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Aedes aegypti is known as the responsible vector transmitting dengue flavivirus. Unavailability of medication to cure the transmission of the virus in the human blood becomes a global health issue in recent decades. World epidemiologists are encouraged to focus on the investigation over the effective and inexpensive way to prevent dengue transmission, i.e. mosquito control. In this paper, we present a model depicting the dynamics of mosquito population based on indoor-outdoor life cycle classification. The basic mosquito offspring number was obtained and analysis of equilibria was shown. We brought along a discussion on the application of optimal control to the model in which two simultaneous schemes were introduced. The first scheme is done by disseminating chemical like temephos in spots where eggs and larvae develop, meanwhile the second scheme is done by deploying fumigation through areas where adult mosquitoes prevalently nest, indoor as well as outdoor. A version of the gradient-based method was presented to set up a workflow in minimizing the objective functional with respect to some control variables. Numerical results from the analysis of the basic mosquito offspring number with constant control and from that with optimal control suggested that the application of fumigation is preferable over that of temephos. It was also suggested that applying both control schemes simultaneously gives the most significant reduction in the population.

COVID-19 pandemic continues to obstruct social lives and the world economy other than questioning the healthcare capacity of many countries. Weather components recently came to notice as the northern hemisphere was hit by escalated incidence in winter. This study investigated the association between COVID-19 cases and two components, average temperature and relative humidity, in the 16 states of Germany. Three main approaches were carried out in this study, namely temporal correlation, spatial auto-correlation, and clustering-integrated panel regression. It is claimed that the daily COVID-19 cases correlate negatively with the average temperature and positively with the average relative humidity. To extract the spatial auto-correlation, both global Moran’s $${\mathscr {I}}$$ I and global Geary’s $${\mathscr {C}}$$ C were used whereby no significant difference in the results was observed. It is evident that randomness overwhelms the spatial pattern in all the states for most of the observations, except in recent observations where either local clusters or dispersion occurred. This is further supported by Moran’s scatter plot, where states’ dynamics to and fro cold and hot spots are identified, rendering a traveling-related early warning system. A random-effects model was used in the sense of case-weather regression including incidence clustering. Our task is to perceive which ranges of the incidence that are well predicted by the existing weather components rather than seeing which ranges of the weather components predicting the incidence. The proposed clustering-integrated model associated with optimal barriers articulates the data well whereby weather components outperform lag incidence cases in the prediction. Practical implications based on marginal effects follow posterior to model diagnostics.

This paper stresses its base contribution on a new SIR-type model including direct and fomite transmission as well as the effect of distinct household structures. The model derivation is modulated by several mechanistic processes inherent from typical airborne diseases. The notion of minimum contact radius is included in the direct transmission, facilitating the arguments on physical distancing. As fomite transmission heavily relates to former-trace of sneezes, the vector field of the system naturally contains an integral kernel with time delay indicating the contribution of undetected and non-quarantined asymptomatic cases in accumulating the historical contamination of surfaces. We then increase the complexity by including the different transmission routines within and between households. For airborne diseases, within-household interactions play a significant role in the propagation of the disease rendering countrywide effect. Two steps were taken to include the effect of household structure. The first step subdivides the entire compartments (susceptible, exposed, asymptomatic, symptomatic, recovered, death) into the household level and different infection rates for the direct transmission within and between households were distinguished. Under predefined conditions and assumptions, the governing system on household level can be raised to the community level. The second step then raises the governing system to the country level, where the final state variables estimate the total individuals from all compartments in the country. Two key attributes related to the household structure (number of local households and number of household members) effectively classify countries to be of low or high risk in terms of effective disease propagation. The basic reproductive number is calculated and its biological meaning is invoked properly. The numerical methods for solving the DIDE-system and the parameter estimation problem were mentioned. Our optimal model solutions are in quite good agreement with datasets of COVID-19 active cases and related deaths from Germany and Sri Lanka in early infection, allowing us to hypothesize several unobservable situations in the two countries. Focusing on extending minimum contact radius and reducing the intensity of individual activities, we were able to synthesize the key parameters telling what to practice.