Abstract
In this paper, a deterministic model involving the transmission dynamics of malaria/visceral leishmaniasis co-infection is presented and studied. Optimal control theory is then applied to investigate the optimal strategies for curtailing the spread of the diseases using the use of personal protection, indoor residual spraying and culling of infected reservoirs as the system control variables. Various combination strategies were examined so as to investigate the impact of the controls on the spread of the disease. And we investigated the most cost-effective strategy of all the control strategies using three approaches, the infection averted ratio (IAR), the average cost-effectiveness ratio (ACER) and incremental cost-effectiveness ratio (ICER). Our results show that the implementation of the strategy combining all the time dependent control variables is the most cost-effective control strategy. This result is further emphasized by using the results obtained from the cost objective functional, the ACER, and the ICER.
Highlights
Malaria and visceral leishmaniasis (VL) are two major parasitic diseases with overlapping distributions which are both epidemiological and geographical in nature
Visceral leishmaniasis patients who live in unstable seasonal malaria areas, such as eastern Sudan are exposed to the risk of co-infection [3]; due to the variation in the geographical distribution of these co-infection cases, there might be some environmental and/or social factors associated with these risks of malaria-visceral leishmaniasis co-infections [3]
Post-kala-azar dermal leishmaniasis (PKDL) occurs as a consequence of VL; it is caused by leishmania donovani in infected patients who have been cured of VL 6 months to 1 or more years prior to its appearance [4, 5]
Summary
Malaria and visceral leishmaniasis (VL) are two major parasitic diseases with overlapping distributions which are both epidemiological and geographical in nature. Visceral leishmaniasis patients who live in unstable seasonal malaria areas, such as eastern Sudan are exposed to the risk of co-infection [3]; due to the variation in the geographical distribution of these co-infection cases, there might be some environmental and/or social factors associated with these risks of malaria-visceral leishmaniasis co-infections [3]. Post-kala-azar dermal leishmaniasis (PKDL) occurs as a consequence of VL; it is caused by leishmania donovani in infected patients who have been cured of VL 6 months to 1 or more years prior to its appearance [4, 5] It is common in VL endemic areas such as Sudan, Bangladesh, and India. The cost-effectiveness analysis and discussions are given in Sections 6 and 7
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