Mathematical analysis of spread and control of the novel corona virus (COVID-19) in China

Abstract

Number of well-known contagious diseases exist around the world that mainly include HIV, Hepatitis B, influenzas etc., among these, a recently contested coronavirus (COVID-19) is a serious class of such transmissible syndromes. Abundant scientific evidence the wild animals are believed to be the primary hosts of the virus. Majority of such cases are considered to be human-to-human transmission, while a few are due to wild animals-to-human transmission and substantial burdens on healthcare system following this spread. To understand the dynamical behavior such diseases, we fitted a susceptible-infectious-quarantined model for human cases with constant proportions. We proposed a model that provide better constraints on understanding the climaxes of such unseen disastrous spread, relevant consequences, and suggesting future imperative strategies need to be adopted. The main features of the work include the positivity, boundedness, existence and uniqueness of solution of the model. The conditions were derived under which the COVID-19 may extinct or persist in the population. Sensitivity and estimation of those important parameters have been carried out that plays key role in the transmission mechanism. To optimize the spread of such disease, we present a control problem for further analysis using two control measures. The necessary conditions have been derived using the Pontryagin’s maximum principle. Parameter values have been estimated from the real data and experimental numerical simulations are presented for comparison as well as verification of theoretical results. The obtained numerical results also present the verification, accuracy, validation, and robustness of the proposed scheme.

Non-pharmaceutical interventions during the COVID-19 pandemic: A review

“…The first column describes the main categories, the second the sub-categories, the last the country/countries focus of each study and the references. Category Subcategory Country/countries of study and reference Compartmental SIR-like Brazil, China [48] ; China [49] , [50] , [51] ; China, Italy [52] ; China, France, Iran, Italy, South Korea, USA [53] ; France, Iran, Italy [54] ; Germany [55] ; India [56] ; Italy [57] ; USA [58] ; 187 countries [45] ; several European countries [44] , [59] SIR-like age structured China [60] , Italy [61] , 143 countries [47] SEIR-like Argentina, Japan, Indonesia, New Zealand, Spain, USA [62] ; Canada [63] , [64] ; Canada, Germany, Italy [65] ; China [66] , [67] , [68] , [69] ; China, Italy [70] ; China, UK [71] ; Germany [72] ; India [73] , [74] ; Indonesia [75] ; Ireland [76] ; Mexico [77] ; Pakistan [78] ; South Korea [79] , [80] ; Switzerland [81] ; USA [82] , [83] ...…”

“…We start considering the body of modeling work based on SIR-like models. This subset of papers studies the effects of isolation and quarantine policies [49] , models NPIs as effective changes of the parameters [44] , [45] , [48] , [50] , [52] , [54] , [55] , [56] , [57] , [59] , investigates the impact of different policies [53] , [58] , and defines the conditions for the optimal control of the spreading [51] . In the following, I will highlight some of these approaches.…”

Dynamics of a stochastic delay differential model for COVID-19 infection with asymptomatic infected and interacting people: Case study in the UAE

“…In [10] , the authors analyzed some environmental factors such as atmospheric humidity, temperature, geographic location of the countries, humidity, etc., that impact the worldwide spread of the COVID-19. Currently, there are many mathematical models used to explain disease processes of COVID-19, for more details, refer the reader to [11] , [12] , [13] , [14] , [15] , [16] .…”

Stochastic COVID-19 SEIQ epidemic model with time-delay

“…After The first attempt of Mckendrick and Kermack [7] , [8] the said models were highly analyzed for controlling of different diseases. Using this gate way and basic concepts, different researchers analyzed the epidemic models of SEIS, SEIRS, SIRS, vaccinated models and delay-models by including different parameter for vaccination and delay-time [9] , [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] .…”