Rainfall risk and the potential of reduced tillage systems to conserve soil water in semi-arid cropping systems of southern Africa

W. Mupangwa; S. Walker; E. Masvaya; M. Magombeyi; P. Munguambe; W. Mupangwa; S. Walker; E. Masvaya; M. Magombeyi; P. Munguambe

doi:10.3934/agrfood.2016.1.85

AIMS Agriculture and Food

2016, Volume 1, Issue 1: 85-101. doi: 10.3934/agrfood.2016.1.85

Previous Article Next Article

Research article

Rainfall risk and the potential of reduced tillage systems to conserve soil water in semi-arid cropping systems of southern Africa

1.
International Crops Research Institute for the Semi-Arid Tropics (ICRISAT), P O Box 776, Bulawayo, Zimbabwe
2.
International Maize and Wheat Improvement Center (CIMMYT), ILRI Sholla Campus, P.O. Box 5689, Addis Ababa, Ethiopia
3.
Department Soil, Crop and Climate Sciences, University of Free State, Bloemfontein, South Africa
4.
School of Civil and Environmental Engineering, Witwatersrand University, Private Bag X3 Wits, 2050, South Africa
5.
Faculty of Agronomy & Forest Engineering, University Eduardo Mondlane, P O Box 257 Maputo, Mozambique

Received: 09 January 2016 Accepted: 23 February 2016 Published: 25 January 2016

Improvement of household food security in the Limpopo Basin has been elusive due to a combination of factors related to information and market constraints, but also farmers’ risk aversion induced by the high variability of rainfall during the growing season. The purpose of this study was to (1) characterize the rainfall and growing season patterns experienced by smallholder farmers, and (2) measure soil water dynamics in ripper and basin tillage systems being promoted in the semi-arid Limpopo Basin of southern Africa. The results show that the second half of the growing season receives more rainfall than the first half in the Limpopo Basin. However, rainfall is more variable during the January-March than the October-December period. Growing seasons start earlier and end later in the Mozambique part of the basin which is closer to the Indian Ocean. The Limpopo Basin is prone to two and three week dry spells with chances of 14 day spells higher (34–42%) than the 21 day spells (8–12%). The chances of 14 and 21 day dry spells increase substantially during the second half of the growing season. The 1980–1990 was one of the driest decades in the Limpopo Basin. Planting basin system conserved more soil water on sandy loam (18–24%) and clay loam (4–12%) soils than the conventional practice during flowering and grain filling maize growth stages. Ripper had 17–29% more soil water than conventional practice during flowering and grain filling maize growth stages. There is a high risk of dry spells and soil water deficits in smallholder cropping systems of the Limpopo basin. There is therefore scope in promoting rain and soil water management technologies, and good land husbandry in order to reduce risk of crop failure in the smallholder cropping systems.

Keywords:

Citation: W. Mupangwa, S. Walker, E. Masvaya, M. Magombeyi, P. Munguambe. Rainfall risk and the potential of reduced tillage systems to conserve soil water in semi-arid cropping systems of southern Africa[J]. AIMS Agriculture and Food, 2016, 1(1): 85-101. doi: 10.3934/agrfood.2016.1.85

Related Papers:

[1]	Eunha Shim, Beth Kochin, Alison Galvani . Insights from epidemiological game theory into gender-specific vaccination against rubella. Mathematical Biosciences and Engineering, 2009, 6(4): 839-854. doi: 10.3934/mbe.2009.6.839
[2]	Hyun Mo Yang, André Ricardo Ribas Freitas . Biological view of vaccination described by mathematical modellings: from rubella to dengue vaccines. Mathematical Biosciences and Engineering, 2019, 16(4): 3195-3214. doi: 10.3934/mbe.2019159
[3]	Lili Liu, Xi Wang, Yazhi Li . Mathematical analysis and optimal control of an epidemic model with vaccination and different infectivity. Mathematical Biosciences and Engineering, 2023, 20(12): 20914-20938. doi: 10.3934/mbe.2023925
[4]	Pannathon Kreabkhontho, Watchara Teparos, Thitiya Theparod . Potential for eliminating COVID-19 in Thailand through third-dose vaccination: A modeling approach. Mathematical Biosciences and Engineering, 2024, 21(8): 6807-6828. doi: 10.3934/mbe.2024298
[5]	Eunha Shim . Optimal strategies of social distancing and vaccination against seasonal influenza. Mathematical Biosciences and Engineering, 2013, 10(5&6): 1615-1634. doi: 10.3934/mbe.2013.10.1615
[6]	Majid Jaberi-Douraki, Seyed M. Moghadas . Optimal control of vaccination dynamics during an influenza epidemic. Mathematical Biosciences and Engineering, 2014, 11(5): 1045-1063. doi: 10.3934/mbe.2014.11.1045
[7]	Xunyang Wang, Canyun Huang, Yuanjie Liu . A vertically transmitted epidemic model with two state-dependent pulse controls. Mathematical Biosciences and Engineering, 2022, 19(12): 13967-13987. doi: 10.3934/mbe.2022651
[8]	Hamed Karami, Pejman Sanaei, Alexandra Smirnova . Balancing mitigation strategies for viral outbreaks. Mathematical Biosciences and Engineering, 2024, 21(12): 7650-7687. doi: 10.3934/mbe.2024337
[9]	Lan Zou, Jing Chen, Shigui Ruan . Modeling and analyzing the transmission dynamics of visceral leishmaniasis. Mathematical Biosciences and Engineering, 2017, 14(5&6): 1585-1604. doi: 10.3934/mbe.2017082
[10]	Hai-Feng Huo, Tian Fu, Hong Xiang . Dynamics and optimal control of a Zika model with sexual and vertical transmissions. Mathematical Biosciences and Engineering, 2023, 20(5): 8279-8304. doi: 10.3934/mbe.2023361

Abstract

References

[1]	FAO (1986) African agriculture: The next 25 years. FAO, Rome, Italy
[2]	Rosegrant M, Cai X, Cline S, et al. (2002) The role of rainfed agriculture in the future of global food production. International Food Policy Research Institute. Discussion Paper N^o 90. Washington, D.C. February 2002.
[3]	Chilonda P, Machethe C, Minde I (2007) Poverty, food security and agricultural trends in Southern Africa. Regional Strategic Analysis and Knowledge Support System for Southern Africa (ReSAKSS-SA), Discussion Paper N^o1. ReSAKSS-SA, IWMI and ICRISAT, Pretoria, South Africa
[4]	Cooper PJM, Dimes J, Rao KPC, et al. (2008) Coping better with current climatic variability in the rain-fed farming systems of sub-Saharan Africa: An essential first step in adapting to future climate change? Agric Ecosyst Environ 126: 24-35. doi: 10.1016/j.agee.2008.01.007
[5]	Twomlow S, Mugabe FT, Mwale M, et al. (2008) Building adaptive capacity to cope with increasing vulnerability due to climatic change in Africa - A new approach. J Phys Chem Earth 33: 780-787. doi: 10.1016/j.pce.2008.06.048
[6]	Graef F, Haigis J (2001) Spatial and temporal rainfall variability in the Sahel and its effects on farmers’ management strategies. J Arid Environ 48: 221-231 doi: 10.1006/jare.2000.0747
[7]	Rockström J, Falkenmark M (2000) Semiarid crop production from a hydrological perspective: gap between potential and actual yields. Crit Rev Plant Sci 19: 319-346. doi: 10.1080/07352680091139259
[8]	Tadross M, Hewitson BC, Usman MT (2005) The interannual variability of onset of the maize growing season over South Africa and Zimbabwe. J Clim 18: 3356-3372. doi: 10.1175/JCLI3423.1
[9]	Rockström J, Barron J, Fox P (2002) Rainwater management for increased productivity among smallholder farmers in drought prone environments. J Phys Chem Earth 27: 949-959. doi: 10.1016/S1474-7065(02)00098-0
[10]	Cook C, Reason CJ, Hewitson BC (2004) Wet and dry spells within particularly wet and dry summers in the South African rainfall region. Clim Res 26: 17-31. doi: 10.3354/cr026017
[11]	Usman MT, Archer E, Johnston P, et al. (2004) A conceptual framework for enhancing the utility of rainfall hazard forecasts for agriculture in marginal environments. Nat Haz 34: 111-129.
[12]	Chibulu B (2007) Effect of rainfall variability on crop yield under semi-arid conditions at sub-catchment level. MSc. Thesis. Department of Civil Engineering, University of Zimbabwe, Harare.
[13]	Oosterhout van SAM (1996) Coping strategies of smallholder farmers with adverse weather conditions regarding seed deployment of small grain crops during 1994/1995 cropping season in Zimbabwe. Volumes 1 to 3. SADC/GTZ, Harare.
[14]	Stewart JJ (1988) Response farming in rainfed agriculture. Wharf Foundation Press, Davis.
[15]	Rockström J (2000) Water resources management in smallholder farms in eastern and southern Africa: An overview. J Phys Chem Earth B 25: 275-283. doi: 10.1016/S1464-1909(00)00015-0
[16]	Rockström J, Barron J, Fox P (2003) Water productivity in rainfed agriculture: Challenges and opportunities for smallholder farmers in drought prone agroecosystems. In: Water Productivity in Agriculture: Limits and Opportunities for Improvement. Kilne JW, Barker R, Molden D (eds.). CAB International. pp145-162.
[17]	Mupangwa W, Love D, Twomlow SJ (2006) Soil-water conservation and rainwater harvesting strategies in the semi-arid Mzingwane Catchment, Limpopo Basin, Zimbabwe. J Phys Chem Earth 31: 893-900. doi: 10.1016/j.pce.2006.08.042
[18]	Motsi KE, Chuma E, Mukamuri BB (2004) Rainwater harvesting for sustainable agriculture in communal lands of Zimbabwe. J Phys Chem Earth 29: 1069-1073. doi: 10.1016/j.pce.2004.08.008
[19]	Mugabe F (2004) Evaluation of the benefits of infiltration pits on soil moisture in semi-arid Zimbabwe. J Agron 3: 188-190. doi: 10.3923/ja.2004.188.190
[20]	Keesstra SD, Geissen V, Mosse K, et al. (2012) Soil as a filter for groundwater quality. Cur Opin Environ Sust 4: 507-516. doi: 10.1016/j.cosust.2012.10.007
[21]	Brevik EC, Cerdà A, Mataix-Solera J, et al. (2015) The interdisciplinary nature of soil. Soil 1: 117-129. doi: 10.5194/soil-1-117-2015
[22]	de Moraes Sá JC, Séguy L, Tivet F, et al. (2015). Carbon depletion by plowing and its restoration by no-till cropping systems in oxisols of sub-Tropical and Tropical agro-ecosystems of Brazil. Land Degrad Develop 26: 531-543. doi: 10.1002/ldr.2218
[23]	Tesfahunegn GB (2016) Soil quality indicators response to land use and soil management systems in northern Ethiopia’s catchment. Land Degrad Develop 27: 438-448. doi: 10.1002/ldr.2245
[24]	Vogel H (1992) Tillage effects on maize yield, rooting depth and soil water content on sandy soils in Zimbabwe. Field Crops Res 33: 376-384.
[25]	Enfors E, Barron J, Makurira H, et al. (2011) Yield and soil system changes from conservation tillage in dryland farming: A case study from North Eastern Tanzania. Agric Water Manage 98: 1687-1695. doi: 10.1016/j.agwat.2010.02.013
[26]	Laudicina VA, Novara A, Barbera V, et al. (2015) Long term tillage and cropping system effects on chemical and biochemical characteristics of soil organic matter in a Meditterrean semi-arid environment. Land Degrad Develop 26: 45-53. doi: 10.1002/ldr.2293
[27]	Makurira H, Savenije HHG, Uhlenbrook S, et al. (2011) The effect of system innovations on water productivity in subsistence rainfed agricultural systems in semi-arid Tanzania. Agric Water Manage 98: 1696-703. doi: 10.1016/j.agwat.2011.05.003
[28]	Mupangwa W, Twomlow S, Walker S (2012) Dead level contours and infiltration pits for risk mitigation in smallholder cropping systems of southern Zimbabwe. J Phys Chem Earth 47-48: 166-172. doi: 10.1016/j.pce.2011.06.011
[29]	Mhizha A, Ndiritu JG (2013) Assessing crop yield benefits from in situ rainwater harvesting through contour ridges in semi-arid Zimbabwe. J Phys Chem Earth 66: 123-130. doi: 10.1016/j.pce.2013.09.008
[30]	Adimassu Z, Mekonnen K, Yirgai C, et al. (2014) Effect of soil bunds on runoff, soil and nutrient losses, and crop yield in the Central Highlands of Ethiopia. Land Degrad Develop 25: 554-564. doi: 10.1002/ldr.2182
[31]	Nyagumbo I (2002) The effect of three tillage systems on seasonal water budgets and drainage of two Zimbabwean soils under maize. Ph.D. Thesis, Department of Soil Science and Agricultural Engineering, University of Zimbabwe. 251pp.
[32]	Mupangwa W, Twomlow S, Walker S, et al. (2007) Effect of minimum tillage and mulching on maize (Zea mays L.) yield and water content of clayey and sandy soils. J Phys Chem Earth 32: 1127-1134.
[33]	Mzezewa J, Gwata ET, van Rensburg LD (2011) Yield and seasonal water productivity of sunflower as affected by tillage and cropping systems under dryland conditions in the Limpopo Province of South Africa. Agric Water Manage 98: 1641-1648. doi: 10.1016/j.agwat.2011.06.003
[34]	FAO (2004) Drought impact mitigation and prevention in the Limpopo River Basin. Land and Water Discussion Paper 4. Food and Agriculture Organization of the United Nations, Rome. Available from: http://www.fao.org/docrep/008/y5744e/y5744e00.HTM.
[35]	Woltering L (2005) Estimating the influence of on-farm conservation practices on the water balance: Case of the Mzinyathini catchment in Zimbabwe. M.Sc. Thesis. Delft University of Technology, The Netherlands.
[36]	Zhu T, Ringler C (2010) Climate change implications for water resources in the Limpopo River Basin. International Food Policy Research Institute. Discussion Paper N^o 00961. Washington, D.C. April 2010.
[37]	Stern R, Knock J, Rijks D, et al. (2006) INSTAT Climatic Guide. Available from http://www.reading.ac.uk/ssc/software/instat/climatic.pdf.
[38]	Evans LT (1979) Crop Physiology. Blackie & Sons Pvt. Ltd., Bombay.
[39]	Stern R, Knock J, Rijks D, et al. (2003) INSTAT Climatic Guide. Available from http://www.reading.ac.uk/ssc/software/instat/climatic.pdf.
[40]	Stern R, Dennett MD, Dale IC (1982) Analyzing daily rainfall measurements to give agronomically useful results. II. A modeling approach. Exp Agric 18: 237-253.
[41]	Stern R, Dennett MD, Garbutt DJ (1981) The start of the rains in West Africa. J Clim 1: 59-68.
[42]	Le Barbe L, Lebel T, Tapsoba D (2002) Rainfall variability in West Africa during the years 1950-90. J Clim 15: 187-202.
[43]	Hayes MJ, Svoboda MD, Wilhite DA, et al. (1999) Monitoring the 1996 drought using the Standardized Precipitation Index. Bull Am Meteorol Soc 80: 429-438.
[44]	Anderson JM, Ingram JSI (1993) Tropical Soil Biology and Fertility. A Handbook of Methods. 2nd Edition. C.A.B. International, Wallingford, UK, 221pp.
[45]	Makuvaro V, Walker S, Munodawafa A, et al. (2014) An overview of current agronomic practices of smallholder farmers in semi-arid Central and Western Zimbabwe. Afr J Agric Res 9: 2710-2720. doi: 10.5897/AJAR11.606
[46]	Rurinda J, Mapfumo P, van Wijk MT, et al. (2014) Sources of vulnerability to a variable and changing climate among smallholder households in Zimbabwe: A participatory analysis. Clim Risk Manage 3: 65-78. doi: 10.1016/j.crm.2014.05.004
[47]	Mason SJ, Lindesay JA, Tyson PD (1994) Simulating drought in southern Africa using sea surface temperature variations. Water SA 20: 15-22.
[48]	Lyon B, Mason JJ (2007) The 1997-98 summer rainfall season in southern Africa. Part 1. Observations. J Clim 20: 5134-5148.
[49]	Thierfelder C, Wall PC (2009) Effects of conservation agriculture techniques on infiltration and soil water content in Zambia and Zimbabwe. Soil Till Res 105: 217-227. doi: 10.1016/j.still.2009.07.007
[50]	Mkoga ZJ, Tumbo SD, Kihupi N, et al. (2010) Extrapolating effects of conservation tillage on yield, soil moisture and dry spell mitigation using simulation modelling. J Phys Chem Earth 35: 686-698. doi: 10.1016/j.pce.2010.07.036
[51]	Bouma JA, Hegde SS, Lasage R (2016) Assessing the returns to water harvesting: A meta-analysis. Agric Water Manage 163: 100-109. doi: 10.1016/j.agwat.2015.08.012
[52]	Shumba EM, Waddington SR, Rukuni M (1992) Use of tine tillage with attrazine weed control to permit earlier planting of maize by small-holder farmers in Zimbabwe. Exp Agric 28: 443-452. doi: 10.1017/S0014479700020159
[53]	Milgroom J, Giller KE (2013) Courting the rain: Rethinking seasonality and adaptation to recurrent drought in semi-arid southern Africa. Agric Syst 118: 91-104. doi: 10.1016/j.agsy.2013.03.002
[54]	Funk C, Budde ME (2008) Phenologically-tuned MODIS NDVI-based production anomaly estimates for Zimbabwe. Rem Sens Environ 113: 115-125.
[55]	Mupangwa W (2008) Water and nitrogen management for risk mitigation in semi-arid cropping systems. PhD Thesis (unpublished). University of Free State, South Africa.
[56]	Dennett MD (1987) Variation of rainfall: the background to soil and water management in dryland regions. Soil Use Manage 3: 47-51. doi: 10.1111/j.1475-2743.1987.tb00709.x
[57]	Tesfaye K, Gbegbelegbe S, Cairns JE, et al. (2015) Maize systems under climate change in sub-Saharan Africa Potential impacts on production and food security. Int J Clim Change Strat Manage 7: 247-271. doi: 10.1108/IJCCSM-01-2014-0005
[58]	Thierfelder C, Rusinamhodzi L, Ngwira AR, et al. (2014) Conservation agriculture in Southern Africa: Advances in knowledge. Ren Agric Food Syst 30: 328-348.
[59]	Patt A, Suarez P, Gwata C (2005) Effects of seasonal climate forecasts and participatory workshops among subsistence farmers in Zimbabwe. Proc Natl Acad Sci U S A 102: 12623-12628. doi: 10.1073/pnas.0506125102
[60]	Füssel HM, Klein RJT (2006) Climate change vulnerability assessments: An evolution of conceptual thinking. Clim Change 75: 301-329. doi: 10.1007/s10584-006-0329-3
[61]	Archer E, Mukhala E, Walker S, et al. (2007) Sustaining agricultural production and food security in southern Africa: An improved role for climate prediction? Clim Change 83: 287-300. doi: 10.1007/s10584-006-9192-5
[62]	Landman WA, Klopper E (1998) 15 year simulation of the December-March rainfall season of the 1980s and 1990s using canonical correlation analysis (CCA). Water SA 24: 281-286
[63]	Bonifacio R (2015) Southern Africa Growing Season 2015-2016: Facing El Nino in Difficult Circumstances. What to Expect: Historical Evidence and Context. VAM Food Security Analysis. World Food Programme. Available from: www.wfp.org.
[64]	FAO (2015) The 2015-2016 El Niño Early action and response for agriculture, food security and nutrition. Working Report, 14 December 2015. Food and Agriculture Organization of the United Nations. Available from: www.fao.org/resilience.
[65]	IPCC (2007) In: Parry ML, Canziani OF, Palutikof JP, van der Linden PJ, Hanson CE (Eds), Climate Change 2007: Impacts, Adaptation and Vulnerability. Fourth Assessment Report of the Intergovernmental Panel on Climate Change, Group II, Cambridge University Press, Cambridge, pp. 273-313.
[66]	Cairns JE, Hellin J, Sonder K, et al. (2013). Adapting maize production to climate change in sub-Saharan Africa. Food Sec 5: 345-360. doi: 10.1007/s12571-013-0256-x
[67]	Rockström J, Karlberg L, Wani SP, et al. (2010) Managing water in rainfed agriculture - The need for a paradigm shift. Agric Water Manage 97: 543-550. doi: 10.1016/j.agwat.2009.09.009
[68]	Mupangwa W, Twomlow S, Walker S (2008) The influence of conservation tillage methods on soil water regimes in semi-arid southern Zimbabwe. J Phys Chem Earth 33: 762-767. doi: 10.1016/j.pce.2008.06.049

This article has been cited by:

1.	Impact of vaccine arrival on the optimal control of a newly emerging infectious disease: A theoretical study, 2012, 9, 1551-0018, 539, 10.3934/mbe.2012.9.539
2.	Bruno Buonomo, Modeling ITNs Usage: Optimal Promotion Programs Versus Pure Voluntary Adoptions, 2015, 3, 2227-7390, 1241, 10.3390/math3041241
3.	Hamadjam Abboubakar, Jean Claude Kamgang, Leontine Nkague Nkamba, Daniel Tieudjo, Bifurcation thresholds and optimal control in transmission dynamics of arboviral diseases, 2018, 76, 0303-6812, 379, 10.1007/s00285-017-1146-1
4.	Benjamin Riche, Hélène Bricout, Marie-Laure Kürzinger, Sylvain Roche, Jean Iwaz, Jean-François Etard, René Ecochard, Modeling and predicting the long-term effects of various strategies and objectives of varicella-zoster vaccination campaigns, 2016, 15, 1476-0584, 927, 10.1080/14760584.2016.1183483
5.	Lingcai Kong, Jinfeng Wang, Weiguo Han, Zhidong Cao, Modeling Heterogeneity in Direct Infectious Disease Transmission in a Compartmental Model, 2016, 13, 1660-4601, 253, 10.3390/ijerph13030253
6.	Nkengafac Villyen Motaze, Zinhle E. Mthombothi, Olatunji Adetokunboh, C. Marijn Hazelbag, Enrique M. Saldarriaga, Lawrence Mbuagbaw, Charles Shey Wiysonge, The Impact of Rubella Vaccine Introduction on Rubella Infection and Congenital Rubella Syndrome: A Systematic Review of Mathematical Modelling Studies, 2021, 9, 2076-393X, 84, 10.3390/vaccines9020084
7.	BRUNO BUONOMO, ON THE OPTIMAL VACCINATION STRATEGIES FOR HORIZONTALLY AND VERTICALLY TRANSMITTED INFECTIOUS DISEASES, 2011, 19, 0218-3390, 263, 10.1142/S0218339011003853
8.	Bruno Buonomo, 2014, Chapter 3, 978-3-319-06922-7, 23, 10.1007/978-3-319-06923-4_3
9.	Chairat Modnak, Jin Wang, Zindoga Mukandavire, Simulating optimal vaccination times during cholera outbreaks, 2014, 07, 1793-5245, 1450014, 10.1142/S1793524514500144
10.	Drew Posny, Jin Wang, Zindoga Mukandavire, Chairat Modnak, Analyzing transmission dynamics of cholera with public health interventions, 2015, 264, 00255564, 38, 10.1016/j.mbs.2015.03.006
11.	Matt J. Keeling, Andrew Shattock, Optimal but unequitable prophylactic distribution of vaccine, 2012, 4, 17554365, 78, 10.1016/j.epidem.2012.03.001
12.	Bruno Buonomo, Cruz Vargas-De-León, Effects of Mosquitoes Host Choice on Optimal Intervention Strategies for Malaria Control, 2014, 132, 0167-8019, 127, 10.1007/s10440-014-9894-z
13.	Bruno Buonomo, Piero Manfredi, Alberto d’Onofrio, Optimal time-profiles of public health intervention to shape voluntary vaccination for childhood diseases, 2019, 78, 0303-6812, 1089, 10.1007/s00285-018-1303-1
14.	Adison Thongtha, Chairat Modnak, Optimal COVID-19 epidemic strategy with vaccination control and infection prevention measures in Thailand, 2022, 7, 24680427, 835, 10.1016/j.idm.2022.11.002
15.	Calvin Tadmon, Arnaud Feukouo Fossi, Berge Tsanou, A two–strain avian–human influenza model with environmental transmission: Stability analysis and optimal control strategies, 2024, 10075704, 107981, 10.1016/j.cnsns.2024.107981
16.	Gui Guan, Zhenyuan Guo, Yanyu Xiao, Dynamical behaviors of a network-based SIR epidemic model with saturated incidence and pulse vaccination, 2024, 137, 10075704, 108097, 10.1016/j.cnsns.2024.108097
17.	Samiullah Salim, Fazal Dayan, Muhammad Azizur Rehman, Husam A. Neamah, Optimization and Control in Rubella Transmission Dynamics: A Boundedness-Preserving Numerical Model with Vaccination, 2024, 23529148, 101595, 10.1016/j.imu.2024.101595
18.	Habtamu Ayalew Engida, Demeke Fisseha, Malaria and leptospirosis co-infection: A mathematical model analysis with optimal control and cost-effectiveness analysis, 2025, 24682276, e02517, 10.1016/j.sciaf.2024.e02517
19.	Giovanni Ziarelli, Stefano Pagani, Nicola Parolini, Francesco Regazzoni, Marco Verani, A model learning framework for inferring the dynamics of transmission rate depending on exogenous variables for epidemic forecasts, 2025, 437, 00457825, 117796, 10.1016/j.cma.2025.117796

Reader Comments

Your name:*

Email:*
© 2016 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)