Spread and control of COVID-19:A mathematical model

A mathematical model is proposed in this paper to study the transmission and control of COVID-19.The mathematical model is formulated using system of nonlinear ordinary differential equations.The model includes disease-related parameters such as contact rate,disease-induced death rates,immigration rate and transition rates along with parameters for control measures such as implementation of social distancing practices,isolation and quarantine rates.From the stability analysis of the model,it is shown that if the social distancing is practiced by the large number of susceptible population,then the disease will not spread,and it may eventually die out.Further,it is derived from the analysis of the model that if most of the infected populations are isolated or quarantined,then the spread of the disease can be eventually controlled.However,from the analysis of the model,it is observed that if there is constant immigration of asymptomatic infected persons,then the disease will continue to spread and will remain pandemic.For controlling the disease,two more parameters,that is,vaccination and testing rates,are introduced in the original mathematical model and from the numerical analysis of this model,it has been shown that the control strategy involving vaccination and testing in combination can have synergistic effect for minimizing the COVID-19 infected cases.

Modeling and analysis of the transmission dynamics of mosquito-borne disease with environmental temperature fluctuation

Most of the vector-borne diseases show a clear dependence on seasonal variation,including climate change.In this paper,we proposed a nonautonomous mathematical model consisting of a periodic system of nonlinear differential equations.In the proposed model,the realistic functional forms for the different temperature-dependent parameters are considered.The autonomous system of the proposed model is also analyzed.The nontrivial solution of the autonomous model is locally asymptotically stable if R0<1.It is shown that a unique endemic equilibrium point of the autonomous model exists when R0>1 and proved that endemic solution is linearly stable when R0>1.The nonautonomous model is shown to have a nontrivial disease-free periodic state,which is globally asymptotically stable whenever temperature-dependent reproduction number is less than unity.It is observed that a unique positive endemic periodic solution of the nonautonomous system exists only when a temperature-dependent reproduction number greater than unity,which makes for the persistence of the disease.Numerical simulation has been carried out to support the analytical results and shows the effects of temperature variability in the life span of mosquitoes as well as the persistence of the disease.