Mathematical Modeling of Schistosomiasis Transmission Using Reaction-Diffusion Equations

Year 2024, Volume: 7 Issue: 2, 118 - 136, 30.06.2024

Dhorasso Junior Temfack Nguefack

https://doi.org/10.33401/fujma.1412958

Abstract

Schistosomiasis, a neglected tropical disease caused by parasitic trematodes of the genus \textit{Schistosoma}, affects millions of people in tropical and subtropical regions lacking access to clean water and proper hygiene. With its impact on health and well-being, the World Health Organization aspires to eliminate schistosomiasis by 2030. This work addresses the challenge of effective control in endemic areas by integrating diffusion in each sub-population using reaction-diffusion equations. The proposed model includes treated individuals who have undergone massive drug administration and a time-dependent function that models the change in human behavior. We present a Partial Differential Equation (PDE) model of schistosomiasis spread that incorporates population movement and human behavior change. Mathematical analysis explores the system's dynamics according to the infection threshold $R_0$, shedding light on the disease's behavior. Sensitivity analysis is used to identify the key parameters affecting disease spread. Numerical simulations under different scenarios elucidate the impact of human behavior on disease dynamics. This research contributes to a deeper understanding of schistosomiasis transmission and provides insights into control strategies.

Keywords

Disease dynamics, Human behaviour, Neglected tropical disease, Reaction-diffusionequations, Schistosomiasis, Sensitivity analysis

References

• [1] World Health Organization, WHO Guideline on Control and Elimination of Human Schistosomiasis, (2022). $ \href{https://www.who.int/publications/i/item/9789240041608}{\mbox{[Web]}}$
• [2] World Health Organization, Ending the Neglect to Attain the Sustainable Development Goals, (2020). $ \href{https://iris.who.int/handle/10665/70809}{\mbox{[Web]}}$
• [3] E.J. Allen and H.D. Victory, Modelling and simulation of a schistosomiasis infection with biological control, Acta Trop., 87(2) (2003), 251–267. $\href{https://doi.org/10.1016/s0001-706x(03)00065-2}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-0038095207&origin=resultslist&sort=plf-f&src=s&sid=afbfd071e401079b937f6f34a99fee9d&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Modelling+and+simulation+of+a+schistosomiasis+infection+with+biological+control%22%29&sl=82&sessionSearchId=afbfd071e401079b937f6f34a99fee9d&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000184046000007}{\mbox{[Web of Science]}} $
• [4] A.G. Ross, D. Vickers, G.R. Olds, S.M. Shah and D.P. McManus, Katayama syndrome, Lancet Infect. Dis., 7(3) (2007), 218–224. $ \href{https://doi.org/10.1016/S1473-3099(07)70053-1}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-33847035457&origin=resultslist&sort=plf-f&src=s&sid=afbfd071e401079b937f6f34a99fee9d&sot=b&sdt=cl&cluster=scoexactsrctitle%2C%22Lancet+Infectious+Diseases%22%2Ct&s=TITLE-ABS-KEY%28%22Katayama+syndrome%22%29&sl=82&sessionSearchId=afbfd071e401079b937f6f34a99fee9d&relpos=2}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000244584700020}{\mbox{[Web of Science]}}$
• [5] E.Y.-Y. Li, D. Gurarie, N.C. Lo, X. Zhu and C.H. King, Improving public health control of schistosomiasis with a modified WHO strategy: A model-based comparison study, Lancet Glob. Health, 7(10) (2019), e1414–e1422 $\href{https://doi.org/10.1016/S2214-109X(19)30346-8}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85072176355&origin=resultslist&sort=plf-f&src=s&sid=90fc18aa5ca90e60aa30f007d2227dcf&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Improving+public+health+control+of+schistosomiasis+with+a+modified+WHO+strategy%3A+A+model-based+comparison+study%22%29&sl=128&sessionSearchId=90fc18aa5ca90e60aa30f007d2227dcf&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000485871100036}{\mbox{[Web of Science]}} $
• [6] G. Macdonald, The dynamics of helminth infections, with special reference to schistosomes, Transactions of the Royal Society of Tropical Medicine and Hygiene, Trans. R. Soc. Trop. Med. Hyg., 59(5) (1965), 489–506 $\href{https://doi.org/10.1016/0035-9203(65)90152-5}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-0013801527&origin=resultslist&sort=plf-f&src=s&sid=90fc18aa5ca90e60aa30f007d2227dcf&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22The+dynamics+of+helminth+infections%2C+with+special+reference+to+schistosomes%22%29&sl=128&sessionSearchId=90fc18aa5ca90e60aa30f007d2227dcf&relpos=0}{\mbox{[Scopus]}} $
• [7] C.E. Madubueze, Z. Chazuka, I.O. Onwubuya, F. Fatmawati and C.W. Chukwu, On the mathematical modeling of schistosomiasis transmission dynamics with heterogeneous intermediate host, Front. Appl. Math. Stat., 8, 1020161. $ \href{https://doi.org/10.3389/fams.2022.1020161}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85140927626&origin=resultslist&sort=plf-f&src=s&sid=90fc18aa5ca90e60aa30f007d2227dcf&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22On+the+mathematical+modeling+of+schistosomiasis+transmission+dynamics+with+heterogeneous+intermediate+host%22%29&sl=128&sessionSearchId=90fc18aa5ca90e60aa30f007d2227dcf&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000876865600001}{\mbox{[Web of Science]}}$
• [8] S. Wang and R.C. Spear, Exploring the contribution of host susceptibility to epidemiological patterns of schistosoma japonicum infection using an individual-based model, Am. J. Trop. Med. Hyg., 92(6) (2015, 1245–1252. $ \href{https://doi.org/10.4269/ajtmh.14-0691}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-84930584269&origin=resultslist&sort=plf-f&src=s&sid=90fc18aa5ca90e60aa30f007d2227dcf&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Exploring+the+contribution+of+host+susceptibility+to+epidemiological+patterns+of+schistosoma+japonicum+infection+using+an+individual-based+model%22%29&sl=128&sessionSearchId=90fc18aa5ca90e60aa30f007d2227dcf&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000355785400027}{\mbox{[Web of Science]}} $
• [9] M. Graham, D. Ayabina, T.C. Lucas, B.S. Collyer, G.F. Medley, T.D. Hollingsworth and J. Toor, Schistox: An individual-based model for the epidemiology and control of schistosomiasis, Infect. Dis. Model., 6 (2021), 438–447. $ \href{https://doi.org/10.1016/j.idm.2021.01.010}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85101001192&origin=resultslist&sort=plf-f&src=s&sid=90fc18aa5ca90e60aa30f007d2227dcf&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Schistox%3A+An+individual-based+model+for+the+epidemiology+and+control+of+schistosomiasis%22%29&sl=128&sessionSearchId=90fc18aa5ca90e60aa30f007d2227dcf&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000621631300001}{\mbox{[Web of Science]}}$
• [10] M. Ciddio, L. Mari, S.H. Sokolow, G.A. De Leo, R. Casagrandi and M. Gatto, The spatial spread of schistosomiasis: A multidimensional network model applied to Saint-Louis region, Senegal, Adv. Water Resour., 108 (2017), 406–415. $ \href{https://doi.org/10.1016/j.advwatres.2016.10.012}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85006010719&origin=resultslist&sort=plf-f&src=s&sid=90fc18aa5ca90e60aa30f007d2227dcf&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22The+spatial+spread+of+schistosomiasis%3A+A+multidimensional+network+model+applied+to+Saint-Louis+region%2C+Senegal%22%29&sl=128&sessionSearchId=90fc18aa5ca90e60aa30f007d2227dcf&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000411868400032}{\mbox{[Web of Science]}}$
• [11] T. Manyangadze, M.J. Chimbari, M. Gebreslasie, P. Ceccato and S. Mukaratirwa, Modelling the spatial and seasonal distribution of suitable habitats of schistosomiasis intermediate host snails using MaxEnt in Ndumo area, KwaZulu-Natal Province, South Africa, Parasit. Vectors, 9(1) (2016), 1–10, 572 $\href{https://doi.org/10.1186/s13071-016-1834-5}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-84995684283&origin=resultslist&sort=plf-f&src=s&sid=90fc18aa5ca90e60aa30f007d2227dcf&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Modelling+the+spatial+and+seasonal+distribution+of+suitable+habitats+of+schistosomiasis+intermediate+host+snails+using+MaxEnt+in+Ndumo+area%2C+KwaZulu-Natal+Province%2C+South+Africa%22%29&sl=128&sessionSearchId=90fc18aa5ca90e60aa30f007d2227dcf&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000388145200004}{\mbox{[Web of Science]}} $
• [12] H. Zhang, P. Harvim and P. Georgescu, Preventing the spread of schistosomiasis in Ghana: possible outcomes of integrated optimal control strategies, J. Biol. Syst., 25(4) (2017), 625–655 $\href{https://doi.org/10.1142/S0218339017400058}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85035811848&origin=resultslist&sort=plf-f&src=s&sid=90fc18aa5ca90e60aa30f007d2227dcf&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Preventing+the+spread+of+schistosomiasis+in+Ghana%3A+possible+outcomes+of+integrated+optimal+control+strategies%22%29&sl=128&sessionSearchId=90fc18aa5ca90e60aa30f007d2227dcf&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000418693000005}{\mbox{[Web of Science]}} $
• [13] E. Kanyi, A.S. Afolabi and N.O. Onyango, Mathematical modeling and analysis of transmission dynamics and control of schistosomiasis, J. Appl. Math., 2021 (2021), 6653796. $\href{https://doi.org/10.1155/2021/6653796}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85107210152&origin=resultslist&sort=plf-f&src=s&sid=90fc18aa5ca90e60aa30f007d2227dcf&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Mathematical+modeling+and+analysis+of+transmission+dynamics+and+control+of+schistosomiasis%22%29&sl=128&sessionSearchId=90fc18aa5ca90e60aa30f007d2227dcf&relpos=0}{\mbox{[Scopus]}} $
• [14] J. M. Haugh, Analysis of reaction-diffusion systems with anomalous subdiffusion, Biophys. J., 97(2) (2009), 435–442. $\href{https://doi.org/10.1016/j.bpj.2009.05.014}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-68949136901&origin=resultslist&sort=plf-f&src=s&sid=90fc18aa5ca90e60aa30f007d2227dcf&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Analysis+of+reaction-diffusion+systems+with+anomalous+subdiffusion%22%29&sl=128&sessionSearchId=90fc18aa5ca90e60aa30f007d2227dcf&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000268428700004}{\mbox{[Web of Science]}} $
• [15] R. Li, Y. Song, H.Wang, G.-P. Jiang and M. Xiao, Reactive–diffusion epidemic model on human mobility networks: Analysis and applications to COVID-19 in China, Phys. A: Stat. Mech. Appl., 609 (2023), 128337. $\href{https://doi.org/10.1016/j.physa.2022.128337}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85145599420&origin=resultslist&sort=plf-f&src=s&sid=90fc18aa5ca90e60aa30f007d2227dcf&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Reactive%E2%80%93diffusion+epidemic+model+on+human+mobility+networks%3A+Analysis+and+applications+to+COVID-19+in+China%22%29&sl=128&sessionSearchId=90fc18aa5ca90e60aa30f007d2227dcf&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000895783100004}{\mbox{[Web of Science]}} $
• [16] W. Nur, Trisilowati1, A. Suryanto andW.M. Kusumawinahyu, Mathematical model of schistosomiasis with health education and molluscicide intervention, J. Phys. Conf. Ser., 1821(1) (2021), 012033 $\href{https://doi.org/10.1088/1742-6596/1821/1/012033}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85103918500&origin=resultslist&sort=plf-f&src=s&sid=90fc18aa5ca90e60aa30f007d2227dcf&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Mathematical+model+of+schistosomiasis+with+health+education+and+molluscicide+intervention%22%29&sl=128&sessionSearchId=90fc18aa5ca90e60aa30f007d2227dcf&relpos=0}{\mbox{[Scopus]}} $
• [17] M. Diaby, Stability analysis of a schistosomiasis transmission model with control strategies, Biomath, 4(1) (2015), 1-13. $ \href{https://doi.org/10.11145/j.biomath.2015.04.161}{\mbox{[CrossRef]}}$
• [18] E.T. Chiyaka and W. Garira, Mathematical analysis of the transmission dynamics of schistosomiasis in the human-snail hosts, J. Biol. Syst., 17(3) (2009), 397–423. $\href{https://doi.org/10.1142/S0218339009002910}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-69049089967&origin=resultslist&sort=plf-f&src=s&sid=90fc18aa5ca90e60aa30f007d2227dcf&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Mathematical+analysis+of+the+transmission+dynamics+of+schistosomiasis+in+the+human-snail+hosts%22%29&sl=128&sessionSearchId=90fc18aa5ca90e60aa30f007d2227dcf&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000269124600004}{\mbox{[Web of Science]}} $
• [19] J. Zwang and P.L. Olliaro, Clinical efficacy and tolerability of praziquantel for intestinal and urinary schistosomiasis-a meta-analysis of comparative and non-comparative clinical trials, PLoS Negl. Trop. Dis., 8(11) (2014), e3286. $ \href{https://doi.org/10.1371/journal.pntd.0003286}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-84920443817&origin=resultslist&sort=plf-f&src=s&sid=90fc18aa5ca90e60aa30f007d2227dcf&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Clinical+efficacy+and+tolerability+of+praziquantel+for+intestinal+and+urinary+schistosomiasis-a+meta-analysis+of+comparative+and+non-comparative+clinical+trials%22%29&sl=128&sessionSearchId=90fc18aa5ca90e60aa30f007d2227dcf&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000345514000025}{\mbox{[Web of Science]}}$
• [20] R. Redlinger, Existence theorem for semilinear parabolic systems with functionals, Nonlinear Anal., 8(6) (1984), 667–682. $ \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-0000699171&origin=resultslist&sort=plf-f&src=s&sid=90fc18aa5ca90e60aa30f007d2227dcf&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Existence+theorem+for+semilinear+parabolic+systems+with+functionals%22%29&sl=128&sessionSearchId=90fc18aa5ca90e60aa30f007d2227dcf&relpos=0}{\mbox{[Scopus]}} $
• [21] W. Wang and X.-Q. Zhao, Basic reproduction numbers for reaction diffusion epidemic models, SIAM J. Appl. Dyn. Syst., 11(4) (2012), 1652–1673. $\href{https://doi.org/10.1137/120872942}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-84871394066&origin=resultslist&sort=plf-f&src=s&sid=90fc18aa5ca90e60aa30f007d2227dcf&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Basic+reproduction+numbers+for+reaction+diffusion+epidemic+models%22%29&sl=128&sessionSearchId=90fc18aa5ca90e60aa30f007d2227dcf&relpos=1}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000312701800017}{\mbox{[Web of Science]}} $
• [22] Y. Song and T. Zhang, Global stability of the positive equilibrium of a mathematical model for unstirred membrane reactors, B. Korean Math. Soc., 54(2) (2017), 383–389. $\href{http://dx.doi.org/10.4134/BKMS.b150560}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85016435417&origin=resultslist&sort=plf-f&src=s&sid=90fc18aa5ca90e60aa30f007d2227dcf&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Global+stability+of+the+positive+equilibrium+of+a+mathematical+model+for+unstirred+membrane+reactors%22%29&sl=128&sessionSearchId=90fc18aa5ca90e60aa30f007d2227dcf&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000401097900003}{\mbox{[Web of Science]}} $
• [23] B. Kammegne, K. Oshinubi, O. Babasola, O. Peter, O. Longe, R. Ogunrinde, E. Titiloye, R. Abah and J. Demongeot, Mathematical modelling of the spatial distribution of a COVID-19 outbreak with vaccination using diffusion equation, Pathogens, 12(1) (2023), 88. $\href{https://doi.org/10.3390/pathogens12010088}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85146783863&origin=resultslist&sort=plf-f&src=s&sid=90fc18aa5ca90e60aa30f007d2227dcf&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Mathematical+modelling+of+the+spatial+distribution+of+a+COVID-19+outbreak+with+vaccination+using+diffusion+equation%22%29&sl=128&sessionSearchId=90fc18aa5ca90e60aa30f007d2227dcf&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000931406700001}{\mbox{[Web of Science]}} $
• [24] R. Peng and M.Wang, Global stability of the equilibrium of a diffusive Holling-Tanner prey-predator model, Appl. Math. Lett., 20(6) (2007), 664–670. $ \href{https://doi.org/10.1016/j.aml.2006.08.020}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-33947158204&origin=resultslist&sort=plf-f&src=s&sid=90fc18aa5ca90e60aa30f007d2227dcf&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Global+stability+of+the+equilibrium+of+a+diffusive+Holling-Tanner+prey-predator+model%22%29&sl=128&sessionSearchId=90fc18aa5ca90e60aa30f007d2227dcf&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000246062200011}{\mbox{[Web of Science]}}$
• [25] J. Kim, W. Su and Y. Song, On stability of a polynomial, J. Appl. Math. Inform., 36(3-4) (2018), 231-236. $ \href{https://doi.org/10.14317/jami.2018.231}{\mbox{[CrossRef]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000441217500006}{\mbox{[Web of Science]}}$
• [26] J.M. Heffernan, R.J. Smith and L.M. Wahl, Perspectives on the basic reproductive ratio, J. R. Soc. Interface., 2(4) (2005), 281–293. $\href{https://doi.org/10.1098%2Frsif.2005.0042}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-32044460132&origin=resultslist&sort=plf-f&src=s&sid=90fc18aa5ca90e60aa30f007d2227dcf&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Perspectives+on+the+basic+reproductive+ratio%22%29&sl=128&sessionSearchId=90fc18aa5ca90e60aa30f007d2227dcf&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000234342000002}{\mbox{[Web of Science]}} $
• [27] H.W. Hethcote and H.R. Thieme, Stability of the endemic equilibrium in epidemic models with subpopulations, Math. Biosci., 75(2) (1985), 205–227. $ \href{https://doi.org/10.1016/0025-5564(85)90038-0}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-0021984692&origin=resultslist&sort=plf-f&src=s&sid=90fc18aa5ca90e60aa30f007d2227dcf&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Stability+of+the+endemic+equilibrium+in+epidemic+models+with+subpopulations%22%29&sl=128&sessionSearchId=90fc18aa5ca90e60aa30f007d2227dcf&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:A1985ARR6100005}{\mbox{[Web of Science]}}$
• [28] C. Tadmon and S. Foko, A transmission dynamics model of COVID-19: Case of Cameroon, Infect. Dis. Model., 7(2) (2022), 211–249. $\href{https://doi.org/10.1016%2Fj.idm.2022.05.002}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85131406574&origin=resultslist&sort=plf-f&src=s&sid=90fc18aa5ca90e60aa30f007d2227dcf&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22A+transmission+dynamics+model+of+COVID-19%3A+Case+of+Cameroon%22%29&sl=128&sessionSearchId=90fc18aa5ca90e60aa30f007d2227dcf&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000808292000005}{\mbox{[Web of Science]}} $
• [29] C.N.T. Mfangnia, H.E.Z. Tonnang, B. Tsanou and J. Herren, Mathematical modelling of the interactive dynamics of wild and microsporidia MB-infected mosquitoes, Math. Biosci. Eng., 20(8) (2023), 15167–15200. $ \href{https://doi.org/10.3934/mbe.2023679}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85169296882&origin=resultslist&sort=plf-f&src=s&sid=90fc18aa5ca90e60aa30f007d2227dcf&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Mathematical+modelling+of+the+interactive+dynamics+of+wild+and+microsporidia+MB-infected+mosquitoes%22%29&sl=128&sessionSearchId=90fc18aa5ca90e60aa30f007d2227dcf&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:001041064200006}{\mbox{[Web of Science]}}$
• [30] J. La Salle, The Stability of Dynamical Systems, Philadelphia, PA, USA: SIAM, (1976). $ \href{https://epubs.siam.org/doi/book/10.1137/1.9781611970432}{\mbox{[Web]}}$
• [31] H. Marquez, Nonlinear Control Systems: Analysis and Design, Hoboken, New Jersey: John Wiley & Sons, Inc., (2003). $ \href{https://www.wiley.com/en-ie/Nonlinear+Control+Systems%3A+Analysis+and+Design+-p-9780471427995#whatsnew-section}{\mbox{[Web]}}$
• [32] S. Marino, I.B. Hogue, C.J. Ray and D.E. Kirschner, A methodology for performing global uncertainty and sensitivity analysis in systems biology, J. Theor. Biol., 254(1) (2008), 178–196. $\href{https://doi.org/10.1016/j.jtbi.2008.04.011}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-45449094504&origin=resultslist&sort=plf-f&src=s&sid=90fc18aa5ca90e60aa30f007d2227dcf&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22A+methodology+for+performing+global+uncertainty+and+sensitivity+analysis+in+systems+biology%22%29&sl=128&sessionSearchId=90fc18aa5ca90e60aa30f007d2227dcf&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000258938200020}{\mbox{[Web of Science]}} $