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Global dynamics of a model of hepatitis B virus infection in a sub-Saharan African rural area

International Journal of Biomathematics 2020年第6期13卷 257-298页

作者： Jean Pierre II Kouenkam Joseph Mbang Yves Emvudu Department of Mathematics Faculty of Science University of Yaounde I P.O.Box 812 YaoundeCameroon umi 209 ird/UPMC ummisco Bondy Projet MASAIE INRIA Grand Est France and Projet GRIMCAPEL1RIMACameroun

We formulate and systematically study a deterministic compartmental model of Hepatitis *** model has some important and novel features compared with the well-known basic model in the ***,it takes into account the differential susceptibility that follows the vaccine formulation employing three-doses *** points up the HbeAg status of carriers,their levels of viral replication,the fact that treatment being not curative is recommended only to a small proportion of chronic carriers,and finally the fact that only inactive carriers are able to recover from *** model has simple dynamical behavior which has a globally asymptotically stable disease-free equilibrium when the basic reproduction number R0≤1 and an endemic equilibrium when R0>*** the use of Lyapunov functions,when it exists,we prove the global asymptotic stability of the endemic equilibrium under some *** data from Tokombere,a rural area in Cameroon,numerical simulations are *** numerical simulations first confirm analytical results,second they suggest that a policy based on treatment could not significantly impact the course of the ***,they show as it is well known that vaccination is a very effective measure to control the ***,they show that neonatal vaccination influences more the course of infection than mass vaccination ***,they picture how much loss between consecutive doses of vaccine could be ***,it is suggested that for a Sub-saharan African rural area,two-thirds of expected incidence of Hepatitis B virus infection and one third of expected prevalence of chronic carriers could be averted by 2030 if the birth dose vaccination becomes systematic and if mass vaccination rate increases to up 10%.

关键词： Nonlinear dynamical systems Lyapunov methods inactive carriers differential susceptibility differential infectivity

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Modeling Microbial Decomposition in Real 3D Soil Structures Using Partial Differential Equations

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International Journal of Geosciences 2013年第10期4卷 15-26页

作者： Doanh Nguyen-Ngoc Babacar Leye Olivier Monga Patricia Garnier Naoise Nunan 1International Joint Unity (umi 209) ummisco IRD Bondy Cedex France 2INRA UMR Environnent and Bigcrops Thiverval Grignon France 3School of Applied Mathematics and Informatics Hanoi University of Science and Technology Hanoi Vietnam 1International Joint Unity (umi 209) ummisco IRD Bondy Cedex France 2UMMISCO-Cameroon International Joint Unity UMMISCO University of Yaounde 1 Cameroon IRD (Institut de Recherche pour le Developpement) University of Paris CNRS UMR 7618-Biochemistery and Continenatal Areas Ecology Thiverval-Grignon France Laboratory of Numericalanalysis and Computer Science (LANI) Ummisco UMI 209 IRD Saint Louis Unit University Gaston Berger of Saint Louis Saint-Louis Senegal School of Applied Mathematics and Informatics Hanoi University of Science and Technology Hanoi Vietnam

Partial Differential Equations (PDEs) have been already widely used to simulate various complex phenomena in porous media. This paper is one of the first attempts to apply PDEs for simulating in real 3D structures. We apply this scheme to the specific case study of the microbial decomposition of organic matter in soil pore space. We got a 3D geometrical representation of the pore space relating to a network of volume primitives. A mesh of the pore space is then created by using the network. PDEs system is solved by free finite elements solver Freefem3d in the particular mesh. We validate our PDEs model to experimental data with 3D Computed Tomography (CT) images of soil samples. Regarding the current state of art on soil organic matter decay models, our approach allows taking into account precise 3D spatialization of the decomposition process by a pore space geometry description.

关键词： Partial Differential Equations Soil Microbial Decomposition Pore Space 3D Geometry Modelling Computed Tomography

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On a diffusive bacteriophage dynamical model for bacterial infections

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International Journal of Biomathematics 2023年第7期16卷 47-89页

作者： Hyacinthe M.Ndongmo Teytsa Berge Tsanou Jean Lubuma Samuel Bowong Department of Mathematics and Computer Science University of Dschang P.O.Bor 67DschangCameroon Department of Mathematics and Applied Mathematics University of Pretoria Pretoria 0002South Africa ird umi 209 ummisco University of Yaounde I P..Bor 337YaoundeCameroon LIRIMA-EPITAG Team Project University of Yaounde I P.O.Bor 812YaoundeCameroon Department of Mathematics and Computer Science University of Douala P.0.Bor 24157DoualaCameroon

Bacteriophages or phages are viruses that infect bacteria and are increasingly used to control bacterial *** develop a reaction-diffusion model coupling the interactive dynamic of phages and bacteria with an epidemiological bacteria-borne disease *** the submodel without phage absorption,the basic reproduction number Ro is *** disease-free equilibrium(DFE)is shown to be globally asymptotically stable whenever Ro is less than one,while a unique globally asymptotically endemic equilibrium is proven whenever Ro exceeds *** the presence of phage absorption,the above stated classical condition based on Ro,as the average number of secondary human infections produced by susceptible/lysogen bacteria during their entire lifespan,is no longer suficient to guarantee the global stability of the *** thus derive an additional threshold No,which is the average offspring number of lysogen bacteria produced by one infected human during the phage-bacteria interactions,and prove that the DFE is globally asymptotically stable whenever both Ro and No are under unity,and infections persist uniformly whenever Ro is greater than ***,the discrete counterpart of the continuous partial differential equation model is derived by constructing a nonstandard finite difference scheme which is dynamically *** consistency is shown by constructing suitable discrete Lyapunov functionals thanks to which the global stability results for the continuous model are *** scheme is implemented in MatLab platform and used to assess the impact of spatial distribution of phages,on the dynamic of bacterial infections.

关键词： Bacterial infections diffusion NSFD phage absorption global stability

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A mathematical model of cholera in a periodic environment with control actions

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International Journal of Biomathematics 2020年第4期13卷 109-140页

作者： G.Kolaye I.Damakoat S.Bowong R.Houe D.Bekolle Saint Jerome Polytechnic Saint Jerome Catholic University Institute of Douala P.O.Box 5949 Douala Cameroon Department of Mathematics and Computer Science Faculty of Science University of Ngaoundere P.O.Box 454 NgaoundereCameroon Laboratory of Mathematics Department of Mathematics and Computer Science Faculty of Science University of Douala P.O.Box 24157 DoualaCameroon umi 209 ird/UPMC ummisco Bondy-France and Project GRIMCAPE LIRIMA University of Yaounde ICameroon University of Toulouse INPTLGP-ENIT 47 Avenue d'AzereixBP 1629F-65016 Tarbes CedexFrance

In this paper,we studied the impact of sensitization and sanitation as possible control actions to curtail the spread of cholera epidemic within a human ***,we combined a model of Vibrio Cholerae with a gencric SIRS cholera *** control strategies in terms of the sensitization of population and sanitation are integrated through the impulsive differential *** we presented the theoretical analysis of the *** precisely,we computed the disease free *** derive the basic reproduction number R0 which determines the extinction and the persistence of the *** show that the trivial disease-free equilibrium is globally asymptotically stable whenever.R0≤1,while when R0>1,the trivial disease-free equilibrium is unstable and there exists a unique endemic equilibrium point which is globally asymptotically *** results are supported by numerical simulations,which further suggest that the control of cholera should consider both sensitization and san itation,with a strong focus on the latter.

关键词： Sensitization sanitation Vibrio Cholerae\cholera and control

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Prediction and control of cholera outbreak:Study case of

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Infectious Disease Modelling 2024年第3期9卷 892-925页

作者： C.Hameni Nkwayep R.GlèlèKakaï S.Bowong Laboratory of Mathematics Department of Mathematics and Computer ScienceUniversity of DoualaPO Box 24157DoualaCameroon ird Sorbonne UniversityUMMISCOF-93143BondyFrance Biomathematics and Forest Modeling University of Abomey-CalaviCalaviBenin

This paper deals with the problem of the prediction and control of cholera outbreak using real data of *** first develop and analyze a deterministic model with seasonality for the cholera,the novelty of which lies in the incorporation of undetected *** present the basic properties of the model and compute two explicit threshold parametersR_(0)and R_(0).that bound the effective reproduction number,from below and above,that is R_(0)≤R_(0)≤R_(0).We prove that cholera tends to disappear whenR_(0)≤1,while when R_(0)>1,cholera persists uniformly within the ***,assuming that the cholera transmission rates and the proportions of newly symptomatic are unknown,we develop the EnKf approach to estimate unmeasurable state variables and these unknown parameters using real data of cholera from 2014 to 2022 in *** use this result to estimate the upper and lower bound of the effective reproduction number and reconstructed active asymptomatic and symptomatic cholera cases in Cameroon,and give a short-term forecasts of cholera in Cameroon until *** simulations show that(i)the transmission rate from free Vibrio cholerae in the environment is more important than the human transmission and begin to be high few week after May and in October,(ii)90%of newly cholera infected cases that present the symptoms of cholera are not diagnosed and(iii)60.36%of asymptomatic are detected at 14%and 86%of them recover *** future trends reveals that an outbreak appeared from July to November 2023 with the number of cases reported monthly peaked in October *** impulsive control strategy is incorporated in the model with the aim to avoid or prevent the cholera *** the first year of monitoring,we observed a reduction of more than 75%of incidences and the disappearance of the peaks when no control are available in Cameroon.A second monitoring of control led to a further reduction of around 60%of incidences the following year,showing how imp

关键词： Vibrio cholerae Mathematical models Ensemble Kalman filterBasic reproduction number Impulsive control

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Numerical simulation of hydrodynamic characteristics and bedload transport in cross sections of two gravel-bed rivers based on one-dimensional lateral distribution method

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International Journal of Sediment Research 2020年第2期35卷 203-216页

作者： Chien Pham Van Vivien Chua Department of River Engineering and Disaster Management Faculty of Hydrology and Water ResourcesThuyloi University Unite de Mod'elisation Mathematiques et Informatiquedes Systemesco Complexes (ummisco) JEAI WARMIRDSorbonne Universit'e Department of Civil and Environmental Engineering Faculty of EngineeringNational University of Singapore

Accurate evaluation and prediction of bedload transport are crucial in studies of fluvial hydrodynamic characteristics and river *** paper presents a one-dimensional numerical model based on the one-dimensional lateral distribution method(1 D-LDM) and six classic bedload transport formulae that can be used to simulate hydrodynamic characteristics and bedload transport discharge in cross *** gravel-bed rivers,*** Danube River located approximately 70 km downstream from Bratislava in Slovakia and the Tolten River in south of Chile are used as *** the 1 D-LDM,gravity,bed shear stress,turbulent diffusion,and secondary flow are included to allow for accurate predictions of flow velocity and consequently bed shear stress in the cross *** classic formulae were applied to evaluate the non-dimensional bedload transport rate,and the bedload transport discharge through a river cross section is obtained by integrating the bedload transport rate over the width of the cross *** results show that the root mean square error(RMSE) and mean absolute error(MAE) of velocity and water discharge were less than 8% of the observed magnitude,while the correlation coefficient between model predictions and observations was close to *** formulae proposed by Ashida and Michiue(1972),in which particle collision with the bed is taken into account,and by Camenen and Larson(2005),which allows for yielding a non-zero bedload transport rate even when the bed shear stress is smaller than the critical bed shear stress value,appeared to be more appropriate for predicting the observed bedload transport rate in the studied cross sections of two gravel-bed *** non-uniform sediment mixtures were considered,the bedload transport discharge through a cross-section could change considerably by up to 22.5% of the observed *** relations proposed by Ashida and Michiue(1972) and Egiazaroff(1965) for parameterizing the hiding factor yielded more

关键词： Bedload Gravel-bed river One-dimensional lateral distribution method Bedload transport discharge

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Observed versus estimated actual trend of COVID-19 case numbers in Cameroon:A data-driven modelling

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Infectious Disease Modelling 2023年第1期8卷 228-239页

作者： Arsène Brunelle Sandie Mathurin Cyrille Tejiokem Cheikh Mbacké Faye Achta Hamadou Aristide Abah Abah Serge Sadeuh Mbah Paul Alain Tagnouokam-Ngoupo Richard Njouom Sara Eyangoh Ngu Karl Abanda Maryam Diarra Slimane Ben Miled Maurice Tchuente Jules Brice Tchatchueng-Mbougua African Population and Health Research Center West Africa Regional OfficeDakarSenegal Centre Pasteur du Cameroon membre du Réseau International des Instituts PasteurCameroon Direction de la lutte contre les Maladiesépidémiques et les pandémies Ministere de la santépubliqueCameroon Fondation pour la recherche l'ingénierie et l'innovation Cameroon Institut Pasteur de Dakar DakarSenegal Institut Pasteur de Tunis TunisTunisia ird umi 209 ummisco University of Yaounde IP.O.Box 337YaoundeCameroon

Controlling the COVID-19 outbreak remains a challenge for Cameroon,as it is for many other countries *** number of confirmed cases reported by health authorities in Cameroon is based on observational data,which is not nationally *** actual extent of the outbreak from the time when the first case was reported in the country to now remains *** study aimed to estimate and model the actual trend in the number of COVID-19 new infections in Cameroon from March 05,2020 to May 31,2021 based on an observed disaggregated *** used a large disaggregated dataset,and multilevel regression and poststratification model was applied prospectively for COVID-19 cases trend estimation in Cameroon from March 05,2020 to May 31,***,seasonal autoregressive integrated moving average(SARIMA)modeling was used for forecasting *** on the prospective MRP modeling findings,a total of about 7450935(30%)of COVID-19 cases was estimated from March 05,2020 to May 31,2021 in ***,the reported number of COVID-19 infection cases in Cameroon during this period underestimated the estimated actual number by about 94 *** forecasting indicated a succession of two waves of the outbreak in the next two years following May 31,*** no action is taken,there could be many waves of the outbreak in the *** avoid such situations which could be a threat to global health,public health Abbreviations:ACF,Autocorrelation Function;AIC,Akaike information criterion;COVID-19,Coronavirus Disease 2019;MAE,Mean Absolute Error;MAPE,Mean Absolute Percentage Error;MASE,Mean Absolute Scaled Error;ME,Mean Error;MPE,Mean Percentage Error;MRP,Multilevel Regression and Post-stratification;PACF,Partial Autocorrelation Function;PLACARD,Platform for Collecting,Analyzing and Reporting Data;SARIMA,Seasonal Autoregressive integrated moving average;SARS-CoV-2,Severe Acute Respiratory Syndrome Coronavirus 2.

关键词： Cameroon COVID-19 Forecasting Observed Post-stratification Underestimated

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Hemorrhagic fever with renal syndrome in China： Mechanisms on two distinct annual peaks and control measures

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International Journal of Biomathematics 2018年第2期11卷 319-340页

作者： Li Li Cui-Hua Wang Shi-Fu Wang Ming-Tao Li Laith Yakob Bernard Cazelles Zhen Jin Wen-Yi Zhang School of Computer and Information Technology Shanxi University Taiyuan Shanxi 030006 P. R. China Science and Technology on Electronic Testand Measurement Laboratory North University of China Taiyuan 030051 P. R. China Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention Shanxi University Taiyuan Shanxi 030006 P. R. China Complex Systems Research Center Shanxi University Taiyuan Shanxi 030006 P. R. China Department of Children's Medical LaboratoryDiagnosis Center Qilu Children's Hospital of Shandong University Jinan 250022 P. R. China Department of Disease ControlLondon School of Hygiene and Tropical Medicine London UK ummisco UMI 209 IRD- UPMC 93142 Bondy France Eco- Evolutionary MathematicsIBENS UMR 8197 ENS Paris France Institute of Disease Control and Prevention Academy of Military Medical Science Beijing 100071 P. R. China

Hemorrhagic fever with renal syndrome （HFRS） is a rodent-borne disease caused by several serotypes of hantavirus and 90% of all reported HFRS cases occur in China. However, the dynamics of such outbreak, particularly the characteristics of two distinct annual peaks in China, are not well understood. Here, we investigate several of the biologically plausible causes for the peaks in monthly HFRS cases, and find that the key factor is the interplay between periodic transmission rates and rodent periodic birth rate. Analysis of dynamicM model reveals that vaccination plays a significant role in the control of HFRS in China. Sensitive analysis of different interventions demonstrates that integrating rodent culling and environmental management with the current vaccination program is effective for HFRS control. Our results suggest that for diseases from animals to human beings, the features of both animals and humans beings should be taken into account in the control and prevention strategies.

关键词： HFRS two annual peaks periodic transmission and birth rate controlstrategies.

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