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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Analysis and Prediction of Future Malaria and Typhoid  Outbreaks based on Time-Varying Contact Rates: an ARIMA Approach

Journal of Applied Nonlinear Dynamics 15(4) (2026) 1025--1052 | DOI:10.5890/JAND.2026.12.015

Padmaja Tripathi$^1$, Harish Chandra$^1$, Ram Keval$^2$, Vinod Baniya$^1$

$^1$ Department of Mathematics and Scientific Computing, MMM University of Technology, Gorakhpur (U.P.), India

$^2$ Department of Applied Mathematics, MJP Rohilkhand University, Bareilly (U.P.), India

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Abstract

This study presents a mathematical model to investigate the dynamics of malaria and typhoid co-infection, focusing on the interplay between the two diseases and their combined impact on public health. The co-infection is driven by shared social and environmental transmission factors, particularly in vulnerable populations. The equilibrium and the threshold values $R_{0_{T}}$, $R_{0_{M}}$ & $R_{0_{TM}}$ of typhoid only, malaria only, and the typhoid malaria co-infection model respectively, were resolved. The stability analysis and occurence of backward bifurcation under certain conditions have been studied. We applied major cost-effectiveness technique to determine the most cost-effective control measures. Motivated by the recent flood crisis in Delhi and the associated contamination of the Yamuna River, we estimate key transmission parameters using the least squares fitting on Delhi cases data. Our model is validated by aligning the infection curves with official government reports. Furthermore, apply the ARIMA time-series forecasting model to predict malaria trends for $2025$ and $2026$. Also, we applied sensitivity analysis to investigate the impact of one disease on the other. The results show a correlation between malaria infection and a higher risk of contracting typhoid, but not an increased risk of malaria.

References

  1. [1] World Health Organization (2023), https://www.who.int/initiatives/sdg3-global-actionplan/progress-and-impact/progress-reports.
  2. [2] Uneke, C. (2008), Concurrent malaria and typhoid fever in the tropics: the diagnostic challenges and public health implications, Journal of Vector Borne Diseases, 45, 133-142.
  3. [3] Raj, P.M., Venkatesh, A., Kumar, K.A., and Manivel, M. (2025), Mathematical modeling of the co-infection dynamics of dengue and malaria using delay differential equations, Advanced Theory and Simulations, 8(2), 2400609.
  4. [4] Alhaj, M.S. (2023), Mathematical model for malaria disease transmission, Journal of Mathematical Analysis and Modeling, 4(1), 1-16.
  5. [5] Muhammad, F.A., Sudirman, R., Zakaria, N.A., and Daud, S.N.S.S. (2025), Morphology classification of malaria infected red blood cells using deep learning techniques, Biomedical Signal Processing and Control, 99, 106869.
  6. [6] World Health Organization (2024), https://www.who.int/news-room/fact-sheets/detail/typhoid.
  7. [7] Afoakwah, R., Acheampong, D.O., Boampong, J.N., Sarpong-Baidoo, M., Nwaefuna, E.K., and Tefe, P.S. (2024), Typhoid-malaria co-infection in ghana.
  8. [8] Centers for Disease Control and Prevention (2019), CDC yellow book 2020: health information for international travel, Oxford University Press.
  9. [9] Kariuki, S., Mwituria, J., Revathi, G., and Onsongo, J. (2004), Typhoid is over-reported in embu and nairobi, kenya, African Journal of Health Sciences, 11(3), 103-110.
  10. [10] Mweu, E. and English, M. (2008), Typhoid fever in children in africa, Tropical Medicine & International Health, 13(4), 532-540.
  11. [11] Pitzer, V.E., Feasey, N.A., Msefula, C., Mallewa, J., Kennedy, N., Dube, Q., Denis, B., Gordon, M.A., and Heyderman, R.S. (2015), Mathematical modeling to assess the drivers of the recent emergence of typhoid fever in blantyre, malawi, Clinical Infectious Diseases, 61(suppl 4), S251-S258.
  12. [12] Pitzer, V.E., Bowles, C.C., Baker, S., Kang, G., Balaji, V., Farrar, J.J., and Grenfell, B.T. (2014), Predicting the impact of vaccination on the transmission dynamics of typhoid in south asia: a mathematical modeling study, PLOS Neglected Tropical Diseases, 8(1), e2642.
  13. [13] Tijani, K.A., Madubueze, C.E., and Gweryina, R.I. (2024), Modelling typhoid fever transmission with treatment relapse response: optimal control and cost-effectiveness analysis, Mathematical Models and Computer Simulations, 16(3), 457-485.
  14. [14] Karunditu, J.W., Kimathi, G., and Osman, S. (2019), Mathematical modeling of typhoid fever disease incorporating unprotected humans in the spread dynamics, Journal of Advances in Mathematics and Computer Science, 32(3), 1-11.
  15. [15] Nyaberi, H.O. and Musaili, J.S. (2021), Mathematical modeling of the impact of treatment on the dynamics of typhoid, Journal of the Egyptian Mathematical Society, 29(1), 15.
  16. [16] Idowu, O.K., Ibrahim, E.L.M., Agbomola, J.O., and Shosanya, S.O. (2025), Effect of environmental precaution on the transmission of typhoid fever: a mathematical modelling approach, EDUCATUM Journal of Science, Mathematics and Technology, 12(1), 89-106.
  17. [17] Rehman, M.U., Alzabut, J., Fatima, N., and Khan, S. (2023), A mathematical tool to investigate the stability analysis of structured uncertain dynamical systems with m-matrices, Mathematics, 11(7), 1622.
  18. [18] Al-Shanfari, S., Elmojtaba, I.M., Al-Salti, N., and Al-Shandari, F. (2024), Mathematical analysis and optimal control of cholera–malaria co-infection model, Results in Control and Optimization, 14, 100393.
  19. [19] Carvalho, A. and Pinto, C.M. (2017), A delay fractional order model for the co-infection of malaria and hiv/aids, International Journal of Dynamics and Control, 5(1), 168-186.
  20. [20] Ibrahim, R.A. (2020), Assessment of breaking waves and liquid sloshing impact, Nonlinear Dynamics, 100(3), 1837-1925.
  21. [21] Irena, T.K. and Gakkhar, S. (2021), A dynamical model for hiv-typhoid co-infection with typhoid vaccine, Journal of Applied Mathematics and Computing, 1-30.
  22. [22] Korobeinikov, A. and Wake, G.C. (2002), Lyapunov functions and global stability for sir, sirs, and sis epidemiological models, Applied Mathematics Letters, 15(8), 955-960.
  23. [23] Nsutebu, E.F., Ndumbe, P.M., and Koulla, S. (2002), The increase in occurrence of typhoid fever in cameroon: overdiagnosis due to misuse of the widal test?, Transactions of the Royal Society of Tropical Medicine and Hygiene, 96(1), 64-67.
  24. [24] Agusto, F.B. and Adekunle, A. (2014), Optimal control of a two-strain tuberculosis-hiv/aids coinfection model, Biosystems, 119, 20-44.
  25. [25] Conteh, I.M., Abdulsalami, A.O., Njai, G. and Du, Q. (2025), A hybrid slime mould algorithm with Levy Flight based mutation for malaria parasite detection, Multiscale and Multidisciplinary Modeling, Experiments and Design, 8(6), 1-32.
  26. [26] Pinto, C.M. and Carvalho, A.R. (2014), New findings on the dynamics of hiv and tb coinfection models, Applied Mathematics and Computation, 242, 36-46.
  27. [27] Duve, P., Charles, S., Munyakazi, J., Luhken, R., and Witbooi, P. (2024), A mathematical model for malaria disease dynamics with vaccination and infected immigrants, Mathematical Biosciences and Engineering, 21(1), 1082-1109.
  28. [28] Bashyam, H. (2007), Surviving malaria, dying of typhoid, The Journal of Experimental Medicine, 204(12), 2774.
  29. [29] Pradhan, P. (2011), Coinfection of typhoid and malaria, Journal of Medical Laboratory and Diagnosis, 2(3), 22-26.
  30. [30] Bishof, N.A., Welch, T.R., and Beischel, L.S. (1990), C4b deficiency: a risk factor for bacteremia with encapsulated organisms, Journal of Infectious Diseases, 162(1), 248-250.
  31. [31] Warren, J., Mastroeni, P., Dougan, G., Noursadeghi, J., Cohen, J., Walport, M.J., and Botto, M. (2002), Increased susceptibility of c1q-deficient mice to salmonella enterica serovar typhimurium infection, Infection and Immunity, 70(2), 551-557.
  32. [32] Nyakoe, N.K., Taylor, R.P., Makumi, J.N., and Waitumbi, J.N. (2009), Complement consumption in children with plasmodium falciparum malaria, Malaria Journal, 8, 1-8.
  33. [33] Boulaaras, S., Yavuz, M., Alrashedi, Y., Bahramand, S., and Jan, R. (2025), Modeling the co-dynamics of vector-borne infections with the application of optimal control theory, Discrete and Continuous Dynamical Systems - Series S, 18(5), 1331-1352.
  34. [34] Nobre, F.F., Monteiro, A.B.S., Telles, P.R., and Williamson, G.D. (2001), Dynamic linear model and sarima: a comparison of their forecasting performance in epidemiology, Statistics in Medicine, 20(20), 3051-3069.
  35. [35] Islam, M.S., Shahrear, P., Saha, G., Ataullha, M., and Rahman, M.S. (2024), Mathematical analysis and prediction of future outbreak of dengue on time-varying contact rate using machine learning approach, Computers in Biology and Medicine, 178, 108707.
  36. [36] Abade, A., Porto, L.F., Scholze, A.R., Kuntath, D., Barros, N.d.S., Berra, T.Z., Ramos, A.C.V., Arcencio, R.A., and Alves, J.D. (2024), A comparative analysis of classical and machine learning methods for forecasting tb/hiv co-infection, Scientific Reports, 14(1), 18991.
  37. [37] Health risks associated with overflowing of yamuna in delhi (2023).
  38. [38] Upadhyay, R., Dasgupta, N., Hasan, A., and Upadhyay, S. (2011), Managing water quality of river yamuna in ncr delhi, Physics and Chemistry of the Earth, 36(9-11), 372-378.
  39. [39] Raj, P.M., Venkatesh, A., Kumar, K.A., and Manivel, M. (2025), Mathematical modeling of the co-infection dynamics of dengue and malaria using delay differential equations, Advanced Theory and Simulations, 8(2), 2400609.
  40. [40] Gebremeskel, A.A. and Krogstad, H.E. (2015), Mathematical modelling of endemic malaria transmission, American Journal of Applied Mathematics, 3(2), 36-46.
  41. [41] Mutua, J.M., Wang, F.B., and Vaidya, N.K. (2015), Modeling malaria and typhoid fever coinfection dynamics, Mathematical Biosciences, 264, 128-144.
  42. [42] Srivastav, A.K. and Ghosh, M. (2021), Modeling the transmission dynamics of malaria with saturated treatment: a case study of india, Journal of Applied Mathematics and Computing, 67(1), 519-540.
  43. [43] Tchoumi, S., Diagne, M., Rwezaura, H., and Tchuenche, J. (2021), Malaria and covid-19 codynamics: a mathematical model and optimal control, Applied Mathematical Modelling, 99, 294-327.
  44. [44] Van den Driessche, P. and Watmough, J. (2002), Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180(1-2), 29-48.
  45. [45] Zhang, J. and Ma, Z. (2003), Global dynamics of an seir epidemic model with saturating contact rate, Mathematical Biosciences, 185(1), 15-32.
  46. [46] Buonomo, B. (2015), A note on the direction of the transcritical bifurcation in epidemic models, Nonlinear Analysis: Modelling and Control, 20(1), 38-55.
  47. [47] Chitnis, N., Hyman, J.M., and Cushing, J.M. (2008), Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, Bulletin of Mathematical Biology, 70, 1272-1296.
  48. [48] Linton, N.M., Kobayashi, T., Yang, Y., Hayashi, K., Akhmetzhanov, A.R., Jung, S.M., Yuan, B., Kinoshita, R., and Nishiura, H. (2020), Incubation period and other epidemiological characteristics of 2019 novel coronavirus infections with right truncation: a statistical analysis of publicly available case data, Journal of Clinical Medicine, 9(2), 538.
  49. [49] Mtisi, E., Rwezaura, H., and Tchuenche, J.M. (2009), A mathematical analysis of malaria and tuberculosis co-dynamics, Discrete and Continuous Dynamical Systems - Series B, 12(4), 827-864.
  50. [50] Mukandavire, Z., Gumel, A.B., Garira, W., and Tchuenche, J.M. (2009), Mathematical analysis of a model for hiv-malaria co-infection, Mathematical Biosciences & Engineering, 6(2), 333-362.
  51. [51] Anguelov, R., Dumont, Y., Lubuma, J., and Mureithi, E. (2013), Stability analysis and dynamics preserving nonstandard finite difference schemes for a malaria model, Mathematical Population Studies, 20(2), 101-122.
  52. [52] Carr, J. (1981), Applications of center manifold theory, Springer-Verlag, New York.
  53. [53] Chiyaka, C., Tchuenche, J.M., Garira, W., and Dube, S. (2008), A mathematical analysis of the effects of control strategies on the transmission dynamics of malaria, Applied Mathematics and Computation, 195(2), 641-662.
  54. [54] Castillo-Chavez, C. and Song, B. (2004), Dynamical models of tuberculosis and their applications, Mathematical Biosciences & Engineering, 1(2), 361-404.
  55. [55] Dushoff, J., Huang, W., and Castillo-Chavez, C. (1998), Backwards bifurcations and catastrophe in simple models of fatal diseases, Journal of Mathematical Biology, 36, 227-248.
  56. [56] World Health Organization (2016-2022), https://ncvbdc.mohfw.gov.in/index4.php?lang=1&level=0&linkid= 420&lid=3699.

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