Gorahava and Others Optimization for Ka Control in Bihar

The visceral form is the most deadly form of the leishmaniasis family, which affects poor and developing countries. The Indian state of Bihar has the highest prevalence and mortality rate due to visceral leishmaniasis in the world, where it is also referred to as Kala-Azar. Insecticide spraying is the current vector control procedure for controlling its spread in Bihar. This study proposes a novel optimization model in order to identify an optimal allocation of insecticide (DDT or Deltamethrin) based on the sizes of both human and cattle populations. As an example, DDT and Deltamethrin have been compared using the model. The model maximizes the insecticide-induced death rate caused by spraying human and cattle dwellings given the limited financial resources available to the public health department. The results suggest that until the first 90 days after spraying, DDT yields more than three times the insecticide-induced death rate achieved by Deltamethrin in the absence of any insecticide resistance. The study implies that ignoring the resistance developed by sandflies to DDT, Deltamethrin might not be a good replacement for DDT. The study also confirms that the present practice of first spraying houses to optimize sandfly mortality ahead of spraying cattle sites is appropriate. GORAHAVA AND OTHERS OPTIMIZATION FOR KA CONTROL IN BIHAR 2 INTRODUCTION Visceral leishmaniasis (VL) is a sandfly-borne infectious disease that is fatal if left untreated. 1 Known as Kala-Azar in India, it is transmitted to the human population when an infected female sandfly bites a susceptible human and transmits the parasite Leishmania donovani. Male sandflies are also known to feed on blood, 2 and blood is a crucial source of protein and iron for female sandflies to develop eggs. Phlebotomus argentipes (a sandfly species) is the primary vector of L. donovani in southern Asia 3 including India. India, an agricultural country, has a sizable cattle population that is frequently visited by sandflies for mating and feeding purposes. The blood-feeding preferences of different sandfly species have been well documented in the literature. An investigation of the stomach contents of P. argentipes from six districts of North Bihar showed that blood-fed female sandflies have a preference for bovine blood (68%), followed by human blood (18%), and avian blood (4%) 4 , hence showing them to be zoopholic. Furthermore, an examination of soil samples in Bihar showed that P. argentipes has a higher tendency to breed in the alkaline soil of cattle sheds than in soil that has a neutral pH found in human houses. 5 Cattle sheds, where the soil might have a high content of moisture and organic matter such as cow dung, provide an ideal breeding site for P. argentipes. 6 The foregoing discussion verifies the importance of considering cattle sites in insecticide residual spraying efforts. Previous studies 7 showed that spraying cattle sheds in Brazil caused increased sandfly density in unprotected human dwellings. Therefore, we develop a model that focuses on insecticide spraying programs in both human and cattle sites. The burden of VL in terms of disability-adjusted life years lost in India was estimated in 1990 to be 0.5 million and 0.68 million for women and men, respectively. 8 The average number of annual VL cases in India between 2004 and 2008 was reported to be 34,918, although this total GORAHAVA AND OTHERS OPTIMIZATION FOR KA CONTROL IN BIHAR 3 dropped to 28,382 cases in 2010. 9 The provisional number of Kala-Azar cases in India in 2011 was 31,000. 10 Given the seriousness of infection, the governments of India, Bangladesh, and Nepal launched an initiative in 2005 to reduce annual incidences of VL to lower than one per 10,000 persons by 2015. 11 As an intervention measure, the Bihar government now carries out insecticide residual spraying every year starting in February. 12 The current policy of the public health department of the Indian state of Bihar considers only the human population size 13 of each district for computing the amount of insecticide (presently DDT) to be allocated for spraying. The cattle population in a district is not included in these insecticide allocation calculations. Because allocating an amount of insecticide to spraying cattle sheds might control the spread of VL more effectively, a mathematical framework that identifies an optimal allocation of insecticide based on local human as well as cattle populations would therefore be valuable. For this purpose, two modeling approaches are presented herein: an optimization model and a Benefit to Materials Cost Ratio (BMCR) function. The present study uses these models in order to investigate an optimal allocation of insecticide based on both cattle and human population sizes. 13 Please note that because the BMCR function approach is completely independent of the optimization model, it provides us with a different perspective on choosing sites for spraying. The model developed herein can be used for comparing insecticides considered for future use in spray campaigns in Bihar. The current insecticide (DDT) residual spray program in Bihar has been reported to have low effectiveness due to the emergence of P. argentipe’s resistance to DDT. Replacing DDT by an alternative insecticide has been suggested. 14 The model in this study can thus be used when considering this replacement. The maximum achievable insecticideGORAHAVA AND OTHERS OPTIMIZATION FOR KA CONTROL IN BIHAR 4 induced death rate within the available budget constraint is used as a criterion by the presented optimization model. Our results suggest that despite spending approximately Rs. 590 million in spray campaigns, spraying more sites does not increase the sandfly population’s insecticide-induced death rate substantially. The model estimates an 18% increase in natural sandfly death rate in Bihar, 90 days after spraying, based on the present insecticide allocation policy. Hence, after covering a certain spray area, it might be better to invest funds in other sandfly control interventions such as bed-nets and ecological vector management. 15 The remainder of the paper is structured as follows. The Data Sources section describes the data sources used to estimate the model parameters. The Methods section explains the equations and assumptions of the three components of the linear optimization model. The Analysis section presents the analytical results and recommendations for choosing a spray coverage option by using a BMCR function. The Numerical Results section presents the numerical results derived from the model. Finally, the Discussion section discusses the implications of the model’s results and offers suggestions for future ideas to improve the model. DATA SOURCES The 1982 Cattle Census 16 and 2010--2011 budget allocation document from the public health department of Bihar 13 were used to estimate the sizes of the cattle and human populations in the VL-affected districts in Bihar, respectively. The average number of cattle per cattle shed in Bihar was assumed to be the average livestock herd size (number of cow equivalents per household) from previous studies. 17 GORAHAVA AND OTHERS OPTIMIZATION FOR KA CONTROL IN BIHAR 5 The cost of the insecticide spray campaign was also formulated using data from the 2010--2011 budget document. 13 The costs related to materials and implementation (including salaries, spray equipment, and miscellaneous expenses) were added in order to calculate the total cost of the insecticide spray campaign. Both the direct and the indirect costs associated with implementation were used to derive the cost equation (Appendix 3). The data include 354 public health centers (PHCs) and 10,686 villages. 13 Furthermore, the number of occupied residential houses was estimated for VL-affected districts (excluding data for the Arwal district) from the 1991 Census of India. 18 Financial constraints preclude the spraying of all houses in a district. Because the model proposed herein aims to optimize the amount of insecticide sprayed per person and per cattle (per capita hereafter), the two decision variables were set as “kilograms of insecticide allocated per person” and “kilograms of insecticide allocated per cattle.” When the available budget cannot procure enough insecticide to cover all sites in the state, it is referred to as a “resource-limited case” and is used to formulate some of the constraints in the model (Appendix 4). The natural sandfly death rate was estimated using 2 years of monthly data representing the daily survival probability of P. papatasi 19 . Moreover, the appropriate literature sources were referred to in order to estimate P. argentipes’s mortality, 24 hours after spraying with DDT 20 and Deltamethrin 14 . An insecticide’s lethal effect is assumed to decay exponentially over time. 21 The decay rates inside houses 14 and cattle sheds 22 were then estimated using data from the literature (Appendix 1). Previous studies (see the references in Table 1 and Table 2) were also consulted in order to estimate the epidemiological and demographical parameters for the host and vector populations. GORAHAVA AND OTHERS OPTIMIZATION FOR KA CONTROL IN BIHAR 6 METHODS The proposed optimization model comprises three components. The first component is the objective function (Equation 3), which captures the insecticide-induced death rate and which is maximized in the model. The insecticide-induced death rate is achieved by spraying insecticide in houses and cattle sheds (derivation in Appendix 2). The decision variables (output from the model) in the objective function are then the amount of insecticide allocated per person and per cattle. The demographic parameters used in the objective function as well as in the constraints are described in Table 1. Table 1. Demographic parameters for Bihar state Symbol Definition Unit Estimates : Mean (SD) g Number of PHCs in Bihar Number of government clinics 354 13 Nh Size of the human population in the 31 VLaffected districts in Bihar Number of humans 33,898,857 13 Nc Size of the cattle population in the 31 VLaffected districts in Bihar Number of cattle 21,571,585 16 Nv Size of the sandfly population in Bihar Number of sandflies Assumed constant in the optimization model H Total number of houses in Bihar Number of houses 7,933,615 18 Average herd size per cattle shed Number of cattle equivalents 4.6 (2.6) 17 Z = Number of cattle sheds Number of cattle sheds 4,689,475 16 SD: standard deviation GORAHAVA AND OTHERS OPTIMIZATION FOR KA CONTROL IN BIHAR 7 The insecticide toxicity and entomological parameters used in the objective function and in the constraints are described in Table 2. Table 2. Insecticide toxicity and entomological parameters Symbol Definition Unit Estimates