W. Hethcote, “The mathematics of infectious diseases,” SIAM Rev,
vol. 42, pp. 599-653, 2000.
[24] P. van den Driessche, and J. Watmough, “Reproduction numbers and
sub-threshold endemic equilibria for compartmental models of disease
transmission,” Math. Biosci, vol. 180, pp. 29-48, 2002.
[25] C. Castillo-Chavez, Z. Feng, and W. Huang “On the computation
of R0 and its role on global stability. In: Castillo-Chavez, C., et al.
(eds.) Mathematical Approaches for Emerging and Reemerging Infectious
Diseases: An Introduction,” IMA, vol. 125, pp. 229-250, 2002.
[26] C. Castillo-Chavez, and B. Song, “Dynamical models of tuberculosis
and their applications. Math. Biosci. Eng, vol. 1(2), pp. 361-404, 2004.
[27] Carr, J: Applications of Centre Manifold Theory. Springer, New York
(1981)
[28] R. Xu, and Z. Ma, “Global stability of a delayed SEIRS epidemic model
with saturation incidence rate,” Nonlinera Dyn vol. 61, pp. 229-239, 2010.
[29] S. Mushayabasa, C. P. Bhunu, and R. J. Smith?, “Assessing the impact
of educational campaigns on controlling HCV among women prisoners,”
Commun Nonlinear Sci Numeri Simulat, vol.17, pp. 1714-1724, 2012.
[30] J. C. Helton, “Uncertainty and sensitivity analysis techniques for use in
performance assessment for waste disposal,” Reliab. Eng. Syst. Saf, vol.
42, pp. 42: 327367, 1993.
[1] C. Kidgell, U. Reichard, and J. Wain J, et al, “Salmonella typhi, the
causative agent of typhoid fever, is approximately 50,000 years old,”
Infect. Genet. Evol, vol. 2, pp. 39-45, 2002.
[2] M. K. Bhan, R. Bahl, and ,S. Bhatnagar, “Typhoid and paratyphoid fever,”
Lancet, vol. 366, pp. 749-762, 2005.
[3] D. S. Merrell, and S. Falkow, “Frontal and stealth attack strategies in
microbial pathogenesis,” Nature, vol. 430, pp. 250-26, 2004.
[4] S. Kariuki, G. Revathi, J. Muyodi, J. Mwituria, A. Munyalo, S. Mirza, and
C. A. Hart, “Characterization of Multidrug-Resistant Typhoid Outbreaks
in Kenya,” J. Clin. Microbiol, vol. 42(4), pp. 1477-1482, 2004.
[5] A. E. Fica, S. Prat-Miranda, A. Fernandez-Ricci, K. DOttone, and F.
C. Cabello, “ Epidemic typhoid in Chile: analysis by molecular and
conventional methods of Salmonella typhi strain diversity in epidemic
(1977 and 1981) and nonepidemic. 1990. years,” J. Clin. Microbiol, vol.
34, pp. 1701-1707, 1996.
[6] J. Olarte, and E. Galindo, “Salmonella typhi resistant to chloramphenicol,
ampicillin and other antimicrobial agents: strains isolated during an extensive
typhoid fever epidemic in Mexico,” Antimicrob. Agents Chemother,
vol. 4, pp. 597-601, 1973.
[7] J. M. Ling, N. W. Lo, Y. M. Ho, K. M. Kam, N. T. Hoa, L. T. Phi,
and A. F. Cheng, “Molecular methods for the epidemiological typing of
Salmonella enterica serotype Typhi from Hong Kong and Vietnam,” J.
Clin. Microbiol vol. 38, pp. 292-300, 2000.
[8] S. H. Mirza, N. J. Beeching, and C. A. Hart, “Multidrug resistant typhoid:
a global problem,” J. Med. Microbiol, vol. 44, pp. 317-319, 1996.
[9] S. Mirza, S. Kariuki, K. Z. Mamun, N. J. Beeching, and C. A. Hart,
“Analysis of plasmid and chromosomal DNA of multidrug-resistant
Salmonella enterica serovar Typhi from Asia”, J. Clin. Microbiol, vol.
38, pp. 1449-1452, 2000.
[10] M. Rahman, A. Ahmad, and S. Shoma, “Decline in epidemic of
multidrug resistant Salmonella typhi is not associated with increased incidence
of antibiotic-susceptible strain in Bangladesh,” Epidemiol. Infect,
vol. 129, pp. 29-34, 2002.
[11] P. M. Shanahan, K. A. Karamat, C. J. Thomson, and S. G. Amyes.
“Molecular analysis of and identification of antibiotic resistance genes in
clinical isolates of Salmonella typhi from India,” J. Clin. Microbiol, vol.
36, pp. 1595-1600, 1998.
[12] S. Kariuki, C. Gilks, G. Revathi, and C. A. Hart, “Genotypic analysis
of multidrug-resistant Salmonella enterica Serovar Typhi, Kenya”, Emerg.
Infect. Dis, vol. 6, pp. 649-651, 2000.
[13] F. Mills-Robertson, M. E. Addy, P. Mensah, and S. S. Crupper, “
Molecular characterization of antibiotic resistance in clinical Salmonella
typhi isolated in Ghana,” FEMS Microbiol. Lett, vol. 215, pp. 249-253,
2002
[14] B. Singh, “Typhoid Fever Epidemiology,” Journal Indian Academy of
Clinical Medicine, vol. 2(1)-(2), pp. 11-12, 2001
[15] D. T. Lauria, B. Maskery, C. Poulos, and D. Whittington, “An optimization
model for reducing typhoid cases in developing countries without
increasing public spending,” Vaccine JVAC-8805 (2009).
[16] I. A. Adetunde, “A Mathematical models for the dynamics of typhoid
fever in Kassena-Nankana district of upper east region of Ghana,” Journal
of Modern Mathematics and statistics, vol. 2(2), pp. 45-49, 2008.
[17] D. Kalajdzievska, and M. Y. LI, “Modeling the effects of carriers on
transmission dynamics of infectious disease”, Math. Biosci. Eng, vol.
8(3), pp. 711-722, 2011.
[18] S. Mushayabasa, C. P. Bhunu, and E. T. Ngarakana-Gwasira, “Mathematical
analysis of a typhoid model with carriers, direct and indirect
disease transmission,” IJMSEA,vol. 7(1), pp. 79-90, 2013.
[19] J. Gonzlez-Guzmn, “ An epidemiological model for direct and indirect
transmission of typhoid fever,” Math. Biosci, vol. 96(1), pp. 33-46, 1989.
[20] P. Katri, S. Ruan, “Dynamics of human T-cell lymphototropic virus I
(HTLV-I) infection of CD4+ T-cells,” C.R. Biol, vol. 327, pp. 1009-1016,
2004.
[21] Y. Kuang, Delay differentail equations springer, new York (1997).
[22] S. Buseng, and K. L. Cooke, Vertically transmitted diseases, models and
dynamics. Biomathematics, vol. 23. Springer, New York (1993)
[23] H. W. Hethcote, “The mathematics of infectious diseases,” SIAM Rev,
vol. 42, pp. 599-653, 2000.
[24] P. van den Driessche, and J. Watmough, “Reproduction numbers and
sub-threshold endemic equilibria for compartmental models of disease
transmission,” Math. Biosci, vol. 180, pp. 29-48, 2002.
[25] C. Castillo-Chavez, Z. Feng, and W. Huang “On the computation
of R0 and its role on global stability. In: Castillo-Chavez, C., et al.
(eds.) Mathematical Approaches for Emerging and Reemerging Infectious
Diseases: An Introduction,” IMA, vol. 125, pp. 229-250, 2002.
[26] C. Castillo-Chavez, and B. Song, “Dynamical models of tuberculosis
and their applications. Math. Biosci. Eng, vol. 1(2), pp. 361-404, 2004.
[27] Carr, J: Applications of Centre Manifold Theory. Springer, New York
(1981)
[28] R. Xu, and Z. Ma, “Global stability of a delayed SEIRS epidemic model
with saturation incidence rate,” Nonlinera Dyn vol. 61, pp. 229-239, 2010.
[29] S. Mushayabasa, C. P. Bhunu, and R. J. Smith?, “Assessing the impact
of educational campaigns on controlling HCV among women prisoners,”
Commun Nonlinear Sci Numeri Simulat, vol.17, pp. 1714-1724, 2012.
[30] J. C. Helton, “Uncertainty and sensitivity analysis techniques for use in
performance assessment for waste disposal,” Reliab. Eng. Syst. Saf, vol.
42, pp. 42: 327367, 1993.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:65232", author = "Steady Mushayabasa", title = "A Simple Epidemiological Model for Typhoid with Saturated Incidence Rate and Treatment Effect", abstract = "Typhoid fever is a communicable disease, found only in man and occurs due to systemic infection mainly by Salmonella typhi organism. The disease is endemic in many developing countries and remains a substantial public health problem despite recent progress in water and sanitation coverage. Globally, it is estimated that typhoid causes over 16 million cases of illness each year, resulting in over 600,000 deaths. A mathematical model for assessing the impact of educational campaigns on controlling the transmission dynamics of typhoid in the community, has been formulated and analyzed. The reproductive number has been computed. Stability of the model steady-states has been examined. The impact of educational campaigns on controlling the transmission dynamics of typhoid has been discussed through the basic reproductive number and numerical simulations. At its best the study suggests that targeted education campaigns, which are effective at stopping transmission of typhoid more than 40% of the time, will be highly effective at controlling the disease in the community.
", keywords = "Mathematical model, Typhoid, saturated incidence rate, treatment, reproductive number, sensitivity analysis.", volume = "6", number = "6", pages = "688-8", }
