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Assessing the impact of adverse reactions associated with ivermectin on the dynamics of onchocerciasis in the Democratic Republic of Congo

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Abstract

Ivermectin is the mainstay of onchocerciasis control. However, it has been discovered that it can induce severe adverse reactions in some individuals. Hence, this model is used to assess the impact of adverse reactions that may occur upon uptake of ivermectin on the control of onchocerciasis. Numerical study of the model shows that the fraction of infectious humans who may refuse to continue with treatment due to the experience of a severe adverse effect as well as the severe adverse reaction induced death rate has significant impact on the dynamics of the model. The adverse reaction induced death rate of infectious humans who may refuse to continue with treatment due to the experience of a severe adverse effect was shown to cause a backward bifurcation. Also, an increase in the fraction of infectious humans who may refuse to continue with treatment due to the experience of an adverse drug effect was shown to increase the backward bifurcation range. Numerical simulation of the optimal control model show that the use of both mass administration of ivermectin and vector control strategies will accelerate the achievement of onchocerciasis elimination.

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Data Availability

The data that support the findings of this study are available in 1. https://www.who.int/data/gho/data/indicators/indicator-details/GHO/reported-number-of-individuals-treated-for-onchocerciasis 2. https://bmcpharmacoltoxicol.biomedcentral.com/articles/10.1186/s40360-019-0327-5.

References

  1. Amazigo U, Noma M, Bump J, Bentin B, Liese B, Yameogo L, Zour\(\acute{e}\) H, Seketeli A (2006) Onchocerciasis disease and mortality in sub Saharan Africa, Chapter 15, World Bank, Washington, DC

  2. Bof Makenga JM, Tshitoka FN, Muteba D, Mansiangi P, Coppieters Y (2019) Review of the national program for onchocerciasis control in the democratic Republic of the Congo. Trop Med Infect Dis 4:92

    Article  Google Scholar 

  3. Kuesel AC (2016) Research for new drugs for elimination of onchocerciasis in Africa. Int J Parasitol Drugs Drug Resist 6:272–286

    Article  Google Scholar 

  4. White G (1991) The natural history of blackflies. Med Vet Entomol 5(2):192

    Article  Google Scholar 

  5. Campillo JT, Boussinesq M, Bertout S, Faillie J-L, Chesnais CB (2021) Serious adverse reactions associated with ivermectin: a systematic pharmacovigilance study in sub-Saharan Africa and in the rest of the World. PLoS Neglect Trop Dis 15(4):e0009354. https://doi.org/10.1371/journal.pntd.0009354

    Article  Google Scholar 

  6. World Health Organization (2018) Onchocerciasis-river blindness. Fact Sheet No. 95

  7. Shirey RJ, Globisch D, Eubanks LM, Hixon MS, Janda KD (2018) Noninvasive Urine biomarker lateral flow immunoassay for monitoring active onchocerciasis. ACS Infect Dis 4:1423–1431

    Article  Google Scholar 

  8. Bof Makenga JM, Maketa V, Bakajika DK, Ntumba F, Mpunga D, Murdoch ME, Hopkins A, Noma MM, Zoure H, Tekle AH, Katabarwa MN, Lutumba P (2015) Onchocerciasis control in the Democratic Republic of Congo (DRC): challenges in a post-war environment. Trop Med Int Health 20:48–62

    Article  Google Scholar 

  9. Bof Makenga JM, Muteba D, Mansiangi P, Ilunga-Ilunga F, Coppieters Y (2019) Analysis of severe adverse effects following community-based ivermectin treatment in the Democratic Republic of Congo. BMC Pharmacol Toxicol 420:49

    Article  Google Scholar 

  10. Dimomfu BL, Lubeji DK, Noma M, Beketeli A, Boussines M (2007) Sociological study in three foci of Central Africa before the implementation of treatments with ivermectin (Mectizan). APOC Trans R Soc Trop Med Hyg 101:674–9

    Article  Google Scholar 

  11. World Health Organisation (WHO) (2018) African Program for Onchocerciasis Control (APOC). Community-directed treatment with ivermectin (CDTI)

  12. Haselow NJ, Akame J, Evini C, Akongo S (2003) Programmatic and communication issues in relation to serious adverse events following ivermectin treatment in areas Co-endemic for onchocerciasis and loiasis. Filaria. J. 2 (Suppl. 1), S10

  13. National Program for Onchocerciasis Control (NPOC). Annual technical report of the National Coordination Group for onchocerciasis (NCGO) Kasai occidental project. Kinshasa, DRC. 2002;2002:1–50

  14. National Program for Onchocerciasis Control (NPOC). Annual technical report of the National Coordination Group for onchocerciasis (NCGO). Bas Uel\(\acute{e}\) project, Kinshasa, DRC. 2009;2009:1–50

  15. Kamgno J, Pion SD, Tejiokem MC, Twum-Danso NA, Thylefors B, Boussinesq M (2007) Randomized, controlled, double-blind trial with ivermectin on Loa loa microfilaraemia: efficacy of a low dose (approximately 25 microg/kg) versus current standard dose (150 microg/kg). Trans R Soc Trop Med Hyg 101:777–85

    Article  Google Scholar 

  16. Omondi EO, Nyabadza F, Bonyah E, Badu K (2017) Modeling the infection dynamics of onchocerciasis and its treatment. J Biol Syst 25(2):247–277

    Article  MathSciNet  Google Scholar 

  17. Omondi EO, Orwa TO, Nyabadza F (2017) Application of optimal control to the onchocerciasis transmission model with treatment. Math Biosci 297:43–57

  18. Hassan A, Shaban N (2020) Onchocerciasis dynamics: modelling the effects of treatment, education and vector control. J Biol Dyn 14(1):245–268. https://doi.org/10.1080/17513758.2020.1745306

    Article  MathSciNet  Google Scholar 

  19. Diekmann O, Heesterbeek JAP (2000) Mathematical epidemiology of infectious diseases: model building, analysis and interpretation. Wiley, New York

    Google Scholar 

  20. van den Driessche P, Watmough J (2002) Reproduction number and sub-threshold endemic equilibria for computational models of disease transmission. Math Biosci 180:29–48

    Article  MathSciNet  Google Scholar 

  21. La Salle JP (1976) The stability of dynamical systems, Regional Conference Series in Applied Mathematics. SIAM Philadephia

  22. Smith Morgan E, Bilal Shakir, Lakwo Thomson L, Habomugisha Peace, Tukahebwa Edridah, Byamukama Edson, Katabarwa Moses N, Richards Frank O, Cupp Eddie W, Unnasch Thomas R, Michael Edwin (2019) Accelerating river blindness elimination by supplementing MDA with a vegetation slash and clear vector control strategy: a data-driven modeling analysis Scientific Reports 9:15274

  23. Tirados I, Thomsen E, Worrall E, Koala L, Melachio TT, Bas\(\acute{a}\tilde{n}\)ez M (2022) Vector control and entomological capacity for onchocerciasis elimination. Trends in Parasitology. 38(7)

  24. Lakwo T, Oguttu D, Ukety T, Post R, Bakajika D (2020) Onchocerciasis Elimination: Progress and Challenges. Res Rep Trop Med 7(11):81–95

    Google Scholar 

  25. Raimon S, Lakwo TL, Sebit WJ, Siewe Fodjo JN, Alinda P, Carter JY, Post RJ, Colebunders R (2021) Slash and clear, a community-based vector control method to reduce onchocerciasis transmission by simulium sirbanum in Maridi, South Sudan: a prospective study. Pathogens 10(10):1329

    Article  Google Scholar 

  26. Fleming WH, Rishel RW (1975) Deterministic and stochastic optimal control. Springer, New York

    Book  Google Scholar 

  27. Pontryagin L, Boltyanskii V, Gamkrelidze R, Mishchenko E (1963) The mathematical theory of optimal control process 4, New York/London 1962. John Wiley & Sons

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Benin, Benin City, Nigeria

    Ann Nwankwo & Daniel Okuonghae

  2. Federal Polytechnic, Nekede, Nigeria

    Chinwe Okereke

Authors
  1. Ann Nwankwo
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  2. Chinwe Okereke
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  3. Daniel Okuonghae
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Contributions

AN contributed to conceptualization; AN and CO contributed to methodology; AN and CO contributed to qualitative analysis; AN contributed to writing-original draft preparation; AN and DO contributed to writing-review and editing

Corresponding author

Correspondence to Ann Nwankwo.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A: Existence of EEP

Appendix A: Existence of EEP

The coefficients of the polynomial equation (5) are given as follows:

$$\begin{aligned} G_4= & {} g8 \mu _v \Pi _h (g_7 \epsilon _d (g_5 + \alpha _e ) (g_3g_6 - (1-p) \alpha _t \omega _t) \\{} & {} \quad + g_5 g_6 g_7 \gamma _h \epsilon _d + g_5 g_6 p \alpha _t \gamma _h \epsilon _d \\{} & {} \quad + g_5 g_7 (1-p) \alpha _t \gamma _h \epsilon _d+g_3 g_7 \alpha _e \gamma _t \epsilon _d + \\{} & {} \quad g_7 \alpha _e \gamma _t \epsilon _d \omega _t \\{} & {} \quad + p \alpha _e \alpha _t \gamma _t \epsilon _d \omega _t) (b_v g_5 g_6 g_7 \beta _v \gamma _h \epsilon _d \\{} & {} \quad + b_v g_5 g_6 p \alpha _t \beta _v \gamma _h \epsilon _d \\{} & {} \quad + b_v g_5 g_7 (1-p) \alpha _t \beta _v \gamma _h \epsilon _d\theta _t \\{} & {} \quad +b_v g_3 g_7 \alpha _e \beta _v \gamma _t \epsilon _d \theta _t + \\{} & {} \quad g_7\mu _v \epsilon _d (g_5 + \alpha _e ) (g_3g_6 - (1-p) \alpha _t \omega _t)\\{} & {} \quad + g_5 g_6 g_7 \gamma _h \epsilon _d \mu _v +g_5 g_6 p \alpha _t \gamma _h \epsilon _d \mu _v \\{} & {} \quad + g_5 g_7 (1-p) \alpha _t \gamma _h \epsilon _d \mu _v + g_3 g_7 \alpha _e \gamma _t \epsilon _d \mu _v + \\{} & {} \quad b_v g_7 \alpha _e \beta _v \gamma _t \epsilon _d \omega _t \\{} & {} \quad + b_v p \alpha _e \alpha _t \beta _v \gamma _t \epsilon _d \omega _t \\{} & {} \quad + g_7 \alpha _e \gamma _t \epsilon _d \mu _v \omega _t + p \alpha _e \alpha _t \gamma _t \epsilon _d \mu _v \omega _t), \end{aligned}$$
$$\begin{aligned} G_3= & {} -b_v^2 g_7 \beta _h \beta _v \gamma _v \epsilon _d \Pi _v (g_2 g_5 \\{} & {} \quad - \alpha _e \omega _e) (g_3 g_6 - (1-p)\alpha _t \omega _t) (g_5 g_6 g_7 \gamma _h \epsilon _d\\{} & {} \quad + g_5 g_6 p \alpha _t \gamma _h \epsilon _d + g_5 g_7 (1-p) \alpha _t \gamma _h \epsilon _d \theta _t +\\{} & {} \quad g_3 g_7 \alpha _e \gamma _t \epsilon _d \theta _t \\{} & {} \quad + g_7 \alpha _e \gamma _t \epsilon _d \omega _t + p \alpha _e \alpha _t \gamma _t \epsilon _d \omega _t)\\{} & {} \quad + g_8 \mu _v \Pi _h ((b_v g_5 g_6 g_7 \beta _v \gamma _h \epsilon _d \\{} & {} \quad +b_v g_5 g_6 p \alpha _t \beta _v \gamma _h \epsilon _d +\\{} & {} \quad b_v g_5 g_7 (1-p) \alpha _t \beta _v \gamma _h \epsilon _d \theta _t\\{} & {} \quad +b_v g_3 g_7 \alpha _e \beta _v \gamma _t \epsilon _d \theta _t\\{} & {} \quad + g_7\mu _v \epsilon _d (g_5 + \alpha _e ) (g_3g_6 - (1-p) \alpha _t \omega _t)\\{} & {} \quad + g_5 g_6 g_7 \gamma _h \epsilon _d \mu _v +\\{} & {} \quad g_5 g_6 p \alpha _t \gamma _h \epsilon _d \mu _v \\{} & {} \quad + g_5 g_7 (1-p) \alpha _t \gamma _h \epsilon _d \mu _v + g_3 g_7 \alpha _e \gamma _t \epsilon _d \mu _v\\{} & {} \quad + b_v g_7 \alpha _e \beta _v \gamma _t \epsilon _d \omega _t\\{} & {} \quad + b_v p \alpha _e \alpha _t \beta _v \gamma _t \epsilon _d\omega _t +\\{} & {} \quad g_7 \alpha _e \gamma _t \epsilon _d \mu _v \omega _t\\{} & {} \quad + p \alpha _e \alpha _t \gamma _t \epsilon _d \mu _v \omega _t) (g_4 g_5 g_7 (g_3g_6\\{} & {} \quad - (1-p) \alpha _t \omega _t) + g_4 g_7 \alpha _e (g_3g_6 - (1-p) \alpha _t \omega _t)\\{} & {} \quad + g_4 g_5 g_6 g_7 \gamma _h +\\{} & {} \quad g_4 g_5 g_6 p \alpha _t \gamma _h + g_4 g_5 g_7 (1-p) \alpha _t \gamma _h \\{} & {} \quad + g_3 g_4 g_7 \alpha _e \gamma _t + g_7 \epsilon _d (g_2g_5\\{} & {} \quad - \alpha _e\omega _e) (g_3g_6 - (1-p) \alpha _t \omega _t) + g_2 g_7 \alpha _s \epsilon _d (g_3g_6 -\\{} & {} \quad (1-p) \alpha _t \omega _t) + g_2 g_3 g_7 \alpha _s \gamma _t \epsilon _d \\{} & {} \quad + g_7 \alpha _s \epsilon _d \omega _e (g_3g_6 - (1-p)\alpha _t\omega _t)\\{} & {} \quad + g_6 g_7 \alpha _s \gamma _h \epsilon _d \omega _e + g_6 p \alpha _s \alpha _t \gamma _h \epsilon _d \omega _e +\\{} & {} \quad g_7 (1-p) \alpha _s \alpha _t \gamma _h \epsilon _d \omega _e + g_4 g_7 \alpha _e \gamma _t \omega ]t\\{} & {} \quad + g_4 p \alpha _e \alpha _t \gamma _t \omega _t + g_2 g_7 \alpha _s \gamma _t \epsilon _d \omega _t\\{} & {} \quad + g_2 p \alpha _s \alpha _t \gamma _t \epsilon _d \omega _t) + (g_7 \epsilon _d (g_5 + \alpha _e ) (g_3g_6 -\\{} & {} \quad (1-p) \alpha _t \omega _t) + g_5 g_6 g_7 \gamma _h \epsilon _d \\{} & {} \quad + g_5 g_6 p \alpha _t \gamma _h \epsilon _d + g_5 g_7(1-p) \alpha _t \gamma _h \epsilon _d\\{} & {} \quad + g_3 g_7 \alpha _e \gamma _t \epsilon _d + g_7 \alpha _e \gamma _t \epsilon _d \omega _t +\\{} & {} \quad p \alpha _e \alpha _t \gamma _t \epsilon _d \omega _t) (b_v g_4 g_5 g_6 g_7 \beta _v \gamma _h\\{} & {} \quad + b_v g_4 g_5 g_6 p \alpha _t \beta _v \gamma _h + b_v g_4 g_5 g_7 (1-p) \alpha _t \beta _v \gamma _h \theta _t\\{} & {} \quad + b_v g_3 g_4 g_7 \alpha _e \beta _v \gamma _t \theta _t +\\{} & {} \quad b_v g_2 g_3 g_7 \alpha _s \beta _v \gamma _t \epsilon _d \theta _t + g_4 g_5 g_7 \mu _v (g_3g_6\\{} & {} \quad - (1-p) \alpha _t \omega _t) + g_4g_7 \alpha _e \mu _v (g_3g_6 - (1-p) \alpha _t \omega _t)\\{} & {} \quad + g_4 g_5 g_6 g_7 \gamma _h \mu _v +\\{} & {} \quad g_4 g_5 g_6 p \alpha _t \gamma _h \mu _v \\{} & {} \quad + g_4 g_5 g_7 (1-p) \alpha _t \gamma _h \mu _v + g_3 g_4 g_7 \alpha _e \gamma _t \mu _v \\{} & {} \quad + g_7 \epsilon _d \mu _v (g_2g_5 - \alpha _e\omega _e) (g_3g_6 - (1-p) \alpha _t \omega _t) +\\{} & {} \quad g_2 g_7 \alpha _s \epsilon _d \mu _v (g_3g_6 -(1-p)\alpha _t \omega _t)\\{} & {} \quad + g_2 g_3 g_7 \alpha _s \gamma _t \epsilon _d \mu _v +b_v g_6 g_7 \alpha _s \beta _v \gamma _h \epsilon _d \omega _e\\{} & {} \quad + b_v g_6 p \alpha _s \alpha _t \beta _v \gamma _h \epsilon _d \omega _e +\\{} & {} \quad b_v g_7 (1-p) \alpha _s \alpha _t \beta _v \gamma _h \epsilon _d \theta _t \omega _e \\{} & {} \quad + g_7 \alpha _s \epsilon _d \mu _v \omega _e (g_3g_6 - (1-p) \alpha _t \omega _t)\\{} & {} \quad +g_6 g_7 \alpha _s \gamma _h \epsilon _d \mu _v \omega _e + g_6 p \alpha _s \alpha _t \gamma _h \epsilon _d \mu _v \omega _e +\\{} & {} \quad g_7 (1-p) \alpha _s \alpha _t \gamma _h \epsilon _d \mu _v \omega _e \\{} & {} \quad + b_v g_4 g_7 \alpha _e \beta _v \gamma _t \omega _t + b_v g_4 p \alpha _e \alpha _t \beta _v \gamma _t \omega _t\\{} & {} \quad + b_v g_2 g_7 \alpha _s \beta _v \gamma _t \epsilon _d \omega _t\\{} & {} \quad + b_v g_2 p \alpha _s \alpha _t \beta _v \gamma _t \epsilon _d\omega _t +\\{} & {} \quad g_4 g_7 \alpha _e \gamma _t \mu _v \omega _t + g_4 p \alpha _e \alpha _t \gamma _t \mu _v \omega _t\\{} & {} \quad + g_2 g_7 \alpha _s \gamma _t \epsilon _d \mu _v \omega _t\\{} & {} \quad + g_2 p \alpha _s \alpha _t \gamma _t \epsilon _d \mu _v \omega _t)), \end{aligned}$$
$$\begin{aligned} G_2= & {} -b_v^2 g_7 \beta _h \beta _v \gamma _v \Pi _v (g_2 g_5 - \alpha _e \omega _e) ((g_4 \\{} & {} \quad + g_1 \epsilon _d) (g_3 g_6 - (1-p) \alpha _t \omega _t) (g_5 g_6 g_7 \gamma _h \epsilon _d \\{} & {} \quad + g_5 g_6 p \alpha _t \gamma _h \epsilon _d + g_5 g_7 (1-p) \alpha _t \gamma _h \epsilon _d \theta _t\\{} & {} \quad + g_3 g_7 \alpha _e \gamma _t \epsilon _d \theta _t + g_7 \alpha _e \gamma _t \epsilon _d \omega _t\\{} & {} \quad + p \alpha _e \alpha _t \gamma _t \epsilon _d \omega _t) + \epsilon _d (g_3 g_6 \\{} & {} \quad - (1-p) \alpha _t \omega _t) (g_4 g_5 g_6 g_7 \gamma _h \\{} & {} \quad + g_4 g_5 g_6 p \alpha _t \gamma _h + g_4 g_5 g_7 (1-p)\alpha _t \gamma _h \theta _t\\{} & {} \quad + g_3 g_4 g_7 \alpha _e \gamma _t \theta _t + g_2 g_3 g_7 \alpha _s \gamma _t \epsilon _d \theta _t \\{} & {} \quad + g_6 g_7 \alpha _s \gamma _h \epsilon _d \omega _e +\quad g_6 p \alpha _s \alpha _t \gamma _h \epsilon _d \omega _e\\{} & {} \quad + g_7 (1-p) \alpha _s \alpha _t \gamma _h \epsilon _d \theta _t \omega _e + g_4 g_7 \alpha _e \gamma _t \omega _t\\{} & {} \quad + g_4 p \alpha _e \alpha _t \gamma _t \omega _t + g_2 g_7 \alpha _s \gamma _t \epsilon _d \omega _t\\{} & {} \quad + g_2 p \alpha _s \alpha _t \gamma _t \epsilon _d \omega _t))\\{} & {} \quad +g_8 \mu _v \Pi _h ((b_v g_5 g_6 g7 \beta _v \gamma _h \epsilon _d \\{} & {} \quad +b_v g_5 g_6 p \alpha _t \beta _v \gamma _h \epsilon _d + b_v g_5 g_7 (1-p) \alpha _t \beta _v \gamma _h \epsilon _d \theta _t\\{} & {} \quad +b_v g_3 g_7 \alpha _e \beta _v \gamma _t \epsilon _d \theta _t +\\{} & {} \quad g_5 g_7 \epsilon _d \mu _v (g_3 g_6 - (1-p) \alpha _t \omega _t)\\{} & {} \quad + g_7 \alpha _e \epsilon _d \mu _v (g_3 g_6 - (1-p) \alpha _t \omega _t)\\{} & {} \quad + g_5 g_6 g_7 \gamma _h \epsilon _d \mu _v + g_5 g_6 p \alpha _t \gamma _h \epsilon _d \mu _v +\\{} & {} \quad g_5 g_7 (1-p) \alpha _t \gamma _h \epsilon _d \mu _v + g_3 g_7 \alpha _e \gamma _t \epsilon _d \mu _v \\{} & {} \quad + b_v g_7 \alpha _e \beta _v \gamma _t \epsilon _d \omega _t \\{} & {} \quad + b_v p \alpha _e \alpha _t \beta _v \gamma _t \epsilon _d \omega _t + g_7 \alpha _e \gamma _t \epsilon _d \mu _v \omega _t +\\{} & {} \quad p \alpha _e \alpha _t \gamma _t \epsilon _d \mu _v \omega _t) ( g_4 g_7 (g_3 g_6\\{} & {} \quad - (1-p) \alpha _t \omega _t) (g_2 g_5 - \alpha _e \omega _e)\\{} & {} \quad + g_7 \alpha _s (g_3 g_6 - (1-p) \alpha _t \omega _t) (g_2 g_5 - \alpha _e \omega _e)) +\\{} & {} \quad (g_5 g_7 \epsilon _d (g_3 g_6 - (1-p) \alpha _t \omega _t) \\{} & {} \quad + g_7 \alpha _e \epsilon _d (g_3 g_6 - (1-p) \alpha _t \omega _t)\\{} & {} \quad + g_5 g_6 g_7 \gamma _h \epsilon _d + g_5 g_6 p \alpha _t \gamma _h \epsilon _d +\\{} & {} \quad g_5 g_7 (1-p) \alpha _t \gamma _h \epsilon _d + g_3 g_7 \alpha _e \gamma _t \epsilon _d\\{} & {} \quad + g_7 \alpha _e \gamma _t \epsilon _d \omega _t + p \alpha _e \alpha _t \gamma _t \epsilon _d \omega _t) (g_4 g_6 \mu _v (g_2 g_5 \\{} & {} \quad - \alpha _e \omega _e) (g_3 g_6 - (1-p) \alpha _t \omega _t) \\{} & {} \quad + g_7 \alpha _s \mu _v (g_2 g_5 - \alpha _e \omega _e) (g_3 g_6 -(1-p) \alpha _t \omega _t))\\{} & {} \quad + ( g_4 g_5 g_7 (g_3 g_6 - (1-p) \alpha _t \omega _t) \\{} & {} \quad + g_4 g_7 \alpha _e (g_3 g_6 - (1-p) \alpha _t \omega _t) \\{} & {} \quad + g_4 g_5 g_6 g_7 \gamma _h + g_4 g_5 g_6 p \alpha _t \gamma _h \\{} & {} \quad + g_4 g_5 g_7 (1-p) \alpha _t \gamma _h + g_3 g_4 g_7 \alpha _e \gamma _t\\{} & {} \quad + g_7 \epsilon _ d(g_2 g_5 - \alpha _e \omega _e) (g_3 g_6 -(1-p) \alpha _t \omega _t)\\{} & {} \quad + g_2 g_7 \alpha _s \epsilon _d (g_3 g_6 - (1-p) \alpha _t \omega _t) + g_2 g_3 g_7 \alpha _s \gamma _t \epsilon _d\\{} & {} \quad + g_7 \alpha _s \epsilon _d \omega _e (g_3 g_6 - (1-p) \alpha _t \omega _t)\\{} & {} \quad + g_6 g_7 \alpha _s \gamma _h \epsilon _d \omega _e +\quad g_6 p \alpha _s \alpha _t \gamma _h \epsilon _d \omega _e \\{} & {} \quad + g_7 (1-p) \alpha _s \alpha _t \gamma _h \epsilon _d \omega _e + g_4 g_7 \alpha _e \gamma _t \omega _t \\{} & {} \quad + g_4 p \alpha _e \alpha _t \gamma _t \omega _t + g_2 g_7 \alpha _s \gamma _t \epsilon _d \omega _t \\{} & {} \quad + g_2 p \alpha _s \alpha _t \gamma _t \epsilon _d \omega _t) \\{} & {} \quad (b_vg_4 g_5 g_6 g_7 \beta _v \gamma _h + b_v g_4 g_5 g_6 p \alpha _t \beta _v \gamma _h \\{} & {} \quad + b_v g_4 g_5 g_7 (1-p) \alpha _t \beta _v \gamma _h \theta _t + b_v g_3 g_4 g_7 \alpha _e \beta _v \gamma _t \theta _t +\\{} & {} \quad \quad b_v g_2 g_3 g_7 \alpha _s \beta _v \gamma _t \epsilon _d \theta _t\\{} & {} \quad + g_4 g_5 g_7 \mu _v (g_3 g_6 - (1-p) \alpha _t \omega _t)\\{} & {} \quad + g_4 g_7 \alpha _e \mu _v (g_3 g_6 - (1-p) \alpha _t \omega _t)\\{} & {} \quad +g_4 g_5 g_6 g_7 \gamma _h \mu _v +g_4 g_5 g_6 p \alpha _t \gamma _h \mu _v\\{} & {} \quad + g_4 g_5 g_7(1-p) \alpha _t \gamma _h \mu _v\\{} & {} \quad + g_3 g_4 g_7 \alpha _e \gamma _t \mu _v + g_7 \epsilon _d \mu _v (g_2 g_5 \\{} & {} \quad - \alpha _e \omega _e) (g_3 g_6 - (1-p) \alpha _t \omega _t) + \\{} & {} \quad g_2 g_7 \alpha _s \epsilon _d \mu _v (g_3 g_6 - (1-p) \alpha _t \omega _dt)\\{} & {} \quad +g_2 g_3 g_7 \alpha _s \gamma _t \epsilon _d \mu _v + b_v g_6 g_7 \alpha _s \beta _v \gamma _h \epsilon _d \omega _e\\{} & {} \quad + b_v g_6 p \alpha _s \alpha _t \beta _v \gamma _h \epsilon _d \omega _e \\{} & {} \quad + b_v g_7 (1-p) \alpha _s \alpha _t \beta _v \gamma _h \epsilon _d \theta _t \omega _e\\{} & {} \quad + g_7 \alpha _s \epsilon _d \mu _v \omega _e (g_3 g_6 -(1-p) \alpha _t \omega _t)\\{} & {} \quad +g_6 g_7 \alpha _s \gamma _h \epsilon _d \mu _v \omega _e +\\{} & {} \quad g_6 p \alpha _s \alpha _t \gamma _h \epsilon _d \mu _v \omega _e\\{} & {} \quad + g_7 (1-p) \alpha _s \alpha _t \gamma _h\epsilon _d \mu _v \omega _e + b_v g_4 g_7 \alpha _e \beta _v \gamma _t \omega _t\\{} & {} \quad + b_v g_4 p \alpha _e \alpha _t \beta _v \gamma _t \omega _t + b_v g_2 g_7 \alpha _s \beta _v \gamma _t \epsilon _d \omega _t \\{} & {} \quad + b_v g_2 p \alpha _s \alpha _t \beta _v \gamma _t \epsilon _d \omega _t\\{} & {} \quad + g_4 g_7 \alpha _e \gamma _t \mu _v \omega _t + g_4 p \alpha _e \alpha _t \gamma _t \mu _v \omega _t\\{} & {} \quad + g_2 g_7 \alpha _s \gamma _t \epsilon _d \mu _v \omega _t+ g_2 p \alpha _s \alpha _t \gamma _t \epsilon _d \mu _v \omega _t)), \end{aligned}$$
$$\begin{aligned} G_1= & {} -b_v^2 g_7 \beta _h \beta _v \gamma _v \Pi _v (g_2 g_5 - \alpha _e \omega _e) ((g_1 g_4 - \alpha _s \omega _s) (g_3 g_6\\{} & {} \quad - (1-p) \alpha _t \omega _t) (g_5 g_6 g_7 \gamma _h \epsilon _d + g_5 g_6 p \alpha _t \gamma _h \epsilon _d +\\{} & {} \quad g_5 g_7 (1-p) \alpha _t \gamma _h \epsilon _d \theta _t + g_3 g_7 \alpha _e \gamma _t \epsilon _d \theta _t\\{} & {} \quad + g_7 \alpha _e \gamma _t \epsilon _d \omega _t + p \alpha _e \alpha _t \gamma _t \epsilon _d \omega _t) + (g_4 + g_1 \epsilon _d)\\{} & {} \quad (g_3 g_6 - (1-p) \alpha _t \omega _t) \\{} & {} \quad (g_4 g_5 g_6 g_7 \gamma _h + g_4 g_5 g_6 p \alpha _t \gamma _h + g_4 g_5 g_7 (1-p) \alpha _t \gamma _h \theta _t\\{} & {} \quad + g_3 g_4 g_7 \alpha _e \gamma _t \theta _t + g_2 g_3 g_7 \alpha _s \gamma _t \epsilon _d \theta _t + g_6 g_7 \alpha _s \gamma _h \epsilon _d \omega _e \\{} & {} \quad +g_6 p \alpha _s \alpha _t \gamma _h \epsilon _d \omega _e + g_7 (1-p) \alpha _s \alpha _t \gamma _h \epsilon _d \theta _t \omega _e \\{} & {} \quad + g_4 g_7 \alpha _e \gamma _t \omega _t + g_4 p \alpha _e \alpha _t \gamma _t \omega _t \\{} & {} \quad + g_2 g_7 \alpha _s \gamma _t \epsilon _d \omega _t + g_2 p \alpha _s \alpha _t \gamma _t \epsilon _d \omega _t)) +\\{} & {} \quad g_8 \mu _v \Pi _h (( g_4 g_5 g_7 (g_3 g_6 - (1-p) \alpha _t \omega _t) \\{} & {} \quad + g_4 g_7 \alpha _e (g_3 g_6 - (1-p) \alpha _t \omega _t) \\{} & {} \quad + g_4 g_5 g_6 g_7 \gamma _h + g_4 g_5 g_6 p \alpha _t \gamma _h +\\{} & {} \quad g_4 g_5 g_7 (1-p) \alpha _t \gamma _h + g_3 g_4 g_7 \alpha _e \gamma _t \\{} & {} \quad + g_7 \epsilon _d (g_2 g_5 - \alpha _e \omega _e) (g_3 g_6 \\{} & {} \quad - (1-p) \alpha _t \omega _t) + g_2 g_7 \alpha _s \epsilon _d (g_3 g_6 - (1-p) \alpha _t \omega _t) \\{} & {} \quad +g_2 g_3 g_7 \alpha _s \gamma _t \epsilon _d + g_7 \alpha _s \epsilon _d \omega _e (g_3 g_6 \\{} & {} \quad - (1-p) \alpha _t \omega _t) +g_6 g_7 \alpha _s \gamma _h \epsilon _d \omega _e \\{} & {} \quad + g_6 p \alpha _s \alpha _t \gamma _h \epsilon _d \omega _e + g_7 (1-p) \alpha _s \alpha _t \gamma _h \epsilon _d \omega _e \\{} & {} \quad + g_4 g_7 \alpha _e \gamma _t \omega _t +g_4 p \alpha _e \alpha _t \gamma _t \omega _t\\{} & {} \quad +g_2 g_7 \alpha _s \gamma _t \epsilon _d \omega _t +g_2 p \alpha _s \alpha _t \gamma _t \epsilon _d \omega _t) ( g_4 g_7 \mu _v (g_2 g_5 \\{} & {} \quad - \alpha _e \omega _e) (g_3 g_6 -(1-p) \alpha _t \omega _t) +\\{} & {} \quad g_3 g_6 g_7 \alpha _s \mu _v (g_2 g_5 - \alpha _e \omega _e) (g_3g_6 - (1-p) \alpha _t \omega _t)) \\{} & {} \quad + ( g_4 g_7 (g_2 g_5 - \alpha _e \omega _e) (g_3 g_6 - (1-p) \alpha _t \omega _t) \\{} & {} \quad + g_7 \alpha _s (g_2 g_5 - \alpha _e \omega _e)\\{} & {} \quad (g_3 g_6 - (1-p)\alpha _t \omega _t)) (b_v g_4 g_5 g_6 g_7 \beta _v \gamma _h \\{} & {} \quad + b_v g_4 g_5 g_6 p \alpha _t \beta _v \gamma _h \\{} & {} \quad + b_v g_4 g_5 g_7 p_1 \alpha _t \beta _v \gamma _h \theta _t + b_v g_3 g_4 g_7 \alpha _e \beta _v \gamma _t \theta _t +\\{} & {} \quad b_v g_2 g_3 g_7 \alpha _s \beta _v \gamma _t \epsilon _d \theta _t + g_4 g_5 g_7 \mu _v (g_3 g_6 - (1-p) \alpha _t \omega _t) \\{} & {} \quad + g_4 g_7 \alpha _e \mu _v (g_3 g_6 - (1-p) \alpha _t \omega _t) + g_4 g_5 g_6 g_7 \gamma _h \mu _v + \\{} & {} \quad g_4 g_5 g_6 p \alpha _t \gamma _h \mu _v + g_4 g_5 g_7 (1-p) \alpha _t \gamma _h \mu _v\\{} & {} \quad + g_3 g_4 g_7 \alpha _e \gamma _t \mu _v\\{} & {} \quad + g_7 \epsilon _d \mu _v (g_2 g_5 - \alpha _e \omega _e) (g_3 g_6 -(1-p) \alpha _t \omega _t) +\\{} & {} \quad g_2 g_7 \alpha _s \epsilon _d \mu _v (g_3 g_6 - (1-p) \alpha _t \omega _t) + g_2 g_3 g_7 \alpha _s \gamma _t \epsilon _d \mu _v \\{} & {} \quad + b_v g_6 g_7 \alpha _s \beta _v \gamma _h \epsilon _d \omega _e + b_v g_6 p \alpha _s \alpha _t \beta _v \gamma _h \epsilon _d \omega _e +\\{} & {} \quad b_v g_7 (1-p) \alpha _s \alpha _t \beta _v \gamma _h \epsilon _d \theta _t \omega _e \\{} & {} \quad + g_7 \alpha _s \epsilon _d \mu _v \omega _e (g_3 g_6 - (1-p) \alpha _t \omega _t)\\{} & {} \quad + g_6 g_7 \alpha _s \gamma _h \epsilon _d \mu _v \omega _e + g_6 p \alpha _s \alpha _t \gamma _h \epsilon _d \mu _v \omega _e +\\{} & {} \quad g_7 (1-p) \alpha _s \alpha _t \gamma _h \epsilon _d \mu _v \omega _e + b_v g_4 g_7 \alpha _e \beta _v \gamma _t \omega _t \\{} & {} \quad + b_v g_4 p \alpha _e \alpha _t \beta _v \gamma _t \omega _t \\{} & {} \quad + b_v g_2 g_7 \alpha _s \beta _v \gamma _t \epsilon _d \omega _t + b_v g_2 p \alpha _s \alpha _t \beta _v \gamma _t \epsilon _d \omega _t +\\{} & {} \quad g_4 g_7 \alpha _e \gamma _t \mu _v \omega _t \\{} & {} \quad + g_4 p \alpha _e \alpha _t \gamma _t \mu _v \omega _t + g_2 g_7 \alpha _s \gamma _t \epsilon _d \mu _v \omega _t \\{} & {} \quad + g_2 p \alpha _s \alpha _t \gamma _t \epsilon _d \mu _v \omega _t)),\\ G_0= & {} g_7^2g_8(g_4+\alpha _s)^2(g_2g_5-\alpha _e\omega _e)^2(g_3g_6\\{} & {} -(1-p)\alpha _t\omega _t)^2\mu _v^2\Pi _h(1-{\mathcal {R}}_o^2). \end{aligned}$$

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Nwankwo, A., Okereke, C. & Okuonghae, D. Assessing the impact of adverse reactions associated with ivermectin on the dynamics of onchocerciasis in the Democratic Republic of Congo. Int. J. Dynam. Control 12, 1346–1365 (2024). https://doi.org/10.1007/s40435-023-01263-w

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