| 1 | Mathematical analysis of a model for zoonotic visceral leishmaniasis显示文摘Zoonotic visceral leishmaniasis(ZVL),caused by the protozoan parasite Leishmania infantum and transmitted to humans and reservoirhosts by female sandflies,is endemic inmany parts of the world(notably in Africa,Asia and the Mediterranean).This study presents a new mathematical model for assessing the transmission dynamics of ZVL in human and non-human animal reservoir populations.The model undergoes the usual phenomenon of backward bifurcation exhibited by similar vector-borne disease transmission models.In the absence of such phenomenon(which is shown to arise due to the disease-induced mortality in the host populations),the nontrivial disease-free equilibrium of the model is shown to be globallyasymptotically stable when the associated reproduction number of the model is less than unity.Using case and demographic data relevant to ZVL dynamics in Arac atubamunicipality of Brazil,it is shown,for the default case when systemic insecticide-based drugs are not used to treat infected reservoir hosts,that the associated reproduction number of the model (ℛ0) ranges from 0.3 to 1.4,with a mean of ℛ0=0:85.Furthermore,when the effect of such drug treatment is explicitly incorporated in the model(i.e.,accounting for the additional larval and sandfly mortality,following feeding on the treated reservoirs),the range ofℛ0 decreases toℛ02∈[0.1,0.6],with a mean ofℛ0=0:35(this significantly increases the prospect of the effective control or eliminationof the disease).Thus,ZVL transmissionmodels(in communities where such treatment strategy is implemented)that do not explicitly incorporate the effect of such treatmentmay be over-estimating the disease burden(asmeasured in terms ofℛ0)in the community.It is shown thatℛ0 ismore sensitive to increases in sandflylifespanthan thatof the animal reservoir(so,a strategy that focuses on reducing sandflies,rather than the animal reservoir(e.g.,via culling),may be more effective in reducing ZVL burden in the community).Further sensitivity analysis of themodel ranks the sandfly removal rate(by natural death or by feeding from insecticide-treated reservoir hosts),the biting rate of sandflies on the reservoir hosts and the progression rate of exposed reservoirs to active ZVL as the three parameters with themost effect on the disease dynamics or burden(as measured in terms of the reproduction number ℛ0).Hence,this study identifies the key parameters that play a key role on the disease dynamics,and thereby contributing in the design of effective control strategies(that target the identified parameters). | Nafiu Hussaini Kamaldeen Okuneye Abba B.Gumel | 2017 | Infectious Disease Modelling2017，2，4： | 1 |
| 2 | Mathematical modeling and analysis of meningococcal meningitis transmission dynamics显示文摘Meningococcal meningitis(MCM)is one of the serious public health threats in the tropical and sub-tropical regions.In this paper,we propose an epidemic model to study the transmission dynamics of MCM with high-and low-risk susceptible populations.The model considers two different groups of susceptible individuals depending on the availability of medical resources(MR,including hospitals,health workers,etc.),which varies the infection risk.We find that the model exhibits the phenomenon of backward bifurcation(BB),which increases the difficulty of MCM control since the dynamics are not merely relying on the basic reproduction number,TZo.This study explores the effects of MR on the MCM epidemics by mathematical analysis and shows the existence of BB on MCM disease.Our findings suggest that providing adequate MR in a community is crucial in mitigating MCM incidences and deaths,especially,in the MCM endemic regions. | Salihu Sabiu Musa Shi Zhao Nafiu Hussaini Abdulrazaq Carba Habib Daihai He | 2020 | International Journal of Biomathematics2020，13，1： | 0 |
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