Factors which contribute to the intricacy of VL in certain regions of the world are many. In this particular study, our focus is on the mathematical model for the transmission of VL between sandflies and humans with key assumptions and features. The R0 and prevalent equilibrium calculated from this particular model coupled with estimations of parameters from a myriad of clinical trials, survey studies, and mathematical modeling studies will be incorporated to differentiate the key parameters that influence an increasing amount of VL endemic behavior in India and Sudan.
VL or,Visceral Leishmaniasis is an infection caused by a parasite found in tropical and subtropical countries, making the country an environmental factor for this infectious disease. The infection is spread to humans via the bite of a female sandfly of the genus Phlebotomus. A family of infectious diseases, the geographical location of Leishmaniasis is tied in to the abundance of sandflies, their life cycle and the presence of parasite reservoirs. "The Leishmaniasis is classified from its clinical manifestation (Visceral Leishmaniasis (VL), Cutaneous Leishmaniasis (CL), Muco Cutaneous Leishmaniasis (MCL) or Diffuse Cutaneous Leishmaniasis (DCL)) and host reservoir (Anthroponotic (A) or Anthropo zoonotic (AZ) or Zoonotic (Z)" (Mubayi et.al).Characterized by both diversity and complexity this disease is caused by more than 20 Leishmanial species and is transmitted to humans by ~30 different species of phlebotomine sandflies” (Chappuis et.al). The sand fly’s bite transfers parasites to the animal or human host, which is then ingested, live, and multiply inside macrophage cells. When multiplication causes these cells to burst, the released parasites invade fresh cells. Sandflies become infected when they feed on the blood of infected individuals. Current data estimates that roughly 12 million people worldwide are infected with the parasite, 1-2 million new cases are registered annually, and 350 million people are at risk (Ready). Part of the genus Leishmania protozoan parasite, Leishmaniasis can be categorized into several types.
The most lethal of these parasites in the developing world today is an intracellular protozoan known as Leishmania Donovani (Sakru). Phlebotomus orientalis is a member of the Larroussisus subgenus that contains most of the "principal vectors of Leishmania donovani complex in East Africa. Kirk and Lewis (155) provided the first noteworthy evidence that P.orientalis is the main L donovani vector in Sudan. Additional evidence supporting the role of P. orientalis as the vector of L. donovani in Sudan came from experiments that compared the susceptibility of P. orientalis and other abundant man-biting sand flies, namely Phlebotomuspapatasi (Scopoli) and Sergentomyia clydei Sinton, to L. donovani infection (Elnaiem). Both India and Sudan are being heavily impacted by the infection and it is causing severe epidemic outbreaks.
Currently, the Indian sub-continent of Bihar is being impacted by Leishmania donovani parasites transmitted to humans by female phlebotomine sand fly (Phlebotomus argentipes). There have been several outbreaks since the last century (Bhunia). After being transmitted by the bite of an infected female sandfly, the parasite finds and latches onto internal organs such as the spleen, liver, lymph nodes, and intestines, as well as the bone marrow and skin of its host (Chappuis; Mubayi; Singh). It then causes the communicable infection known as clinical Visceral Leishmaniasis (VL) locally known as Kala-azar (Hindi for “black fever”). VL can present symptoms such as prolonged fever, weight loss, hepatosplenomegaly, pancytopenia, delirium, and ultimately results in death in the bulk of cases where it presents clinically (Barao). Among the nastiest area’s hit by VL pandemic are India and Sudan. VL hits poor countries the hardest. In India, there are approximately 270,900 cases accounting for a total burden of 21 cases per 100,000 population in the effected countries including Sudan (Seaman et.al). Research has shown that the poorer the household the higher the risk for VL contraction and mortality (Boelaert).
The leishmaniases are transmitted to humans via sylvatic, domestic and periodomestic cycles in both India and the Sudan. A change in climate and over environmental prospects has shown the potential to expand the geographic range of the transmission of leishmaniasis in the future (Bern et.al). Visceral leishmaniasis continues to remain a significant public health concern. There are underlying factors that may show forth a distinction in the difference between strains in India and Sudan. Studies on Asian strains "using PCR primers based on LcKin have identified rK39 homologous sequences [10–12]. Gerald et al  reported the first East African (Sudanese) L.donovani kinesin homologue, LdK39. The first two of the 39-aa repeats of LdK39, flanked by sequences of the L. donovani antigens HASPB1 and HASPB2 , comprise rK28, a novel recombinant protein for diagnosis of VL, designed to be an improvement over rK39 [15–16]" (Bhattacharyya et.al).
VL was almost wiped out completely in India during the 1950s and 1960s as a consequence of the National Malaria Eradication programme. In the late 1970s, there was a resurgence of VL of epidemic proportions. There was a varying amount of response to treatments at that time. Theoretical basis for VL elimination is India is "(i) human beings are the only reservoir; (ii) there is only one vector species, which can be controlled; and (iii) the geographical distribution is limited and quite well defined" (Cheeran et.al). The sub-continent of Bihar faces the most significant issue with treatments due to VL being a growing problem. Current treatments are amphotericin B and its lipid formulations, pentamidine, miltefosine and parmomycin (Olliaro et.al).New therapeutic approaches have been developed to treat visceral leishmaniasis within the last decade. Several studies have been performed to assess the combinations of various antileishmanial drugs with high efficacy. This is in part due to the emergence of large-scale resistance to conventional antimony treatment in Bihar, India. A study performed in India however showed that paromomycin was efficacious and safe. A study on the same drug has been previously initiated in Sudan (Perry et.al; Sundar et.al; Musa et.al). In 2010, a patient was treated for VL using a lengthy hospitalization and an "arduous 28 days of one-daily intravenous pentavalent antimony accompanied by well-recognized adverse reactions and the requirement for frequent laboratory monitoring" (Murray). Sudan continues to be an area of concern with regard to treatment. The stronghold of treatment in Sudan remains to be pentavalent antimony compounds. Pentostam sodium stibogluconate produced by GlaxoWellcome is used (Veeken et.al). Analysis of treatment is typically assessed using uncertainty or sensitivity analysis.
Due to the density and uncertainties that are present in experimental data, the results from mathematical and computer models regarding biological diseases is often elaborate. Current epidemiological studies report uncertainty intervals around the estimates in the data regarding the VL disease. Uncertainty analysis officially quantifies the limitations of data, while sensitivity analysis examines how key outputs of analysis vary when certain quantities are varied on a systematic basis. Sensitivity analysis is necessary when seeking to design control strategies as a well as future direction in research (Marino et.al; Mathers et.al; Samsuzzoha et.al). An "epidemiologic parameter, the basic reproductive rate (Ro), can be derived from a mathematical model of the transmission dynamics of an infectious disease. George Macdonald formally introduced the R0 in his 1952 paper analyzing the equilibrium in malaria transmission. R0 represents the average number of secondary cases acquired from a primary case introduced into a totally susceptible population; hence, the magnitude of R0 indicates the severity of an epidemic (l-4)." R0 is usually ascertained through specific input parameter value estimation. As a result of this, a single output value is derived for R0 (Sanchez and Blower). Leishmaniasis is currently found in more than 90 countries and people of all ages are at risk for infection.
Barao, S C. "Human asymptomatic infection in visceral leishmaniasis: a seroprevalence study in an urban area of low endemicity. Preliminary results." The American Journal of Tropical Medicine and Hygiene 77.6 (2007): 1051-53.Academic Search Premier. Web. 18 Mar. 2013.
Bern, Caryn, et al. "Complexities of Assessing the Disease Burden Attributable to Leishmaniasis." PLOS 2 (2008): Academic Search Premier. Web. 18 Mar. 2013.
Bhattacharya, Sujit K. "Phase 4 Trial of Miltefosine for the Treatment of Indian Visceral Leishmaniasis." The Journal of Infectious Diseases 196 (2007): 591-8.Academic Search Premier. Web. 18 Mar. 2013.
Bhunia, Gouri S., Shreekant Kesari, Nandini Chatterjee, and Pradeep Das. "The burden of visceral leishmaniasis in India: Challenges in using remote sensing and GIS to understand and control." Paper. 2Presidency University, Department of Geography, Kolkata, West Bengal, India, 2012. 43. Print.
Boelaert, Marleen. "Evaluation of rapid diagnostic tests: visceral leishmaniasis." Nature Reviews Microbiology (2007): 30-39. Academic Search Premier. Web. 18 Mar. 2013.
Chappuis, Francois. "Visceral leishmaniasis: what are the needs for diagnosis, treatment and control?" Nature Reviews 5 (2007): 873-882. Academic Search Premier. Web. 18 Mar. 2013.
Cheeran, Messiah M, Shyam Sundar, Sumar Rijal, and Piero L. Olliaro."A review of clinical trials of treatments for visceral leishmaniasis in the Indian subcontinent (India, Bangladesh and Nepal)." TropIKA.net. May 2008. Web. 18 Mar. 2013. <http://journal.tropika.net>.
Elnaiem, Dia-Eldin. "Ecology and control of the sand fly vectors of Leishmania donovani in East Africa, with special emphasis on Phlebotomus orientalis." Journal of Vector Ecology 36 (2011): 523-531. Print.
Marino, Simeone, Ian B. Hogue, Christian J. Ray, and Denise E. Kirschner. "A methodology for performing global uncertainty and sensitivity analysis in systems biology." Journal of Theoretical Biology 254 (2008): 178-196. Print.
Mathers, Colin D. "Sensitivity and Uncertainty Analyses for Burden of Disease and Risk Factor Estimates." Global Burden of Disease and Risk Factors. 2006. 399-426. Print.
Mubayi, Anuj. "Transmission dynamics and underreporting of Kala-azar in the Indian state of Bihar." Journal of Theoretical Biology 262 (2010): 177-185. Academic Search Premier. Web. 18 Mar. 2013.
Murray, Henry W. "Treatment of visceral leishmaniasis in 2010: direction from Bihar State, India." Future Microbiology 5.9 (2010): 1301. Print.
Musa, Ahmed M. "Paromomycin for the Treatment of Visceral Leishmaniasis in Sudan: A Randomized, Open-Label, Dose-Finding Study." PLOS 4.10 (2010):Academic Search Premier. Web. 18 Mar. 2013.
Olliaro, Piero L. "Treatment options for visceral leishmaniasis: a systematic review of clinical studies done in India, 1980–2004." Lancet Infectious Diseases 2005: 763-74. Academic Search Premier. Web. 18 Mar. 2013.
Perry, Meghan R. "Visceral Leishmaniasis and Arsenic: An Ancient Poison Contributing to Antimonial Treatment Failure in the Indian Subcontinent?"Viewpoints 5.9 (2011): Academic Search Premier. Web. 18 Mar. 2013.
Ready, Paul D. "Biology of Phlebotomine Sand Flies as Vectors of Disease Agents."The Annual Review of Entomology 58 (2013): 227-50. Print.
Sakru, Nermin N. "The infection risk of visceral leishmaniasis among household members of active patients." Parasitology International 55 (2006): Academic Search Premier. Web. 18 Mar. 2013.
Samsuzzoha, Md, Manmohan Singh, and David Lucy. "Uncertainty and sensitivity analysis of the basic reproduction number of a vaccinated epidemic model of influenza." Applied Mathematical Modelling (2012): 1-13. Print.
Sanchez, Melissa A., and Sally M. Blower. "Uncertainty and Sensitivity Analysis of the Basic Reproductive Rate." Amatlcan Journal of Epidemiology 145.12 (1997): 1127-1137. Print.
Seaman, J, D Pryce, H Sondorp, and R N. Davidson. "Epidemic Visceral Leishmaniasis in Sudan: A Randomized Trial of Aminosidine Plus Sodium Stibogluconate Versus Sodium Stibogluconate Alone." The Journal of Infectious Diseases (1993): Print.
Singh, Niti. "Animal Reservoirs of Visceral Leishmaniasis in India." Journal of Parasitology 99.1 (2013): 64-67. Academic Search Premier. Web. 18 Mar. 2013.
Sundar, Shyam, et al. "Comparison of short-course multidrug treatment with standard therapy for visceral leishmaniasis in India: an open-label, non-inferiority, randomised controlled trial." Lancet 377 (2011): 477-86. Academic Search Premier. Web. 18 Mar. 2013.
Sundar, Shyam, et al. "New Treatment Approach in Indian Visceral Leishmaniasis: Single-Dose Liposomal Amphotericin B Followed by Short-Course Oral Miltefosine." Clinical Infectious Diseases 2008: 1000-6. Academic Search Premier. Web. 18 Mar. 2013.
Veeken, Hans, Koert Ritmeijer, Jill Seaman, and Robert Davidson. "A randomized comparison of branded sodium stibogluconateand generic sodium stibogluconate for the treatment of visceral leishmaniasis under field conditions in Sudan."Tropical Medicine and International Health 5.5 (2000): 312-317. Print.