Understanding Visceral Leishmaniasis Disease Transmission and its Control—A Study Based on Mathematical Modeling

Mathematical analysis of a model for zoonotic visceral leishmaniasis

Zoonotic visceral leishmaniasis (ZVL), caused by the protozoan parasite Leishmania infantum and transmitted to humans and reservoir hosts by female sandflies, is endemic in many 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 globally-asymptotically stable when the associated reproduction number of the model is less than unity. Using case and demographic data relevant to ZVL dynamics in Arac̣atuba municipality 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 ( ℛ 0 ) ranges from 0.3 to 1.4, with a mean of ℛ 0 = 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 of ℛ 0 decreases to ℛ 0 ∈ [ 0.1 , 0.6 ] , with a mean of ℛ 0 = 0.35 (this significantly increases the prospect of the effective control or elimination of the disease). Thus, ZVL transmission models (in communities where such treatment strategy is implemented) that do not explicitly incorporate the effect of such treatment may be over-estimating the disease burden (as measured in terms of ℛ 0 ) in the community. It is shown that ℛ 0 is more sensitive to increases in sandfly lifespan than that of 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 the model 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 the most effect on the disease dynamics or burden (as measured in terms of the reproduction number ℛ 0 ). 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).

A Mathematical Study to Control Visceral Leishmaniasis: An Application to South Sudan

In this manuscript, we propose and analyze a compartmental model of visceral leishmaniasis (VL). We model the human population with six compartments including asymptomatic, symptomatic and PKDL-infected, animal population as second host and sandfly population as the vector. Furthermore, the non-adult stage of the sandfly population is introduced in the system, which was not considered before in the literature. We show that the increase in the number of host of sandfly population generates a backward bifurcation. Thus, multiple hosts will cause disease persistence even if the basic reproduction number ([Formula: see text]) is below unity. We perform a sensitivity analysis of important model parameters with respect to some epidemiologically significant responses. We validate our model by calibrating it to weekly VL incidence data from South Sudan for the year 2013. We perform cost-effectiveness analysis on different interventions: treatment, non-adult control, adult control and their different layered combinations based on their implementation cost (in USD) and case reduction. We also use a global sensitivity analysis technique to understand the effect of important parameters of our model on the implementation cost of different controls. This cost-effectiveness study and cost-sensitivity analysis are relatively new in existing literature of this disease.

Optimal combinations of control strategies and cost-effective analysis for visceral leishmaniasis disease transmission

Visceral leishmaniasis (VL) is a deadly neglected tropical disease that poses a serious problem in various countries all over the world. Implementation of various intervention strategies fail in controlling the spread of this disease due to issues of parasite drug resistance and resistance of sandfly vectors to insecticide sprays. Due to this, policy makers need to develop novel strategies or resort to a combination of multiple intervention strategies to control the spread of the disease. To address this issue, we propose an extensive SIR-type model for anthroponotic visceral leishmaniasis transmission with seasonal fluctuations modeled in the form of periodic sandfly biting rate. Fitting the model for real data reported in South Sudan, we estimate the model parameters and compare the model predictions with known VL cases. Using optimal control theory, we study the effects of popular control strategies namely, drug-based treatment of symptomatic and PKDL-infected individuals, insecticide treated bednets and spray of insecticides on the dynamics of infected human and vector populations. We propose that the strategies remain ineffective in curbing the disease individually, as opposed to the use of optimal combinations of the mentioned strategies. Testing the model for different optimal combinations while considering periodic seasonal fluctuations, we find that the optimal combination of treatment of individuals and insecticide sprays perform well in controlling the disease for the time period of intervention introduced. Performing a cost-effective analysis we identify that the same strategy also proves to be efficacious and cost-effective. Finally, we suggest that our model would be helpful for policy makers to predict the best intervention strategies for specific time periods and their appropriate implementation for elimination of visceral leishmaniasis.