Mathematical Analysis of Typhoid Fever Dynamics with Age-Structured Control Measures

Mutairu Kayode Kolawole; Rasheed Gbemisola Ayoola; Folasade Ajimot Adebisi

doi:10.37905/jjom.v8i1.35225

Mathematical Analysis of Typhoid Fever Dynamics with Age-Structured Control Measures

Mutairu Kayode Kolawole, Rasheed Gbemisola Ayoola, Folasade Ajimot Adebisi

Abstract

This research develops a mathematical model to investigate the dynamics of typhoid fever by incorporating age structure, vaccination and treatment strategies. Recognizing that different age groups display varying susceptibility and contact rates, the model provides a detailed representation of transmission. The analysis is to emphasize how vaccination programs and treatment interventions, when tailored to age-specific characteristics, can significantly reduce transmission and control outbreaks. The system of nonlinear differential equations describing the disease dynamics is analyzed and solved using the homotopy perturbation method. This analytical approach allows for an approximation of solutions while capturing the nonlinear interactions within the system. Sensitivity analysis is carried out to determine the most influential parameters on disease spread, particularly those affecting the basic reproduction number. The simulations reveal that increasing vaccination coverage and treatment rates leads to a decline in typhoid fever cases across all age groups. Age-targeted interventions are shown to enhance the effectiveness of control strategies compared with uniform measures. Sensitivity analysis result further indicate that parameters such as vaccination rate, treatment efficacy and contact patterns play vital roles in disease progression and a potential for its eradication.

Keywords

Typhoid outbreaks; Age-structure; Basic reproduction number; Homotopy perturbation method; Sensitivity analysis

Full Text:

PDF

References

V. Keshav, N. Potgieter, and T. Barnard, “Detection of vibrio cholerae o1 in animal stools collected in rural areas of the limpopo province,” Water SA, vol. 36, no. 2, p. 167, 2019, doi: 10.4314/wsa.v36i2.183724.

O. J. Peter, A. F. Adebisi, M. O. Ajisope, F. O. Ajibade, A. I. Abioye, and F. A. Oguntolu, “Global stability analysis of typhoid fever model,” Advances in Systems Science and Applications, vol. 20, no. 2, 2020, doi: 10.25728/assa.2020.20.2.792.

T. A. Ayoola, H. O. Edogbanya, O. J. Peter, F. A. Oguntolu, K. Oshinubi, and M. L. Olaosebikan, “Modelling and optimal control analysis of typhoid fever,” Journal of Mathematics and Computer Science (J. Math. Comput. Sci.), vol. 11, no. 6, pp. 6666–6682, 2021.

P. O. James and M. O. Ibrahim, “Application of variational iteration method in solving typhoid fever model,” in 2019 Big Data, Knowledge and Control Systems Engineering (BdKCSE), Sofia, Bulgaria, 2019, pp. 1–5, doi: 10.1109/BdKCSE48644.2019.9010598.

O. J. Peter, M. O. Ibrahim, H. O. Edogbanya, F. A. Oguntolu, K. Oshinubi, A. A. Ibrahim, T. A. Ayoola, and J. O. Lawal, “Direct and indirect transmission of typhoid fever model with optimal control,” Results in Physics, vol. 27, p. 104463, 2021, doi: 10.1016/j.rinp.2021.104463.

A. S. Shaikh and K. S. Nisar, “Transmission dynamics of fractional order typhoid fever model using caputo–fabrizio operator,” Chaos, Solitons & Fractals, vol. 128, pp. 355–365, 2019, doi: 10.1016/j.chaos.2019.08.012.

F. Dayan, N. Ahmed, A. H. Ali et al., “Numerical investigation of a typhoid disease model in fuzzy environment,” Scientific Reports, vol. 13, p. 21993, 2023, doi: 10.1038/s41598-023-48405-w.

J. I. Irunde, J. Z. Ndendya, J. A. Mwasunda, and P. K. Robert, “Modeling the impact of screening and treatment on typhoid fever dynamics in unprotected population,” Results in Physics, vol. 54, p. 107120, 2023, doi: 10.1016/j.rinp.2023.107120.

S. Edward and N. Nyerere, “Modelling typhoid fever with education, vaccination and treatment,” International Journal of Theoretical and Applied Mathematics, vol. 2, no. 2, 2017, doi: 10.11648/j.ijtam.20160202.30.

P. Bwalya, E. S. Solo, J. Y. Chizimu, D. Shrestha, G. Mbulo, J. Thapa, C. Nakajima, and Y. Suzuki, “Characterization of embb mutations involved in ethambutol resistance in multi-drug resistant mycobacterium tuberculosis isolates in zambia,” Tuberculosis, vol. 133, p. 102184, 2022, doi: 10.1016/j.tube.2022.102184.

G. Dougan and S. Baker, “Salmonella enterica serovar typhi and the pathogenesis of typhoid fever,” Annual Review of Microbiology, vol. 68, no. 1, pp. 317–336, 2014, doi: 10.1146/annurev-micro-091313-103739.

M. Amouch and N. Karim, “Mathematical modeling of covid-19 and omicron outbreak spread: Optimal control approach for intervention strategies,” Optimal Control Applications and Methods, vol. 44, no. 5, pp. 2916–2937, 2023, doi: 10.1002/oca.3019.

M. K. Kolawole, K. A. Odeyemi, A. O. Oladapo, and K. A. Bashiru, “Dynamical analysis and control strategies for capturing the spread of covid-19,” Tanzania Journal of Science, vol. 48, no. 3, pp. 680–690, 2022, doi: 10.4314/tjs.v48i3.15.

R. Kuehn, N. Stoesser, D. Eyre, T. C. Darton, B. Basnyat, and C. M. Parry, “Treatment of enteric fever (typhoid and paratyphoid fever) with cephalosporins,” Cochrane Database of Systematic Reviews, no. 11, 2022, doi: 10.1002/14651858.cd010452.pub2.

A. El-Mesady, A. Elsonbaty, and W. Adel, “Stability analysis and optimal control strategies of a fractional-order monkeypox virus infection model,” Physica Scripta, vol. 98, no. 9, p. 095256, 2023, doi: 10.1088/1402-4896/acf16f.

——, “On nonlinear dynamics of a fractional order monkeypox virus model,” Chaos, Solitons & Fractals, vol. 164, p. 112716, 2022, doi: 10.1016/j.chaos.2022.112716.

A. Ahmad, U. Atta, M. Farman, K. S. Nisar, H. Ahmad, and E. Hincal, “Investigation of lassa fever with relapse and saturated incidence rate: Mathematical modeling and control,” Modeling Earth Systems and Environment, vol. 11, no. 3, p. 202, 2025, doi: 10.1007/s40808-025-02370-7.

M. Farman, A. Ahmad, U. Atta, K. S. Nisar, and A. Ghaffar, “Hyers–ulam stability and bifurcation control of leptospirosis disease dynamics and preventions: Modeling with singular and non-singular kernels,” PLoS ONE, vol. 20, no. 3, p. e0314095, 2025, doi: 10.1371/journal.pone.0314095.

F. K. Alalhareth, U. Atta, A. H. Ali, and M. H. Alharbi, “Analysis of leptospirosis transmission dynamics with environmental effects and bifurcation using fractional-order derivative,” Alexandria Engineering Journal, vol. 80, pp. 372–382, 2023, doi: 10.1016/j.aej.2023.08.063.

B. Liu, “Analysis on the current situation, problems and potential solutions for the chinese precious metals futures market,” BCP Business & Management, vol. 38, pp. 1239–1244, 2023, doi: 10.54691/bcpbm.v38i.3852.

A. Manesh, E. Meltzer, C. Jin, C. Britto, D. Deodhar, S. Radha, E. Schwartz, and P. Rupali, “Typhoid and paratyphoid fever: a clinical seminar,” Journal of Travel Medicine, vol. 28, no. 3, 2021.

V. G. Melnikov, A. Berger, A. Dangel, and A. Sing, “Lateral flow immunoassay-based laboratory algorithm for rapid diagnosis of diphtheria,” Open Research Europe, vol. 3, p. 62, 2023, doi: 10.12688/openreseurope.15038.1.

B. Muchmore, P. Muchmore, C. W. Lee, M. E. Alarcón-Riquelme, and A. Muchmore, “Tracking potential covid-19 outbreaks with influenzalike symptoms urgent care visits,” Pediatrics, vol. 146, no. 4, 2020, doi: 10.1542/peds.2020-1798.

D. Muthuirulandi Sethuvel, N. Devanga Ragupathi, S. Anandan, B. Veeraraghavan, and L. Sangal, “Molecular epidemiology of c. diphtheriae shows rapid evolution of strains in india: An update from national diphtheria surveillance network,” International Journal of Infectious Diseases, vol. 101, p. 372, 2020, doi: 10.1016/j.ijid.2020.09.978.

N. Lawal, S. A. Abdullahi, and D. S. Abolude, “Physicochemical characteristics and fish abundance and diversity of mairua reservoir water, funtua, katsina state, north-western nigeria,” Journal of Applied Sciences and Environmental Management, vol. 27, no. 1, pp. 125–132, 2023, doi: 10.4314/jasem.v27i1.18.

M. Kolawole, A. Oluwarotimi, K. Odeyemi, and A. Popoola, “Analysis of corona-virus mathematical model in asymptomatic and symptomatic cases with vaccine using homotopy perturbation method,” Journal of Applied Computer Science & Mathematics, vol. 17, no. 1, pp. 20–27, 2023, doi: 10.4316/jacsm.202301003.

E. I. Komarovskaya and V. Perelygyna, “Assay of diphtheria vaccine potency by intradermal challenge test,” Epidemiology and Vaccinal Prevention, vol. 22, no. 4, pp. 12–23, 2023, doi: 10.31631/2073-3046-2023-22-4-12-23.

J. M. Heffernan, R. J. Smith, and L. M. Wahl, “Perspectives on the basic reproductive ratio,” Journal of the Royal Society Interface, vol. 2, no. 4, pp. 281–293, 2005, doi: 10.1098/rsif.2005.0058.

O. Diekmann, J. A. P. Heesterbeek, and M. G. Roberts, “The construction of next-generation matrices for compartmental epidemic models,” Journal of the Royal Society Interface, vol. 7, no. 47, pp. 873–885, 2010, doi: 10.1098/rsif.2009.0386.

P. van den Driessche and J. Watmough, “Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission,” Mathematical Biosciences, vol. 180, no. 1–2, pp. 29–48, 2002, doi: 10.1016/S0025-5564(02)00108-6.

O. J. Peter, H. S. Panigoro, A. Abidemi, M. M. Ojo, and F. A. Oguntolu, “Mathematical model of covid-19 pandemic with double dose vaccination,” Acta Biotheoretica, vol. 71, no. 2, p. 9, 2023, doi: 10.1007/s10441-023-09460-y.

M. Z. Ndii and Y. A. Adi, “Modelling the transmission dynamics of covid-19 under limited resources,” Commun. Math. Biol. Neurosci., vol. 2020, pp. Article–ID, 2020.

M. D. Miller-Dickson, V. A. Meszaros, S. Almagro-Moreno, and C. B. Ogbunugafor, “Hepatitis c virus modelled as an indirectly transmitted infection highlights the centrality of injection drug equipment in disease dynamics,” Journal of the Royal Society Interface, vol. 16, no. 158, p. 20190334, 2019, doi: 10.1098/rsif.2019.0334.

DOI: https://doi.org/10.37905/jjom.v8i1.35225