Considering the stochastic urban continuous-time complex system in requisites of urban evolution Ue= Ue (Pm Mp, EC, HD) as a function of urban population dynamics P and morphological pattern/structure M along with urban environmental/climatically variability E concerning human urban infectious dengue disease H, this dissertation studies the variation and their interactions of P, M and H with E components for the city of Karachi. Chapter 0, Looks into the urban evolution as a complex system, the megacity Karachi has challenged numerous problems due to uncontrolled urban population dynamics, morphological pattern, their socio-health and climatically impacts on seasonal urban vector-borne disease methodology and objectives are debated. Chapter 1, Consider the general literature review regards as our selected four functional components (Pm, Mp, EC, HD) for the urban complex system. Chapter 2, Studies the Stochastic ARIMA models prefer to intend for estimation and forecasting of urban population of the Karachi (from 1951 to 2016) by diagnostic checking with Bayesian and Non-Seasonal Holt- Winters forecasting algorithm. For the most adequate ARIMA (1,2,1) model with Holt-Winter forecasting algorithm obtain the small values of MAPE and high value of the Geary’s α statistic normality check test suggests for the prediction in the years of 2020, 2025 and 2015 to 2030. These results show that the ARIMA (1,2,1) seem to similar Winter’s forecast for upcoming 15-years interval. Chapter 3, An investigation of logarithm irregular and regular population (from 1729 to 1946 and 1951 to 2015) over three centuries of the Karachi city, this work uses statistical probability distribution tails to define the dynamics of centuries and the decades as well as whole population intervals. The adequate probability distributions analyze with the help of fitting tests (CST, KST and ADT) and analytical data plotting. The Lognormal distribution can better explain the population behavior in centuries wise total irregular (1729 to 1946) interval, although the Weibull distribution is initiate to be the adequate population fitting for the total regular (1951 to 2015) interval of Karachi. Additionally, The Log Normal and Weibull distributions find the most suitable to the fitting as a heavy tail of the population''s irregular and regular intervals, the Log normal and Weibull distribution is found subsuper exponential tails using methods of validation for both intervals. The actual population data analysis indicates that the heavy-tailed distributions are fitted contract than the more commonly seen lighter tailed Gamma distribution. So, the Monte Carlo Simulation performs the appropriate Lognormal and Weibull distributions for irregular and regular data and generate data values (298 and 69) from duration of 1729 to 2020 and 1951 to 2020. Now, deliberate the second most important part (urban morphology) of this dissertation in chapter 4, studies the 5-districts and 18-town’s population-area relationship using our develop novel Oncologic surface mapping Techniques. Also, the population census data of subunits (districts and towns) of the Karachi city for the year of 1981, 1998 and 2002 respectively, we determine population density by using our construct spatial surface GIS maps. It is determined that the 18-town form has improved than the 5-district pattern. By the help of Mann-Kendall test for spatial population Linear Trend Models determine irregular (1729 to 1946) and regular (1951 to 2015) interval. It is communicating that regular decade’s intervals for population-morphological evolution express that the trends is statistically significant base on alpha P-values (α= 5%).The Persistency of the irregular and regular interval test by Fractal dimension is 1.371 in 1729 to 1946 and 1.058 in 1951 to 2015.The Hurst exponents both methods (Range increment and second moments) are also confirms the prolonged Mean-Tail distributions persistency, The Hurst exponent values are more than 0.5 for the centuries and decades are too revealing persistency seems to remain relational towards the gradient increases of trend close-fitting for these intervals. Our develop morphological spatial maximum dense (SMaxP) and minimum densest (SMinP) pivotal techniques for measurement of the one to other pivotal distance reveal that on 5-districts and 18-towns base in the census years 1981,1998 and 2002 with the help of Spatial GIS-based Mapping enquiries and Flatten Gradient Density Modeling. To, compute the population densities for all the districts and towns, which is also declare that SMinP for town wise density distribution results appear to be better than the SMaxP results, Log linear, Exponential, Logarithmic and second order polynomial transformation trend models is verified the results. Chapter 5, studies the vector-borne dengue fever is the utmost imperative arboviral disease of urban population, stirring in the subtropical city of Karachi, Pakistan. Dengue is recorded as an urban human disease since it binges in urban morphology and climatic variables, including Land Surface Mean Temperature ( ), Rainfalls ( ) and El Niño Southern Oscillation index ( ) from January 2001 to December 2016. The basic oncological statistical treatment with trend analysis of climate and dengue outbreaks are observing high in dengue incidences during the months of September to November, as well as the descriptive kurtosis value of dengue count (27.765 >3) suggests that leptokurtic and increasing flattened tail for dengue data because of the influence of climatic parameters. The fractal spectrum analysis also confirms the anti-persistent behavior of dengue for the months of September to November (highest seasonal epidemic dengue periods) and the normality tests indicate the robust sign of the intricacy of data. In this stage the comparative research shows a significant association between monthly dengue and climatic variation by probabilistic ARIMAX (p), PARX (p)-NBARX (p) models, although Over Dispersion tests values also smallest value of AIC (3.897), NBARX (p) is prefer more appropriate model for next twelve months forecasting. Chapter 6, Concludes the principle results and Mathematical Oncological methodologies, which are found in our selected four functional components (Pm, Mp, EC, HD) for the urban stochastic complex system. At the end of this chapter, it has been revealed in addition to the future work and suggestions.