Transmission Dynamics Of Two Epidemic Models

Infectious diseases are caused by various pathogens and can spread among the same or different populations.Under the help of monotone dynamical system,almost periodic differential equation and nonlinear functional analysis,we define the infectivity of the disease,that is,the basic reproduction number (?)₀.To propose the optimal prevention and control strategy,we study transmission dynamics of two epidemic models.Firstly,we investigate a malaria model with Insecticide-treated bed nets(ITNs)and time-dependent delays in the almost periodic environment.We introduce the basic repro-duction number (?)_vand (?)₀for mosquito and human,respectively.It is shown that the mosquito will die out if (?)_v<1,and uniformly persistent if (?)_v>1.Furthermore,in the case of (?)_v>1,if (?)₀<1,the disease will extinct;if (?)₀>1,the disease will uniformly persistent.At last,by numerical simulation,we verify the threshold results.Secondly,based on the mechanism,we propose a SVEIR COVID-19 model with vac-cination and non-pharmaceutical interventions(NPIs).By the basic reproduction number (?)₀,it is shown that the disease-free equilibrium is globally attractive if (?)₀<1,and COVID-19 is uniform persistence if (?)₀>1.Taking Indian dates for example in the nu-merical simulation,we find that our dynamical results fits well with the statistical dates.Consequently,we forecast the spreading trend of COVID-19 in India.Furthermore,our results imply that improving the intensity of NPIs will greatly reduce the number of con-firmed cases.In order to achieve the herd immunity,NPIs are indispensable even if all the people were vaccinated when the efficiency of vaccine is lower than 76.9%.By simulating the relationships of (?)₀,the vaccination rate and the efficiency of vaccine,we confirm the herd immunity area.In the study of two patchy,we give the conditions for India and China to be open to navigation and an appropriate dispersal.