Vector-borne diseases threat lives of millions of people in many countries of the world. Zika is one of the vector-borne diseases which initially spread by the bite of an infected Aedes species mosquito (Ae. aegypti and Ae. albopictus) and then it transmits vertically from a pregnant woman to her fetus or from an infected human to their sexual partners. The congenital transmission of Zika virus (ZIKV) results in new born with microcephaly and other neurological abnormalities. The control of infected mosquitos is the best efficient way to control spread of ZIKV. Spraying insecticide is the safest and easiest way to control mosquitos, but sometimes it is cost worthy for long period of spraying. Controlled prevention from the vector bites can also help to control disease spread. To control congenital transmission and sexual transmission of ZIKV, preventions should be taken to reduce/stop pregnancy rate and safe heterosexual transmission among adults. Also, there is no specific treatment available for Zika disease. Treatment is aimed at relieving symptoms with rest, fluids and medications. Controlled combinations of rest, fluids and medications will help to recover early. As costs are incorporated with spraying, preventions and treatment, our aim is to minimise the total cost associated by controlling spraying, preventions and treatment. To fulfil this purpose a mathematical model is developed with disease dynamics in nine compartments namely Susceptible human child, Susceptible human male, Susceptible human female, Infected human child, Infected human male, Infected human female, Recovered human, Susceptible vector and Infected vector including vertical transmission of Zika disease. Numerical simulations have been carried out to optimise controls, and basic reproduction number and stability are calculated.

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In this paper, the transmission of HIV-HBV co-infection is carried out. The individuals who are infected with both diseases HIV and HBV simultaneously, are said to be HIV-HBV co-infected. These infected individuals have high risk of liver failure. It is the main cause for serious liver complications like cirrhosis and liver cancer at younger age. A deterministic model is considered with liquor habit in men and vaccination to new-borns and carrier mother. Carrier class results in the vertical transmission. In this paper, the transmission dynamics of the model is analyzed. The total population is divided in to twenty eight class viz. Susceptible, HBV Vaccinated, HBV-infected female, HBV-carrier female, HBV infected alcoholic male, HBV carrier alcoholic male, HBV infected non-alcoholic male, HBV carrier non-alcoholic male, HBV recovered class, pre-AIDS female, AIDS female, pre-AIDS-HBV co-infected female, AIDS-HBV co-infected female, pre-AIDS-HBV carrier female, AIDS-HBV carrier female, pre-AIDS alcoholic male, AIDS alcoholic male, pre-AIDS non-alcoholic male, AIDS non-alcoholic male, pre-AIDS-HBV co-infected alcoholic male, pre-AIDS-HBV co-infected non-alcoholic male, pre-AIDS-HBV carrier alcoholic male, pre-AIDS-HBV carrier non-alcoholic male, AIDS-HBV co-infected alcoholic male, AIDS-HBV co-infected non-alcoholic male, AIDS-HBV carrier non-alcoholic male, HIV infected -HBV recovered classes. The basic reproduction numbers for HIV, for HBV and for HIV-HBV are found using next generation matrix. Local and global stability of HIV-HBV disease free equilibrium is worked out. Model is validated with the numerical simulation.

Syphilis is a sexually transmitted disease having different signs and symptoms with four main stages, namely primary, secondary, latent, and tertiary. Congenital (vertical) transmission of syphilis from infected mother to fetus or neonatal is still a cause of high perinatal morbidity and mortality. A model of transmission of syphilis with three different ways of transmission, namely vertical, heterosexual, and homosexual, is formulated as a system of nonlinear ordinary differential equations. Treatment is also incorporated at various stages of infection. Total male and female population is divided in various classes (i.e., were susceptible, exposed, primary and secondary infected, early and late latent, tertiary, infected treated, latent treated, infected child [newborn], and treated infected child [at birth time]). Stability of disease-free equilibrium and endemic equilibrium is established. Control treatment is applied. It is observed that safe sexual habits and controlled treatment in each stage including pregnancy are effective parameters to curb disease spread.

Demonetization is a fundamental regulatory act of stripping in which a currency unit's status as an exchange is professed worthless. Generally, it is done whenever there is a change of national currency, often to be replaced of the old notes or coins with a new one. Sometimes, a country totally replaces the old currency with new currency. For example, in India recently the government demonetized RS. 500 and 1000 notes. So, one has to deposit their cash within limited time in the banks. The demonetization affects individuals mildly or potentially, which in turn affects banking sector. So, SMPB-model is proposed and analyzed for demonetization. The SMP-model is formulated with the system of nonlinear differential equations. The effect of demonetization is studied by calculating threshold using next generation matrix. The local and global stability for demonetization free equilibrium and demonetization equilibrium is worked out. The existence of the equilibrium is investigated. The model is validated with numerical simulation.