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In this paper, a mathematical model for malaria-dysentery co-infection was formulated in order to study and examine its dynamic relationship in the presence of malaria and dysentery preventive and treatment measures. First, analysis of the single infection steady states was done and then the basic reproduction number was obtained. Furthermore, investigation into the existence and stability of equilibria carried out. The single infection models were found to exhibit the possibility of backward bifurcation. Thereafter, the impact of malaria on the dynamics of dysentery is further investigated. Second, incorporating time-dependent controls, using Pontryagin’s Maximum Principle, the necessary conditions for the optimal control of the disease was derived. It is found that malaria infection may be associated with an increased risk of dysentery. Also, that dysentery infection may be associated with an increased risk for malaria. Therefore, to effectively control malaria, the malaria intervention strategies by policy makers must at the same time it also includes effective prevention and control measures for dysentery. Policy makers should take efforts on preventive strategies in combating dysentery and malaria.

Dysentery is a water- and food-borne infectious disease and its incidence is sensitive to climate change. Although the impact of climate change on dysentery is being studied in specific areas, a study in Iran is lacking. In this study, RCP 4.5 and RCP 8.5 scenarios were used to predict the prevalence of dysentery in Iran between 2050 and 2070. This study is a secondary analysis using Geographically Weighted Regression, and 273 cities of Iran were analyzed between March 2011 and March 2017. Bioclimate variables were used as independent variables. Ecological data about the prevalence and incidence of dysentery, which were collected between 2011 and 2017, were used as the dependent variables. The result shows the incidence of dysentery is significantly associated with bioclimate change exposure, in 2050 and 2070, based on RCP 4.5 and RCP 8.5. Our findings showed that in the absence of adaptation of the population, an increase in the risk of bioclimate-related diseases is expected by around 95.6% in the mid-century compared with the beginning of the century with regional variations. Based on these findings, the geographical distribution of the disease will also change. In 2050, the pattern of disease distribution would be changed, and the north of Iran will be included in the vulnerable regions. In 2070, the southeastern and northern parts of Iran will have the most vulnerability to climate change. Our study contributes important knowledge to this perspective by providing insightful findings and pieces of evidence for climate change adaptation and mitigation.